Metallic Mechanical Metamaterials Produced by LPBF for Energy Absorption Systems

Abstract

Metallic mechanical metamaterials have attracted the attention of many industrial sectors due to their unique properties which enable them to outperform natural materials in unconventional ways. Metal metamaterials encompass multiple fields, including materials science, mechanics, and industrial technology, and they have become particularly popular following the implementation of reliable, high-resolution, efficient metal additive manufacturing processes. This review takes a joint approach, providing an in-depth analysis of the base materials and geometries that characterize metamaterials in order to understand their behavior in response to impacts at different load regimes and to offer readers a critical overview of the most suitable design choices for energy absorption systems. Furthermore, this review highlights advanced metamaterial optimization methods that are useful for increasing the mechanical energy absorbed avoiding peak impulse transfer to the people, instrumentation, or generic loads that mechanical metamaterials are designed to protect.

1. Introduction

Demanding environments forced nature to adapt and optimize the use of available resources, resulting in the development of various intelligent designs with unique and specific properties [1,2,3,4]. When conducting a mechanical analysis of these naturally occurring materials, researchers discovered a common characteristic that encompasses them all: they are designed as multifunctional geometric patterns, which can also be observed at different hierarchical levels. These patterns provide cross-functional properties that are fundamental to a wide range of optimized features. Currently, researchers are trying to use, optimize, and enhance structural strategies developed by nature to pursue target performance for different purposes in many domains, such as the following:

• Biomedics: Complicated patterns and desired surface roughness, as well as materials with varying levels of porosity, are used in the biomedical field to create porous structures with optimized mechanical and bioactive behaviors [5,6,7].
• Automotive: Typically associated with the production of crash boxes, brackets, brakes, and heat exchangers [8,9]. Using complex shapes allows for the mechanical response to thermal and mechanical loads to be optimized and the total weight to be decreased [10].
• Aerospace: Manufacture of metal sandwich panels, nozzle channels, CubeSats, and multipurpose structures is one of the main research fields in aerospace. It is important to acknowledge that, in this field, the constant and crucial goal is to achieve lightweighting and performance optimization [11,12,13]. In this regard, metamaterials and compliant mechanisms have emerged as highly effective solutions, enabling designers to achieve optimum performance.

One of the most important fields in which these metallic architectures are used is the design of cellular structures for mechanical energy absorption systems. They are particularly used as sacrificial structures due to their ability to accommodate large plastic deformation caused by external quasi-static or impact loads [14,15,16]. This characteristic of large deformation depends on the complex arrangement and porous structures of the generated architecture, as described by Gibson and Ashby in their analysis of cellular solids [17]. This class of geometrical architecture is commonly labeled ‘metamaterials’. The Greek word meta (μετά) can have various meanings. The main two relevant to research are “beyond” and “in between.” The engineering literature always associated metamaterials with the “beyond”, meaning that it defines them as engineered structures designed to develop unusual properties not presented in conventional materials, derived from the spatial repetition of single units called base cells with a characteristic geometry optimized to perform a specific function [18,19,20]. Nevertheless, a reduction in metamaterial properties to the geometry that characterizes them would be a simplistic approach. This underscores the significance of contemplating the properties “in between” (as per the secondary connotation of the term μετά) in conjunction with geometric architecture and the attributes of the base material. This approach is instrumental in optimizing the performance of components, particularly in the context of contemporary technologies that facilitate the fabrication of sophisticated manufactured goods in addition to an unprecedented control over microstructural and solidification properties.

Indeed, the manufacturing processes involving the production of such complex structures have evolved significantly over the years, even if it still involves well-known manufacturing procedures like cutting (water-cutting or EDM) combined with assembly [21,22], foaming of stochastic structures [23,24], investment casting [25,26], folding [27], or a mix of all these methods. The principal limitation of these processes is that they are characterized by multiple steps and preclude designers from exploring complex shapes and designs, unless additional steps and costs are taken into account [13]. For this reason, in the last 15 years [28], additive manufacturing (AM) has become the prominent and widespread technology to manufacture metals and alloys, with a diversified market uptake including different technologies for metals and alloys (Figure 1 [29]).

Between the various metal additive manufacturing processes, Laser Powder Bed Fusion (LPBF) systems exhibit the best capability in achieving complex and intricate structures [30,31], both extremely important in order to assure the perfect quality of metamaterial and avoid performance mismatch between the designed parts and the final component. LPBF [32,33,34,35] is an additive manufacturing technology which uses a laser to selectively melt metal powder particles layer by layer (Figure 2). LPBF process parameters such laser power (P), scanning velocity (v) and strategy, layer thickness (t), and hatch spacing (h_d), and must be tuned to avoid the production of defects as porosity and non-congruent geometries [36,37,38]. For this purpose, some Key Performance Indexes (KPIs), such as the Volumetric Energy Density (VED) factor, which is obtained by merging the main process parameters, must be perfectly tuned (Figure 2b) [39,40]. When the VED is too high, keyhole porosity and solidification cracks are likely to form during solidification, while when VED values are too low, they generate a lack of fusion [36,40,41]. Moreover, due to high-temperature gradients generated by the rapid cooling of metal powder particles, microstructural anisotropy, element segregation, stress-concentration, and non-equilibrium phases can be found in samples in the as-built (AB) condition. Nevertheless, the enhanced efficiency of in situ monitoring systems (even for extended AM printing operations) has been demonstrated to augment reliability and facilitate on-demand analysis of LPBF process developments [42,43]. This capability enables the acquisition of comprehensive information concerning processing maps and defect formation/evolution [44,45,46,47,48]. This innovative approach has the potential to be implemented in a stand-alone experimental campaign, or, alternatively, it can be associated with conventional and consolidated approaches, such as the aforementioned VED-based analysis. The primary benefits stem from a profound understanding of the physics and metallurgical phenomena that occur during ultrafast heating and supercooling in LPBF. Furthermore, it has been demonstrated to reduce the analysis time required to fully standardize and validate a stable and reliable LPBF process.

It is evident that both the base cell topology and the base material properties generated during the LPBF process are fundamentally correlated with the definition of metallic metamaterials’ mechanical performance. To optimize the workflow and analysis of such complex systems, a common approach involving three fundamental steps, as shown in Figure 3, is generally adopted [49,50,51,52,53,54,55,56,57,58,59,60,61,62,63].

As outlined in Figure 3, Step 1 is strictly focused on base material characterization following process parameter identification, metallurgical implication, mechanical test implementation, and constitutive model definition [51,52,53,54,55,56,57,58]. Step 2 involves selecting the base cell according to the desired mechanical behavior, refining the topology and spatial arrangement, and performing numerical simulations to predict the behavior of metamaterials. This step uses a recursive approach involving continuous cycles of optimization until satisfactory performance is achieved [59,60,61]. In Step 3, the data obtained in Step 2 is assessed and validated. This is performed to optimize the overall process, ensuring consistent performance between simulation and experimental testing and during printing jobs involving different 3D-printing equipment. The aim is to enable the consistent and reliable production of components in different facilities at different times [62,63]. From the workflow presented in Figure 3, a review of metallic metamaterials is needed, covering everything from the base materials to mesoscopic analysis at different strain rate regimes. This will provide a baseline for approaching the optimization of energy absorption. As previously mentioned, to achieve the best possible results, the base cell topology and the base material must be perfectly tuned to each other. Rather than considering the properties of the base material and the geometric cellular topology separately, this review focuses on one ultimate goal: maximizing energy absorption by understanding how the base material and the cellular topology interact. Section 2 and Appendix A analyze the base material’s properties by focusing on how microstructural features affect the mechanical properties. Section 3 focus on metamaterial energy absorption behavior, with a description of the stress–strain curve and of how different base cells and their parametrization affect the overall mechanical characteristics. Section 4 explains how adjusting the process parameters and applying special material distribution arrangement can increase the overall energy absorption capabilities.

The aim of the review is therefore to provide in-depth insight into metallic metamaterials’ mechanical behavior by considering both the microstructural and topology effects. The detailed description of the base metal behavior (referred as microscopic behavior) and base unit cell behavior (referred as mesoscopic behavior) aims to generate a sort of workflow in which everything needed to understand how to achieve optimal energy absorption performance is analyzed. To do so, this work has been based on general and focused questions, as reported in

Table 1. Research questions.

General Question		Area
GQ1	What are the mechanical metamaterials for energy absorption?	Innovation field
GQ2	Which is the workflow involved in designing mechanical metamaterials?	Design stage
GQ3	How can metallic mechanical metamaterials be manufactured?	Technology and manufacturing
Focused Question		Technical aspect
FQ1	What are the main microstructural features governing deformation of base metal materials at different strain rates?	Mechanical behavior correlation to metallurgical properties
FQ2	What are the main structural behavior governing deformation of metallic metamaterials at different strain rates?	Structural response of different type of metamaterials
FQ4	How base cell parameters affect the overall mechanical properties?	Base cell parametrization and effects
FQ5	How can mechanical metamaterials behavior be optimized?	Future challenges and early-stage innovations

. The Introduction has been written to provide an overview of the general questions, while the following chapters have been developed to be technical, to deliver all of the useful aspects related to mechanical metamaterials and metal alloys for energy absorption optimization.

2. Alloy Behavior Related to Conventional and Additive Manufactured Processes: Microstructural and Mechanical Coupled Characteristics

The field of strength of materials is concerned with the relationships between internal forces, deformation, and external loads. Pure metals and metal alloys represent a distinct category of materials, distinguished by their crystalline structure, which can be modified through alloying and/or thermal treatments [61]. In particular, these processes can induce the formation of specific phases and show a unique response to external loads. Usually, metals are characterized by a certain equilibrium microstructure that can be strictly predicted by varying micro-constituent proportions based on phase diagrams [61]. The implementation of LPBF has resulted in the generation of non-equilibrium microstructures, which have been observed to exhibit a distinct variation in the properties of the base materials produced by conventional manufacturing systems, as shown in Table 2 (fully dense parts).

These properties are closely related to the supercooling phenomena occurring during LPBF processes [62,63]. The most common approach to reach this target is to experimentally characterize the processability window of a certain alloy, starting from a DOE in which process parameters such layer thickness (t), hatch distance (h_d), laser power (P), and laser speed (v) are combined [64] (as shown in Figure 2).

Analytical models and process simulations have been developed to improve the quality of printed parts and to determine the cooling rate and microstructure of the final product. This allows for a reasonable analysis speed based on the physical and mechanical properties of the powder and base material combined with the process parameters and heat source specifications. In particular, the shape, intensity, and speed of the laser define a certain cooling rate [65] from which the different mechanical performances of the final part are obtained. In this context, dislocation density generated during solidification plays a pivotal role: sub-microstructural configurations formed during LPBF rapid solidification strongly affect the mechanical behavior of the base material at different strain rates (as discussed in Appendix A.2).

The high dislocation density associated with additively manufactured parts can be ascribed to the following phenomena [66]:

• The formation of coherency strains is a consequence of steep solute concentration gradients at the boundary of the cellular structure. This strain energy can be dissipated by forming dislocations.
• High thermal stress may act as a nucleation source for dislocation motion, which could then dissipate strain energy.
• It is feasible that the misorientation of neighboring cells could result in the formation of interfacial dislocations upon their mutual interactions.

Due to their complex thermal history, therefore, LPBF as built samples (AB) typically show high-strength and non-uniform properties arising from non-equilibrium microstructures and phase compositions. Moreover, the high dislocation density and residual stress can result in a reduced plasticity phase and catastrophic failures due to stress accumulation, crack nucleation, and propagation. In order to limit or avoid these detrimental effects, post-processing heat treatments (HTs) such as stress relief can be applied [67,68,69]. As can be seen in Table 3, when stress relief is applied, the microstructure tends to relax by rearranging dislocations, and the base material is most likely to show high deformation and slight decrease in yield strength. Further heat treatments such as solution annealing can lead to a lower strength but increased ductility compared to the as-built data due to recrystallization and, if the conditions allow it, grain growth.

When mechanical metamaterials are considered, high deformation of the metamaterial structure itself is requested; therefore, the base material must be as ductile as possible to accommodate large amounts of local strains without undergoing stress localization, crack nucleation, and failure.

Table 2. LPBF vs. conventional manufacturing alloys basic mechanical properties (high-density sample considered).

As-Built LPBF Material Properties
Heat Treatment	Microstructure	Alloy	σy (MPa)	UTS (MPa)	εR (%)	Reference
/	Elongated β-grain microstructure.	Ti5553 (AB)	903 ± 8	915 ± 10	15 ± 1	[70]
/	α’ lamellar.	Ti6Al4V (AB)	1040 ± 11	1201 ± 10	9.5 ± 0.2	[71]
/	Austenitic columnar grain and fine sub-grains structures.	AISI 316L SS (AB)	500	600 ± 2.2	55 ± 2.5	[72]
/	Columnar grains and equiaxed grain of supersatured α-Al solid solution in a network of fine Si phase.	AlSi10Mg (AB)	293.5 ± 4.7	456.3 ± 5.9	13.4 ± 0.51	[73]
/	Acicular α’ martensite due to the high cooling below the β-transus temperature.	CPTi (AB)	521 ± 13.1	607 ± 16.5	10.4 ± 2.6	[74]
/	Columnar grains + γ and Laves phases.	Inconel 718 (AB)	800 ± 8	997 ± 10	29.7 ± 0.8	[75]
/	Columnar grains with a large size distribution + columnar and cellular dendritic substructures + Nb,Ti-rich MC carbides.	Inconel 625 (AB)	783 ± 23	1041 ± 36	33 ± 1	[76]
Solution annealing (SA) 1150 °C × 2 h	Recrystallization + coarse Nb,Ti-rich MC carbides dispersed on intra- and inter-grains.	Inconel 625 (HT)	396 ± 9	883 ± 15	55 ± 1
/	Mainly ferrite with a small amount of austenite, small grains in meltpool boundary, with increased dimension towards the center of meltpool.	Duplex SS2205 (AB)	897	1035	15.3	[77]
Conventional manufacturing material properties
Heat treatment	Microstructure	Alloy	σy (MPa)	UTS (MPa)	εR (%)	Reference
/	As-cast: columnar grains in the outer region of the part. Directional growth of columnar grain takes place as the thermal gradient is maximum near the mold.	Ti5553	670 ± 53	716 ± 10	1.2 ± 0.2	[78]
/	As-cast: Widmannstetter structure with alternate lamellas of (hcp) α and (bcc) β oriented along particular directions within individual colonies (within the prior-β grains).	Ti6Al4V	837 ± 14	1022 ± 22	9.0 ± 0.6	[79]
/	As-cast: austenite and delta ferrite.	AISI 316L	311.62	643.82	62.72	[80,81]
/	As-cast: α-Al phase surrounded by the acicular eutectic Si particles.	AlSi10Mg	237.4 ± 3.4	305.8 ± 7.2	11	[82]
Annealing	Cold rolled and annealed: equiaxed Ti structures.	CPTi	307	443	/	[83]
/	As-cast: coarse dendritic microstructure along transverse and vertical cross sections.	Inconel 718				[84]
Homogenization treatment (1080 °C, 1.5 h/air cooling) + solution treatment (980 °C, 1 h/air cooling) + double aging (720 °C, 8 h/furnace cooling at 55 °C/h to 620 °C, 8 h/air cooling)	Heat treated from casting: segregation is difficult to be completely eliminated. Some coarse acicular δ precipitates and globular carbides can also be observed in the inter dendritic zones.	Inconel 718 (HT)	1046	1371	12.3
Direct artificial aging (DAH) 10 °C/min-720 °C × 8 h-0.9 °C/min-620 °C × 8 h-5 °C/min until RT (furnace cooling)	Columnar grains + γ, γ′, γ″ and Laves phases.	Inconel 718 (HT)	1341 ± 2			[75]
/	As-cast: coarse dendritic microstructure along transverse and vertical cross sections.	Inconel 625				[85]
Solution annealed 1050° × 1 h	Heat treated from casting: primary MC carbides remain intact after solution treatment, redissolution of partial γ/Laves. eutectics occurs and their shapes are transformed from mesh-like to block-like.	Inconel 625 (HT)	375	1225	60.8
/	Cold rolled: ferrite and austenite content depending on cooling rate, thank to mold high heat transfer the transformation of δ-ferrite into austenite is suppressed and much supercooled δ-ferrite, which can transform into the Widmanstätten austenite.	Duplex SS2205	450	655	25	[86]

RT = room temperature.

Table 2. LPBF vs. conventional manufacturing alloys basic mechanical properties (high-density sample considered).

As-Built LPBF Material Properties
Heat Treatment	Microstructure	Alloy	σy (MPa)	UTS (MPa)	εR (%)	Reference
/	Elongated β-grain microstructure.	Ti5553 (AB)	903 ± 8	915 ± 10	15 ± 1	[70]
/	α’ lamellar.	Ti6Al4V (AB)	1040 ± 11	1201 ± 10	9.5 ± 0.2	[71]
/	Austenitic columnar grain and fine sub-grains structures.	AISI 316L SS (AB)	500	600 ± 2.2	55 ± 2.5	[72]
/	Columnar grains and equiaxed grain of supersatured α-Al solid solution in a network of fine Si phase.	AlSi10Mg (AB)	293.5 ± 4.7	456.3 ± 5.9	13.4 ± 0.51	[73]
/	Acicular α’ martensite due to the high cooling below the β-transus temperature.	CPTi (AB)	521 ± 13.1	607 ± 16.5	10.4 ± 2.6	[74]
/	Columnar grains + γ and Laves phases.	Inconel 718 (AB)	800 ± 8	997 ± 10	29.7 ± 0.8	[75]
/	Columnar grains with a large size distribution + columnar and cellular dendritic substructures + Nb,Ti-rich MC carbides.	Inconel 625 (AB)	783 ± 23	1041 ± 36	33 ± 1	[76]
Solution annealing (SA) 1150 °C × 2 h	Recrystallization + coarse Nb,Ti-rich MC carbides dispersed on intra- and inter-grains.	Inconel 625 (HT)	396 ± 9	883 ± 15	55 ± 1
/	Mainly ferrite with a small amount of austenite, small grains in meltpool boundary, with increased dimension towards the center of meltpool.	Duplex SS2205 (AB)	897	1035	15.3	[77]
Conventional manufacturing material properties
Heat treatment	Microstructure	Alloy	σy (MPa)	UTS (MPa)	εR (%)	Reference
/	As-cast: columnar grains in the outer region of the part. Directional growth of columnar grain takes place as the thermal gradient is maximum near the mold.	Ti5553	670 ± 53	716 ± 10	1.2 ± 0.2	[78]
/	As-cast: Widmannstetter structure with alternate lamellas of (hcp) α and (bcc) β oriented along particular directions within individual colonies (within the prior-β grains).	Ti6Al4V	837 ± 14	1022 ± 22	9.0 ± 0.6	[79]
/	As-cast: austenite and delta ferrite.	AISI 316L	311.62	643.82	62.72	[80,81]
/	As-cast: α-Al phase surrounded by the acicular eutectic Si particles.	AlSi10Mg	237.4 ± 3.4	305.8 ± 7.2	11	[82]
Annealing	Cold rolled and annealed: equiaxed Ti structures.	CPTi	307	443	/	[83]
/	As-cast: coarse dendritic microstructure along transverse and vertical cross sections.	Inconel 718				[84]
Homogenization treatment (1080 °C, 1.5 h/air cooling) + solution treatment (980 °C, 1 h/air cooling) + double aging (720 °C, 8 h/furnace cooling at 55 °C/h to 620 °C, 8 h/air cooling)	Heat treated from casting: segregation is difficult to be completely eliminated. Some coarse acicular δ precipitates and globular carbides can also be observed in the inter dendritic zones.	Inconel 718 (HT)	1046	1371	12.3
Direct artificial aging (DAH) 10 °C/min-720 °C × 8 h-0.9 °C/min-620 °C × 8 h-5 °C/min until RT (furnace cooling)	Columnar grains + γ, γ′, γ″ and Laves phases.	Inconel 718 (HT)	1341 ± 2			[75]
/	As-cast: coarse dendritic microstructure along transverse and vertical cross sections.	Inconel 625				[85]
Solution annealed 1050° × 1 h	Heat treated from casting: primary MC carbides remain intact after solution treatment, redissolution of partial γ/Laves. eutectics occurs and their shapes are transformed from mesh-like to block-like.	Inconel 625 (HT)	375	1225	60.8
/	Cold rolled: ferrite and austenite content depending on cooling rate, thank to mold high heat transfer the transformation of δ-ferrite into austenite is suppressed and much supercooled δ-ferrite, which can transform into the Widmanstätten austenite.	Duplex SS2205	450	655	25	[86]

RT = room temperature.

Table 3. PBF as built properties vs. PBF heat treated properties of a series of alloys produced by additive manufacturing.

Built Plate Orientation	Microstructure	Heat Treatment	Alloy	σy (MPa)	UTS (MPa)	εR (%)	Ref.
/	Elongated β-grain microstructure	/	Ti5553 (AB)	903 ± 8	915 ± 10	15 ± 1	[70]
/	β-grain microstructure + isothermal ω nanoprecipitates + needle-shaped α nanoprecipitates	Stress relief (300 °C for 1 h)	Ti5553 (HT)	848 ± 11	849 ± 11	19 ± 2
/	β-grain microstructure + α-phase precipitation both within β grains and along the β grain boundaries	Stress relief (300 °C for 1 h) + 600 °C-1 h	Ti5553 (HT)	1332 ± 32	1371 ± 21	3.5 ±0.6	[87]
/	β + 25% α	Stress relief (300 °C for 1 h) + 800 °C-1 h	Ti5553 (HT)	895 ± 39	951 ± 23	15.6 ± 4.5
H	α’ lamellar	/	Ti6Al4V (AB)	1040 ± 11	1201 ± 10	9.5 ± 0.2	[71]
V	α’ lamellar	/	Ti6Al4V (AB)	1008	1080	1.6
H	Partially decomposed α’ lamellar	700 °C/2 h/furnace cooling	Ti6Al4V (HT)	1012 ± 9	1109 ± 10	9.5 ± 0.2
H	α + β lamellar	800 °C/6 h/furnace cooling	Ti6Al4V (HT)	937 ± 4	1041 ± 5	19 ± 1
V	α + β lamellar	1050 °C/2 h/furnace cooling	Ti6Al4V (HT)	798	956	11.6
V	Austenitic columnar grain and fine sub-grains structures	/	AISI 316L SS (AB)	500	600 ± 2.2	55 ± 2.5	[72]
V	Mostly similar to the as-built condition	SLM + stress relief 650 °C × 2 h	AISI 316L SS (HT)	475	617.9 ± 1.4	54.1 ± 1.6
H	Austenitic columnar grain and fine sub-grains structures	/	AISI 316L SS (AB)	517 ± 7	634 ± 7	33 ± 0.6	[88]
H	Mostly similar to as built condition	SLM + stress relief 388 °C × 4 h	AISI 316L SS (HT)	496	717	28	[89]
/	Austenitic grains with dispersed dislocation cells	SLM + solution annealing 1095 °C × 1 h	AISI 316L SS (HT)	375 ± 11	635 ± 17	51 ± 3	[90]
/	Columnar grains and equiaxed grain of supersatured α-Al solid solution in a network of fine Si phase	/	AlSi10Mg (AB)	293.5 ± 4.7	456.3 ± 5.9	13.4 ± 0.51	[73]
/	Segregated structure destroyed, coarsening of Si and precipitation (residual stress near to zero)	T6	AlSi10Mg (HT)	248.7 ± 3.6	326.8 ± 4.4	14.5 ± 0.5
/	Maintain the original as-built microstructure and increase internal precipitation	Direct aging 200° × 1 h (peak aging)	AlSi10Mg (HT)	306.3 ± 5.7	461.4 ± 3.6	7.6 ± 0.2
H	Acicular α’ martensite due to the high cooling below the β-transus temperature	/	CPTi (AB)	521 ± 13.1	607 ± 16.5	10.4 ± 2.6	[74]
V	Acicular α’ martensite due to the high cooling below the β-transus temperature	/	CPTi (AB)	630 ± 20.6	720 ± 22.5	8.3 ± 1.6
H	(HIP below beta-transus temperature) microstructure fully converted to α phase	HIP 730 °C × 60 min + furnace cooling	CPTi (HT)	512 ± 14.3	587 ± 21.6	7.3 ± 1.3
V	(HIP below beta-transus temperature) microstructure fully converted to α phase	HIP 730 °C × 60 min + furnace cooling	CPTi (HT)	622 ± 10.1	716 ± 12.6	15.1 ± 3.1
H	(HIP above beta-transus temperature) coarse α phase elongated and equiaxed grains	HIP 950 °C × 60 min + furnace cooling	CPTi (HT)	482 ± 12.7	573 ± 26.6	6.3 ± 1.3
V	(HIP above beta-transus temperature) coarse α phase elongated and equiaxed grains	HIP 950 °C × 60 min + furnace cooling	CPTi (HT)	573 ± 33.3	662 ± 38.8	7.4 ± 2.2
/	Meltpool + columnar grain preferentially oriented in the build direction	/	CuCrZr (AB)	185.6 ± 4.1	247.2 ± 5.3	23.8 ± 1.5	[91]
/	Recrystallization and precipitation of coarse Cr rich particles at the grain boundaries	Solution annealing + aging hardening (950 °C × 0.5 h + water quenching + 450 × 2 h + furnace cooling)	CuCrZr (HT)	141.7 ± 6.8	252.1 ± 8.4	24.4 ± 1.1
/	Maintain the original as-built microstructure, inhibits Cr coarse particles formation at grain boundaries, uniform precipitation of nano Cr phases in the grains, change in the orientation of the grains	Direct aging hardening (450 °C/2 h + Furnace Cooling)	CuCrZr (HT)	320.4 ± 5.1	415.6 ± 4.5	10.4 ± 0.7
/	Maintain the original as-built microstructure, inhibits Cr coarse particles formation at grain boundaries, uniform precipitation of nano Cr phases in the grains, change in the orientation of the grains (Peak aging)	Direct aging hardening (450 °C/4 h + Furnace Cooling)	CuCrZr (HT)	405.8 ± 3.7	481.7 ± 7.6	9.6 ± 0.9
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-4Mg-Sc-Zr (AB) Sc 0.7 wt.%	345	362	>10	[92]
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool + non uniform precipitation of primary fine intergranular Al3Sc precipitate and primary coarse intragranular Al3Sc	Direct aging 350° × 2 h	Al-4Mg-Sc-Zr (HT) Sc 0.7 wt.%	520	525	>1.6
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-3.4Mg-Sc-Zr (AB) Sc 1.08 wt.%	>275	>300	>5	[93]
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool + non uniform precipitation of primary fine intergranular Al3Sc precipitate and primary coarse intragranular Al3Sc	Direct aging 300° × 12 h	Al-3.4Mg-Sc-Zr (HT) Sc 1.08 wt.%	460	480	>1.5
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-5Mn-Sc (AB) Sc 0.6 wt.%	266	349	10.35	[67]
/	Fine grains microstructure + primary Al3Sc type and Alx(Mn, Fe)-type precipitates	Direct Aging 300° × 4 h	Al-5Mn-Sc (HT) Sc 0.6 wt.%	397	430	4.89
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-4.52Mn-Sc-Zr (AB) Sc 0.79 wt.%	438	460	19	[68]
/	Fine grains microstructure + primary Al3Sc type and Alx(Mn, Fe)-type precipitates	Direct aging 300° × 5 h	Al-4.52Mn-Sc-Zr (HT) Sc 0.79 wt.%	556	570	18
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-4.58Mn-Sc-Zr (AB) Sc 0.91 wt.%	430–438	446–451	17.8–20	[69]
/	Fine grains microstructure + primary Al3Sc type and Alx(Mn, Fe)-type precipitates	Direct aging 300° × 6 h	Al-4.58Mn-Sc-Zr (HT) Sc 0.91 wt.%	559	572	10
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-5.5Mn-2.69Mg-Sc-Zr (AB) Sc 1.03 wt.%	520	700	8	[94]
/	Fine grains microstructure + primary Al3Sc type and Alx(Mn, Fe)-type precipitates	Direct aging 300° × 6 h	Al-5.5Mn-2.69Mg-Sc-Zr (HT) Sc 1.03 wt.%	621	712	4.5
/	Columnar grains + γ and Laves phases	/	Inconel 718 (AB)	800 ± 8	997 ± 10	29.7 ± 0.8	[75]
/	Microstructural homogenization, recrystallization, grain growth + γ, γ′, γ″ and δ	Homogenization annealing (HA) 10 °C/min–1100 °C × 1 h–35 °C/min until reaching room temperature + Solution annealing (SA) 10 °C/min–980 °C × 1 h–35 °C/min until reaching room temperature (furnace cooling) + artificial aging (AH) 10 °C/min–720 °C × 8 h-0.9 °C/min–620 °C × 8 h–5 °C/min + furnace cooling	Inconel 718 (HT)	1279 ± 14	1406 ± 4	13.9 ± 1
/	Microstructural homogenization, partial recrystallization + γ, γ′, γ″ and Leaves phases	Solution annealing (SA) 10 °C/min–980 °C × 1 h–35 °C/min until reaching room temperature (furnace cooling) + artificial aging (AH) 10 °C/min–720 °C × 8 h–0.9 °C/min–620 °C × 8 h–5 °C/min until reaching room temperature (furnace cooling)	Inconel 718 (HT)	1291 ± 10	1440 ± 1	13 ± 0.7
/	Columnar grains + γ, γ′, γ″ and Leaves phases	Direct artificial aging (DAH) 10 °C/min–720 °C × 8 h–0.9 °C/min–620 °C × 8 h–5 °C/min + until reaching room temperature (furnace cooling)	Inconel 718 (HT)	1341 ± 2	1478 ± 4	10 ± 1.5
/	Columnar grains with a large size distribution + columnar and cellular dendritic substructures + Nb,Ti-rich MC carbides	/	Inconel 625 (AB)	783 ± 23	1041 ± 36	33 ± 1	[76]
/	Mostly like as-built condition + Cr-rich M23C6 carbides precipitates in grains boundary + inhomogeneous precipitation of fine γ″	Direct artificial aging (DAH) 700 °C × 24 h	Inconel 625 (HT)	1012 ± 54	1222 ± 56	23 ± 1
/	Recrystallization (development of equiaxed grains with numerous twin boundary) + coarse Nb,Ti-rich MC carbides dispersed on intra- and inter-grains	Solution annealing (SA) 1150 °C × 2 h	Inconel 625 (HT)	396 ± 9	883 ± 15	55 ± 1
/	Equiaxed grains + Cr-rich M23C6 carbides at grain boundary + homogeneous precipitation of ellipsoidal γ″ precipitates	Solution annealing (SA) 1150 °C × 2 h + artificial aging (AH) 700 °C × 24 h	Inconel 625 (HT)	722 ± 7	1116 ± 6	35 ± 5
/	Nearly vertical columnar grain growth	/	GRCop42 (AB)	173	355	33.6	[95]
/	Fine grain formation compared to classical powder metallurgy	/	Tantalum (AB)	450	739	2	[96]
/	Columnar grains grow along the building direction (BD) across multiple layers, showing a pronounced epitaxial characteristic	/	Ta10W (AB)	663	765	28	[97]
/	Mainly ferrite with a small amount of austenite, small grains in meltpool boundary that increase their dimension toward the center of meltpool	/	Duplex 2205 (AB)	897	1035	15.3	[77]
/	Mainly ferrite with a small amount of austenite, small grains in meltpool boundary that increase their dimension toward the center of meltpool	/	Duplex 2507 (AB)	1196	1276	15	[98]

Table 3. PBF as built properties vs. PBF heat treated properties of a series of alloys produced by additive manufacturing.

Built Plate Orientation	Microstructure	Heat Treatment	Alloy	σy (MPa)	UTS (MPa)	εR (%)	Ref.
/	Elongated β-grain microstructure	/	Ti5553 (AB)	903 ± 8	915 ± 10	15 ± 1	[70]
/	β-grain microstructure + isothermal ω nanoprecipitates + needle-shaped α nanoprecipitates	Stress relief (300 °C for 1 h)	Ti5553 (HT)	848 ± 11	849 ± 11	19 ± 2
/	β-grain microstructure + α-phase precipitation both within β grains and along the β grain boundaries	Stress relief (300 °C for 1 h) + 600 °C-1 h	Ti5553 (HT)	1332 ± 32	1371 ± 21	3.5 ±0.6	[87]
/	β + 25% α	Stress relief (300 °C for 1 h) + 800 °C-1 h	Ti5553 (HT)	895 ± 39	951 ± 23	15.6 ± 4.5
H	α’ lamellar	/	Ti6Al4V (AB)	1040 ± 11	1201 ± 10	9.5 ± 0.2	[71]
V	α’ lamellar	/	Ti6Al4V (AB)	1008	1080	1.6
H	Partially decomposed α’ lamellar	700 °C/2 h/furnace cooling	Ti6Al4V (HT)	1012 ± 9	1109 ± 10	9.5 ± 0.2
H	α + β lamellar	800 °C/6 h/furnace cooling	Ti6Al4V (HT)	937 ± 4	1041 ± 5	19 ± 1
V	α + β lamellar	1050 °C/2 h/furnace cooling	Ti6Al4V (HT)	798	956	11.6
V	Austenitic columnar grain and fine sub-grains structures	/	AISI 316L SS (AB)	500	600 ± 2.2	55 ± 2.5	[72]
V	Mostly similar to the as-built condition	SLM + stress relief 650 °C × 2 h	AISI 316L SS (HT)	475	617.9 ± 1.4	54.1 ± 1.6
H	Austenitic columnar grain and fine sub-grains structures	/	AISI 316L SS (AB)	517 ± 7	634 ± 7	33 ± 0.6	[88]
H	Mostly similar to as built condition	SLM + stress relief 388 °C × 4 h	AISI 316L SS (HT)	496	717	28	[89]
/	Austenitic grains with dispersed dislocation cells	SLM + solution annealing 1095 °C × 1 h	AISI 316L SS (HT)	375 ± 11	635 ± 17	51 ± 3	[90]
/	Columnar grains and equiaxed grain of supersatured α-Al solid solution in a network of fine Si phase	/	AlSi10Mg (AB)	293.5 ± 4.7	456.3 ± 5.9	13.4 ± 0.51	[73]
/	Segregated structure destroyed, coarsening of Si and precipitation (residual stress near to zero)	T6	AlSi10Mg (HT)	248.7 ± 3.6	326.8 ± 4.4	14.5 ± 0.5
/	Maintain the original as-built microstructure and increase internal precipitation	Direct aging 200° × 1 h (peak aging)	AlSi10Mg (HT)	306.3 ± 5.7	461.4 ± 3.6	7.6 ± 0.2
H	Acicular α’ martensite due to the high cooling below the β-transus temperature	/	CPTi (AB)	521 ± 13.1	607 ± 16.5	10.4 ± 2.6	[74]
V	Acicular α’ martensite due to the high cooling below the β-transus temperature	/	CPTi (AB)	630 ± 20.6	720 ± 22.5	8.3 ± 1.6
H	(HIP below beta-transus temperature) microstructure fully converted to α phase	HIP 730 °C × 60 min + furnace cooling	CPTi (HT)	512 ± 14.3	587 ± 21.6	7.3 ± 1.3
V	(HIP below beta-transus temperature) microstructure fully converted to α phase	HIP 730 °C × 60 min + furnace cooling	CPTi (HT)	622 ± 10.1	716 ± 12.6	15.1 ± 3.1
H	(HIP above beta-transus temperature) coarse α phase elongated and equiaxed grains	HIP 950 °C × 60 min + furnace cooling	CPTi (HT)	482 ± 12.7	573 ± 26.6	6.3 ± 1.3
V	(HIP above beta-transus temperature) coarse α phase elongated and equiaxed grains	HIP 950 °C × 60 min + furnace cooling	CPTi (HT)	573 ± 33.3	662 ± 38.8	7.4 ± 2.2
/	Meltpool + columnar grain preferentially oriented in the build direction	/	CuCrZr (AB)	185.6 ± 4.1	247.2 ± 5.3	23.8 ± 1.5	[91]
/	Recrystallization and precipitation of coarse Cr rich particles at the grain boundaries	Solution annealing + aging hardening (950 °C × 0.5 h + water quenching + 450 × 2 h + furnace cooling)	CuCrZr (HT)	141.7 ± 6.8	252.1 ± 8.4	24.4 ± 1.1
/	Maintain the original as-built microstructure, inhibits Cr coarse particles formation at grain boundaries, uniform precipitation of nano Cr phases in the grains, change in the orientation of the grains	Direct aging hardening (450 °C/2 h + Furnace Cooling)	CuCrZr (HT)	320.4 ± 5.1	415.6 ± 4.5	10.4 ± 0.7
/	Maintain the original as-built microstructure, inhibits Cr coarse particles formation at grain boundaries, uniform precipitation of nano Cr phases in the grains, change in the orientation of the grains (Peak aging)	Direct aging hardening (450 °C/4 h + Furnace Cooling)	CuCrZr (HT)	405.8 ± 3.7	481.7 ± 7.6	9.6 ± 0.9
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-4Mg-Sc-Zr (AB) Sc 0.7 wt.%	345	362	>10	[92]
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool + non uniform precipitation of primary fine intergranular Al3Sc precipitate and primary coarse intragranular Al3Sc	Direct aging 350° × 2 h	Al-4Mg-Sc-Zr (HT) Sc 0.7 wt.%	520	525	>1.6
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-3.4Mg-Sc-Zr (AB) Sc 1.08 wt.%	>275	>300	>5	[93]
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool + non uniform precipitation of primary fine intergranular Al3Sc precipitate and primary coarse intragranular Al3Sc	Direct aging 300° × 12 h	Al-3.4Mg-Sc-Zr (HT) Sc 1.08 wt.%	460	480	>1.5
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-5Mn-Sc (AB) Sc 0.6 wt.%	266	349	10.35	[67]
/	Fine grains microstructure + primary Al3Sc type and Alx(Mn, Fe)-type precipitates	Direct Aging 300° × 4 h	Al-5Mn-Sc (HT) Sc 0.6 wt.%	397	430	4.89
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-4.52Mn-Sc-Zr (AB) Sc 0.79 wt.%	438	460	19	[68]
/	Fine grains microstructure + primary Al3Sc type and Alx(Mn, Fe)-type precipitates	Direct aging 300° × 5 h	Al-4.52Mn-Sc-Zr (HT) Sc 0.79 wt.%	556	570	18
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-4.58Mn-Sc-Zr (AB) Sc 0.91 wt.%	430–438	446–451	17.8–20	[69]
/	Fine grains microstructure + primary Al3Sc type and Alx(Mn, Fe)-type precipitates	Direct aging 300° × 6 h	Al-4.58Mn-Sc-Zr (HT) Sc 0.91 wt.%	559	572	10
/	Fine grains microstructure at meltpool boundaries + columnar grain inside the meltpool	/	Al-5.5Mn-2.69Mg-Sc-Zr (AB) Sc 1.03 wt.%	520	700	8	[94]
/	Fine grains microstructure + primary Al3Sc type and Alx(Mn, Fe)-type precipitates	Direct aging 300° × 6 h	Al-5.5Mn-2.69Mg-Sc-Zr (HT) Sc 1.03 wt.%	621	712	4.5
/	Columnar grains + γ and Laves phases	/	Inconel 718 (AB)	800 ± 8	997 ± 10	29.7 ± 0.8	[75]
/	Microstructural homogenization, recrystallization, grain growth + γ, γ′, γ″ and δ	Homogenization annealing (HA) 10 °C/min–1100 °C × 1 h–35 °C/min until reaching room temperature + Solution annealing (SA) 10 °C/min–980 °C × 1 h–35 °C/min until reaching room temperature (furnace cooling) + artificial aging (AH) 10 °C/min–720 °C × 8 h-0.9 °C/min–620 °C × 8 h–5 °C/min + furnace cooling	Inconel 718 (HT)	1279 ± 14	1406 ± 4	13.9 ± 1
/	Microstructural homogenization, partial recrystallization + γ, γ′, γ″ and Leaves phases	Solution annealing (SA) 10 °C/min–980 °C × 1 h–35 °C/min until reaching room temperature (furnace cooling) + artificial aging (AH) 10 °C/min–720 °C × 8 h–0.9 °C/min–620 °C × 8 h–5 °C/min until reaching room temperature (furnace cooling)	Inconel 718 (HT)	1291 ± 10	1440 ± 1	13 ± 0.7
/	Columnar grains + γ, γ′, γ″ and Leaves phases	Direct artificial aging (DAH) 10 °C/min–720 °C × 8 h–0.9 °C/min–620 °C × 8 h–5 °C/min + until reaching room temperature (furnace cooling)	Inconel 718 (HT)	1341 ± 2	1478 ± 4	10 ± 1.5
/	Columnar grains with a large size distribution + columnar and cellular dendritic substructures + Nb,Ti-rich MC carbides	/	Inconel 625 (AB)	783 ± 23	1041 ± 36	33 ± 1	[76]
/	Mostly like as-built condition + Cr-rich M23C6 carbides precipitates in grains boundary + inhomogeneous precipitation of fine γ″	Direct artificial aging (DAH) 700 °C × 24 h	Inconel 625 (HT)	1012 ± 54	1222 ± 56	23 ± 1
/	Recrystallization (development of equiaxed grains with numerous twin boundary) + coarse Nb,Ti-rich MC carbides dispersed on intra- and inter-grains	Solution annealing (SA) 1150 °C × 2 h	Inconel 625 (HT)	396 ± 9	883 ± 15	55 ± 1
/	Equiaxed grains + Cr-rich M23C6 carbides at grain boundary + homogeneous precipitation of ellipsoidal γ″ precipitates	Solution annealing (SA) 1150 °C × 2 h + artificial aging (AH) 700 °C × 24 h	Inconel 625 (HT)	722 ± 7	1116 ± 6	35 ± 5
/	Nearly vertical columnar grain growth	/	GRCop42 (AB)	173	355	33.6	[95]
/	Fine grain formation compared to classical powder metallurgy	/	Tantalum (AB)	450	739	2	[96]
/	Columnar grains grow along the building direction (BD) across multiple layers, showing a pronounced epitaxial characteristic	/	Ta10W (AB)	663	765	28	[97]
/	Mainly ferrite with a small amount of austenite, small grains in meltpool boundary that increase their dimension toward the center of meltpool	/	Duplex 2205 (AB)	897	1035	15.3	[77]
/	Mainly ferrite with a small amount of austenite, small grains in meltpool boundary that increase their dimension toward the center of meltpool	/	Duplex 2507 (AB)	1196	1276	15	[98]

The high yield strength and good plasticity performance exhibited by AISI 316L in the AB condition are mainly due to the cellular substructure formed during processing at high cooling rates. Furthermore, solute segregation and the precipitation of nanoscale oxides at grain boundaries help to adjust the microstructural properties when heat treatments such as annealing are applied. Indeed, as demonstrated by Niu et al. [99], higher ductility values at acceptable plastic stress can be obtain by applying an HT at 900 °C for 5 h. In particular, nano-oxide coarsening inhibits excessive grain growth, maintaining a microstructure similar to that of LPBF AB. It also reduces the amount of dislocation at grain boundaries, thereby inhibiting stress concentration and crack formation and propagation. Furthermore, the presence of nano-oxides within grains acts as a dislocation barrier, hindering dislocation motion and enhancing strength. This translates into an increased plasticity region and the higher energy-absorption capabilities of AISI 316L.Titanium alloys show a particular trend upon the response to LPBF high cooling rate and heat treatments. In particular, apart from aging (which will be discussed subsequently), stress relief and annealing heat treatments are characterized by microstructural changes induced by temperature and time. Starting with the α-, β-, and (α + β)-alloys, it has been demonstrated that the fine α’-acicular martensite phase undergoes totally different microstructural evolution depending on whether heat treatment is conducted below or above the β-transus temperature. It has been demonstrated that heating the alloys above the β-transus point results in severe microstructure coarsening, as well as a substantial decline in strength and a minor improvement in ductility. This makes the alloy ineffective for increasing energy absorption capabilities [100]. Conversely, heating below β-transus generates a completely different microstructure by maintaining a constant time of 2 h and altering the temperature. In particular, as demonstrated by Kesavan et al. on Ti6Al4V [101], temperatures of 750 °C (labeled HT1), 850 °C (labeled HT2), and 950 °C (labeled HT3) have a completely different influence on α’ dissolution and microstructure evolution. HT3 is the only heat treatment that can completely dissolve the α’ acicular martensitic phase, generating a microstructure composed of coarse and globular α alternating with uniform β. Conversely, HT1 and HT2 cannot fully dissolve the α’, and are characterized by an increasing amount of β, as well as coarser α laths with a decreasing aspect ratio as the temperature rises. The evolution of the microstructural features strictly reflects the mechanical properties: generally, a higher amount of β and coarser α laths increase ductility and reduce strength, as can clearly be seen in Table 2. This trend is useful for energy absorption, since the amount of energy gained due to increased ductility is greater than the amount lost due to reduced plastic flow stress. This result can be obtained by finely tuning the heat treatment, not only considering phase shape and percentage, but also β grain boundary α phase (αGB). This phase is particularly brittle and continuous in the AB sample and acts as a crack nucleation and propagation site, given that its low bearing capacity makes it act as a stress concentration site. The phase transition due to the heat treatments enables the formation of a more ductile microstructure, which can withstand higher deformations. On the other hand, if the solution heat treatment is conducted at a temperature that is too high (reaching the β-transus temperature), this phase tends to grow too much, leading to sudden failure [101].

A similar behavior can be observed in duplex stainless steel. The energy absorption capabilities of as-built components, which primarily consist of a ferritic phase, can be enhanced by heat treatment. This process has been shown to increase ductility through recrystallisation and the growth of the austenitic phase, as well as the transformation of the ferritic and austenitic domain morphologies [102,103]. Solution annealing also involves the dissolution of chromium nitrides, which are responsible for a significant increase in strength at the expense of low ductility in as-built microstructures. The effect of phase boundaries is still unclear, although some preliminary studies have demonstrated that they are characterized by heterogeneous elemental segregation, which can act as stress concentration and crack nucleation sites [104].

AlSi-based AM alloys are among the most thoroughly studied and industrialized aluminum alloys for LPBF. The narrow solidification temperature range is key to their success, as it prevents crack formation during printing [105]. The AM microstructure is characterized by a supersaturated aluminum matrix embedded in fibrous silicon eutectic walls [106]. It has been established that extreme distortion of the crystal lattice generated by supersaturation acts as an impediment to dislocation motion. Additionally, the fine primary Al matrix and brittle Si eutectic fibrous structure act as robust walls that hinder plasticity phenomena further. It is important to understand that the ductility of AlSi-based aluminum alloys can only be significantly increased through heat treatment. This is a critical factor when designing structures that primarily function to absorb energy. Solution annealing has been demonstrated to fragment the Si fibrous structure into multiple Si spheroidal particles, thus increasing ductility and avoiding extreme crack propagation [106]. A consistent decrease in strength has been observed due to solute redistribution and atomic lattice relaxation. Regarding AlSi10Mg, the strength can be increased by performing a final aging heat treatment, which allows for the precipitation of the Mg2Si reinforcing second phase to occur. The time required to optimize energy absorption properties will be discussed further later [107]. To improve the mechanical performance of AM-fabricated aluminum alloys, new aluminum–scandium combinations have been developed specifically for LPBF. These alloys mitigate the issue of hot cracking caused by the rapid cooling rate by precipitating an Al₃Sc inoculant (incoherent particles), which act as nucleation sites for aluminum crystals [105]. The presence of this inoculant results in advanced grain refinement in the as-built (AB) state. When combined with precipitation during solidification, this creates a strong yet ductile microstructure [108]. The strength of AlSc alloys can be increased further by applying direct aging heat treatments; however, this will come at the expense of ductility. As always, it is important to carefully consider the optimum balance between ductility and strength [92].

Concerning Inconel 718, Santoni et al. [109] have shown that the AB microstructure is characterized by a γ matrix consisting of columnar grains with dendritic substructures, in which leaves and δ phases can be observed. The presence of these phases can be correlated with higher strength and lower plasticity due to their elevated hardness. Homogenization of the microstructure and dissolution of these detrimental phases can be achieved through precise annealing. Lu et al. investigated the effects of different annealing temperatures (980 °C, 1020 °C, and 1080 °C) on a 1 h long heat treatment [110]. They found that the T1 temperature was not high enough to dissolve the Leaves and δ phases, nor did it have a significant effect on grain morphology or orientation. Conversely, the T2 temperature was high enough to dissolve the Leaves phase, but not the δ phase. Furthermore, a small number of grains underwent recrystallisation to form typical annealing twins. The T3 temperature was found to dissolve both the Leaves and δ phases. This also resulted in significant grain recrystallisation, characterized by long, straight annealing twins. Tensile tests demonstrated an increase in ductility and a decrease in strength as the annealing temperature increased. The optimal condition is, once again, subject to the perfect balance between the ductility and strength of the heat-treated material. Alloy strength can be further increased by applying aging heat treatments, which require an in-depth understanding of the loss of ductility in favor of strength gain through the precipitation of γ′ and γ″ phases [111,112,113]. Similar considerations can be made for Inconel 625, with the difference being that the formation of γ′ is not thermodynamically favored and solidification and aging are more likely to generate different types of carbides at grain boundaries [114,115].

In relation to CuCrZr, it has been noted that its AB microstructure, characterized primarily by supersaturated columnar grains, demonstrates excellent ductility but comparatively low strength. This makes it unsuitable for use in the design of energy absorption systems [91]. Therefore, the evaluation of heat treatments is strictly recommended to achieve the desired performance. Solution annealing has been shown to be ineffective in improving the performance of CuCrZr. This is because it is primarily associated with grain coarsening, resulting in a subsequent loss of strength. In addition, Karuppasamy et al. [116] demonstrated, in their study, that water-quenching and air-cooling processes can result in various microstructural defects such as craters. These defects significantly impact alloy performance. Therefore, although furnace cooling can generate defect-free microstructures, it results in poor mechanical properties. These properties can be improved through aging and the precipitation of Cr-rich secondary particles. However, as demonstrated by Zeng et al. [91], this approach has not been shown to improve alloy performance. This is strictly correlated to coarse chromium precipitation, which mainly occurs on grain boundaries. Consequently, alloy performance can only be improved by exploiting copper matrix supersaturation induced by the LPBF process and by subjecting it to direct aging. A range of aging temperatures and times have been analyzed. While a 450 °C aging process for 4 h demonstrates optimal strength, a 400 °C heat treatment for 4 h is recommended to enhance energy absorption capabilities. This is primarily because CuCrZr exhibits good toughness and high strength.

For all of the aforementioned reasons, the conventional perception of hardening heat treatments must be reconsidered to optimize the performance of an energy absorption system. As can be seen in Table 3, direct aging and all other conventional multi-step heat treatments that include aging as the final step generate less ductile base material due to the precipitation of hardening second phases.

Hence, when it comes to absorbing energy, hardening heat treatments should be used in a different way to the usual approach. Indeed, a small loss of deformation, coupled with higher stresses, can be a useful condition for absorbing a lot more energy during the plastic regime. From this point of view, aging should not be conducted to the peak, but rather to increase the mechanical response of the material by increasing the stress and energy absorbed plastically to a certain extent, while maintaining a more ductile behavior than the peak-aged alloy [117]. Table 3 also shows how the printing orientation affects the mechanical properties of the base material. The literature shows that many alloys exhibit anisotropic mechanical properties when specimens are loaded in the building growth direction rather than the in-plane direction [118,119,120,121,122]. For this reason, annealing is strictly recommended when isotropic properties need to be fulfilled.

To fully understand the physical metallurgy correlations which are responsible for material response at different loading conditions, Appendix A is strictly recommended. This section provides an in-depth analysis of the materials science background on the interaction between microstructural features and plastic deformation phenomena such as dislocation motion, twinning, and phase transformation. The key information contained in Appendix A must be analyzed based on the information contained in Table 2 and Table 3 and the description of main heat treatments.

3. Analysis of Mechanical Metamaterial for Energy Absorption Systems

3.1. Mechanical Metamaterials for Energy Absorption Systems: Definition and Conceptualization

Section 2 and Appendix A discuss how metals behave under different loading conditions, including different loading regimes and temperatures. A full description of the type of heat treatments, microstructure characterization, and effect on mechanical properties during plastic deformation is reported. These extended analyses form the foundation of this work for two main reasons: First, the base material models should be introduced, along with an explanation of the mechanisms governing mechanical performance. Secondly, it is useful to understand the mechanisms that occur locally in metallic architected structures. Many studies in the literature only analyze how a certain structure topology performs, but only a few report the importance of base material and how it affects the behavior of a certain architecture [123,124,125,126]. Dynamic loading is strictly interconnected to stress wave propagation, since stress propagates at a speed dependent on the strain rate and density of the base material [127]. Stress waves propagate faster in metals that are characterized by higher stiffness and lower density and slower in metals that are characterized by low stiffness and high density. Additionally, greater ductility enables greater deformation, but is generally associated with lower plastic flow strength (lower stress in the plateau region). Conversely, higher strength is generally associated with lower ductility, resulting in a lack of deformation and material failure.

Energy absorption generally requires a high stress level during plastic deformation, depending on the maximum threshold that can be reached without causing damage to people or protected loads. It also requires high ductility and toughness to extend the time over which kinetic energy is absorbed [128]; hence, the energy absorption properties are mainly related to mechanical properties such yield strength, plastic flow stress, material stiffness, and density. All of these properties can be tuned by taking advantage of mechanical metamaterials. These can be strictly defined as rationally designed structures composed of building blocks allowing them to enable functionality that surpasses that of natural materials [129].

The base unit cell has a topological arrangement defining how the metamaterial behaves under certain external force field [130]. The main topologies used in the field of mechanical metamaterials are represented in Figure 4a.

Following a thorough study of the state of the art in terms of mechanical metamaterials and cell topologies, the need for an additional, new way to classify mechanical metamaterials based on how the base cell is geometrically designed has been found.

The following classes of metamaterials have been identified based on their geometric features such as rods, planes, and curved surfaces: (i) rod-based metamaterials and (ii) surface-based metamaterials. The former are characterized by a unique architecture based on the linear elements connecting nodes. The latter can be further classified into two groups, characterized by variation in the axis normal to the surface along the structural elements of the base cells. Two types of surface-based lattice were thus identified: (i) a planar surface lattice, in which the normal surface remains nearly constant along the structural elements of the base cell; and (ii) a curved surface lattice, in which the surface normally varies along the singular structural elements of the base cell. It should also be noted that the main distinction in mechanical metamaterials, first introduced for lattice structures, relates to the stiffness and deformation behavior of the sample under a certain load. Using these terms, two types of metamaterials are being recognized during mechanical tests [133,134,135,136,137,138]:

• Stretch-dominated (SD) behavior: Structural elements of the mechanical metamaterial carry loads through axial stretching or compression. This type of behavior is structurally efficient and offers higher stiffness-to-weight ratios [107,108]. By a first approximation, SD-metamaterial elastic modulus ($E^{*})$ and yield stress (${\sigma }^{*})$ can be expressed as shown in Equations (1) and (9) [135,136]:

  $${\displaystyle \frac{E^{*}}{E_S}}=C\left({\displaystyle \frac{{\rho }^{*}}{{\rho }_S}}\right)$$

  (1)

  $${\displaystyle \frac{{\sigma }^{*}}{{\sigma }_{ys}}}=C\left({\displaystyle \frac{{\rho }^{*}}{{\rho }_S}}\right)$$

  (2)

  where $E_S$ is the Young’s modulus of the bulk, ${\rho }_S$ is the density of the bulk, ${\rho }^{*}$ is the density of the metamaterial, and C is a constant defined experimentally depending on base cell geometry and its topology arrangement.
• Bend-dominated (BD) behavior: Structural elements of the base cell primarily deform through bending. This type of behavior is less efficient in terms of the stiffness-to-weight ratio compared to stretch-dominated structures [135,136,137,138]. By a first approximation, the BD-metamaterial elastic modulus ($E^{*})$ and yield stress (${\sigma }^{*})$ can be expressed as shown in Equations (3) and (11) [135,136]:

  $${\displaystyle \frac{E^{*}}{E_S}}=C{\left({\displaystyle \frac{{\rho }^{*}}{{\rho }_S}}\right)}^2$$

  (3)

  $${\displaystyle \frac{{\sigma }^{*}}{{\sigma }_{ys}}}=C{\left({\displaystyle \frac{{\rho }^{*}}{{\rho }_S}}\right)}^{{\displaystyle \frac{3}{2}}}$$

  (4)

  Again, $E_S$ is the Young modulus of the bulk, ${\rho }_S$ is the density of the bulk, ${\rho }^{*}$ is the density of the metamaterial, and C is a constant defined experimentally depending on the base cell geometry and its topology arrangement.

Figure 4b,c shows applied Equations (1)–(11) for some stretch- and bend-dominated architectures [132]. Equations (1)–(11) do not perfectly match the data, since the constant C needs to be always experimentally determined; hence, real behavior will always exhibit a certain deviation from the ideal one. Moreover, a comparison of Calladine and English [138] with Hössinger-Kalteis’s [135] work concerning the bend vs. stretch definition provided above, reveals that the dominant deformation mechanism governing the deformation structure can be precisely identified through their loading curves. Before diving into this characterization, a brief description of a metamaterial stress–strain curve is needed to completely understand the behavior of an architected structure. Figure 5a represents the typical stress–strain compressive curve of a metamaterial.

Three stages of the stress–strain compressive curve can be identified [50]:

• Initial stage: This stage corresponds to the base material elastic stress–strain region and can be termed as pre-collapsing. It shows a linear stress–strain relation in which, at the end, a local maximum is reached. The local maximum stress is called collapse-initiation stress (σ_c0) and can be assumed as the yield point of a mechanical metamaterial. The strain level related to σ_c0 takes the name of collapse initiation strain (ε_c0).
• Plateau stage: In this deformation phase, stress is relatively constant. This behavior is due to mechanisms by which base cells deform and collapse. This region extends from the collapse initiation strain (ε_c0) to the onset densification strain (ε_d0) that represent the point in which the effectiveness of cellular structure to accommodate deformation is lowered. In the context of metamaterial design for energy absorption systems, this region of the stress–strain curve assumes paramount importance. Indeed, the energy absorbed by the metamaterial in this phase is directly proportional to the effective useful performance of the architected structure itself and can be calculated as in Equation (5):

  $$U_{pl}={\int }_{{\epsilon }_{c0}}^{{\epsilon }_{d0}}\sigma \left(\epsilon \right)d\epsilon$$

  (5)

  where $\sigma$ and $\epsilon$ are the nominal compressive stress and strain, respectively.
• Densification stage: This phase of the stress strain curve has been defined by Gibson and Ashby [17] as a stage in which stress rapidly increases since cell walls, which start impacting each other, leading the metamaterial to a complete and inevitable full compression. The most important thing related to this region is the identification of onset densification strain (ε_d0). Many mathematical definitions have been proposed for this term. The authors decided to present the workhorse formulation proposed by Li et al. [139], which states that the onset densification strain (${\epsilon }_{d0}$) is reached when the energy efficiency ($\eta \left(\epsilon \right)$) attains its maximum, as shown in Equations (6) and (7):

  $$\eta \left(\epsilon \right)={\displaystyle \frac{1}{\sigma \left(\epsilon \right)}}{\int }_0^{\epsilon }\sigma \left(\epsilon \right)d\epsilon$$

  (6)

  $${\displaystyle \frac{d\eta \left(\epsilon \right)}{d\epsilon }} {|}_{\epsilon ={\epsilon }_{d0}}=0$$

  (7)

  where $\sigma$ and $\epsilon$ are the nominal compressive stress and strain, respectively. The condition expressed by Equations (6) and (7) are qualitatively represented in the smaller graph of Figure 4a. The key information that readers must extract is that the onset densification strain (${\epsilon }_{d0}$) occurs when the ratio between the sum of energy absorbed and the stress reaches its maximum. Subsequently, the rise in stress due to structure collapse, structural element collision, and the strengthening mechanisms related to these aspects caused the metamaterial to become ineffective in absorbing energy without significant stress transfer.

  Figure 5. (a) Mechanical metamaterial stress–strain characteristics (red) and energy efficiency characteristics (blue) (adapted from Ref. [50] with permission of Elsevier). (b) SD metamaterial typical stress–strain behavior. (c) BD metamaterial typical stress–strain behavior (adapted from Ref. [137]).

  Figure 5. (a) Mechanical metamaterial stress–strain characteristics (red) and energy efficiency characteristics (blue) (adapted from Ref. [50] with permission of Elsevier). (b) SD metamaterial typical stress–strain behavior. (c) BD metamaterial typical stress–strain behavior (adapted from Ref. [137]).

As mentioned above, the analysis of stress–strain curves (derived from force-displacement curves) can be used to determine whether a bend-dominated or stretch-dominated behavior is present. This is shown in Figure 5b,c, which relates to the mechanical compression tests [50,137]. A detailed analysis of the behavioral tendencies exhibited by diverse structural configurations supports the following conclusions [17,50,137]:

• Stretch-dominated (SD) behavior: Stress–strain curves of stretching-dominated lattices are generally defined by higher initial stiffness and yield strength compared to bending-dominated lattices of the same relative density. Additionally, post-yield softening is evident due to sudden failure by buckling or brittle crush of a layer of cells. This results in a plateau region characterized by peaks and valleys (see Figure 5b), indicating progressive layer failure. This explains why stretching-dominated structures, despite being more structurally efficient, are vulnerable to sudden failure and ineffective at dissipating deformation energy [50].
• Bend-dominated (BD) behavior: Bend-dominated structures exhibit enhanced compliance and a more flexible response to external forces. This behavior allows them to exhibit a smooth stress–strain response (as shown in Figure 5c) due to the lower fluctuation of forces induced during deformation [140].

This analysis of stress–strain curves in relation to mechanical metamaterials mainly concerns the quasi-static regime. When testing at higher deformation rates, however, metamaterials are generally influenced by velocity-dependent phenomena. The impact conditions affecting the metamaterial differ from those of the base material (see Appendix A,

Table A4. Dislocation interaction with lattice defects at different strain rates and associated phenomena.

			Micro-Mechanism		Macro-Effect
		Crystal Lattice in Which Phenomena Originate	Phenomena Overview	Effect on Strain Rate Sensitivity	Stress–Strain Response	Strain Rate
Solid solution strengthening	Interstitial atoms	All crystal structures	At high strain rates, the arrest time of dislocation in front of an obstacle is considered short. Hence, for a certain range of temperature, diffusion phenomena involving the formation of solute atom clouds near dislocation does not produce an effective enhancement of the shear stress needed to move the dislocation [341,378,379,380]	Softening	Less stress needed to deform the base material and less serration of the stress–strain curve due to the reduction in pinning and unpinning phenomena between solute and dislocations.	${10}^{-5}\to {10}^4$
	Substitutional atoms
Precipitation strengthening	Coherent precipitates	FCC	They increase yield strength and plastic stress, as shown in Table 3, without affecting strain rate hardening [347,381].	/	/	${10}^{-5}\to {10}^4$
	Incoherent precipitates	FCC	The interaction with high-speed dislocations depends on the pressure of the load input and the size of the precipitates. In particular, the Orowan bypass mechanism is favored for larger precipitates, while radiating dislocation emission is favored for nanoprecipitates. By originating new dislocation, this second behavior will promote the hardening of the alloy [347].	Hardening	Depending on precipitate size and pressure level of the load. Nano-sized precipitates exhibit hardening mechanisms at low stresses and toughening mechanisms at high stresses. In contrast, larger precipitates exhibit hardening phenomena both at low and high stresses [347].	${10}^4\to {10}^8$
Dislocation interaction	Dislocation drag	All crystal structures	Metals act as viscous Newtonian solids. Hence, under the application of external stress, dislocations responsible of plastic deformation will accelerate until the reaching of a certain steady state velocity. In particular, metal viscosity can be analyzed as a parameter that correlate linearly dislocation velocity and stress [382,383].	Hardening effect that can be evaluated as: $\sigma ={\displaystyle \frac{2BM}{\rho b}}\dot{\epsilon }$ where $\dot{\epsilon }$ is the strain rate, $b$ the Burgers vector, M the orientation factor, and $\rho$ dislocation density	Higher stress needed to deform the base material.	${10}^0\to {10}^4$
	Relativistic effect	All crystal structures	Deformation of the stress field of dislocation and increase in dislocation self-energy [51].	Hardening	By enhancing the dislocation self-energy, the local stress field created by the dislocation will be enhanced and will create a hardening mechanism while interacting with other dislocations and defects [374,375,376,377,378,379,380,381,382,383,384].	${10}^4\to {10}^8$
	Dislocation forest	All crystal structures, but primarily in FCC	As the pressure and pulse duration of the load increase, the dislocation density. Higher pulse duration means that dislocations have more time to nucleate and, rearrange, interact and create more defined substructures [51].	Hardening	Higher dislocation density means more dislocation interaction and, consequently, a hardening effect on the base material that will be translated in more stress needed to continue to deform or sudden failure [51].	${10}^4\to {10}^8$
	Jogs drags and point defects generation	All crystal structures	Jogs effectiveness to constrain dislocation motion is less as the impact velocity rises. Non conservative motion of jogs creates a large amount of point defects [51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389].	Softening	Jogs are less effective than in quasi-static tests. This means their hardening effect is less effective.	${10}^4\to {10}^8$

). Metamaterials generally have a lower bearing capacity to withstand loads than their larger counterparts, so they will be characterized by lower velocities required to generate dynamic and shock loading conditions, as shown in

Table 4. Metamaterials test regimes and phenomena involved at different strain rates.

Strain Rate	${10}^{-5} \to {10}^{-1} {\mathbf{s}}^{-1}$	${10}^{-1} \to {10}^3 {\mathbf{s}}^{-1}$	${10}^3 \to {10}^6 {\mathbf{s}}^{-1}$	Ref.
Phenomena during deformation	Quasi-static test: tests are conducted with the same velocity throughout the whole specimen length. Force balance is guaranteed.	Dynamic test: strain rate effect starts to arise on the samples that are still under a force equilibrium condition. Deformation modes can change from quasi-static test since metamaterial can find a different internal equilibrium state depending on strain rate phenomena involved at base material and base cell level. These phenomena are related to microinertial response that arise from acceleration of materials points.	Shock loading test: discontinuity front formed in which cell row collapsed subsequently. Macro-inertia effect appears in the samples since the acceleration of a macroscopic region is no longer zero (no force equilibrium).	[50]

.

During dynamic tests (${\dot{\epsilon }=10}^{-1}\to {10}^3 {\mathrm{s}}^{-1}$), phenomena governing the strain rate response of a mechanical metamaterial are strictly related to both the base material (discussed deeply in Appendix A.3 and the base cell selected, as follows:

• Microscopic strain rate: The effect of the microscopic strain rate refers to local phenomena occurring at the base material level on single points of structural elements, where deformation is highly localized. The macroscopic strain rate generates a microscopic strain rate locally that can be higher or lower than the macroscopic strain rate, depending on the characteristic behavior of the cellular structure of the analyzed sample [50]. According to Calladine and English [138], stretch-dominated structures (SD) are more sensitive to strain rate, given the localization of stresses during deformation, while bend-dominated (BD) architectures exhibit lower local strain rates due to their inherently lower stress concentration.
• Microinertia phenomena: These arise from the sudden acceleration of material points in the structural elements of individual cells and can generate a hardening effect [50]. According to the work of Calladine and English [138], bend-dominated structures seem to be insensitive to microinertia. On the other hand, microinertia promotes two major hardening effects in stretch dominated structures. In particular, the main effect on microinertia is related to the initial stage of stress–strain curve (Figure 5a): the higher the impact velocity, the higher is the increment in stress needed to deform the metamaterial, since the base cell structural element buckling is retarded (Figure 5b). This is why it is believed that the microinertial effect disappears after the initial stage of deformation. However, Karagiozova [141] has demonstrated that the initial microinertial effect can influence the plateau stage. Indeed, microinertial buckling delay under impact loading increases the strain experienced by the base cell’s structural elements. Consequently, the crushing force required to deform the metamaterials further increases.

It should be noted that the effect of the microscopic strain rate typically outweighs that of micro-inertia, as illustrated in Figure 6, particularly when the base material is highly sensitive to strain rate [142]. Regarding the densification strain and its relationship to strain rate, no clear conclusion can be found in the literature, since, as with the plastic deformation behavior, it is strictly connected to the base material and base unit cell of the architected structure [143,144,145,146,147,148].

The local dynamic response of an architected material is expected to differ from the dynamic base material properties, which are determined from bulk samples. For this reason, the literature results [149,150,151,152] suggest that, in the case of mechanical metamaterials for energy absorption, test methods and specimens should be designed to fully understand the complexity and the properties of the structural elements. Embryonic studies are limited in number, and further research is required to evaluate the testing methods and develop a base material model capable of capturing the complexity and properties of structural elements. These properties are defined by a thickness-related size effect (and concomitant cooling rate variation).

If the strain rate increases and a certain critical velocity impact (which is strictly correlated to the base material cell structures and their parametrizations—to be clarified in the following analysis) is exceeded, the metamaterials will start to deform under shock loading conditions. At sub-critical velocity values in dynamic conditions, the deformation pattern of metamaterials is similar to that of quasi-static loading and depends on the distribution of stresses inside the cell to counteract the applied force and minimize internal energy [153]. In particular, the X, V, Bi-V, and Z deformation modes can be identified and can be classified as the deformation shear band of the cellular array, as shown in Figure 7a–e [154]. When the deformation occurs at super-critical velocity, the deformation modes change completely: the severe impact conditions generate a compaction shock wave, which progressively crushes the structure (I mode). In particular, the residual momentum transferred to the second row after the first row of cells is compressed creates a domino-like compaction mode characterized by the discontinuity of stress and deformation at the boundary of the shock structural wave (Figure 7f) [155,156].

This progressive effect is strongly related to macroinertia. Given the high-speed loading conditions applied, the tested samples are no longer subject to a force equilibrium condition, meaning the deformation does not dissipate in a way that minimizes thermodynamic internal energy [50].

The phenomena correlated with this behavior typical of mechanical metamaterials during shock loading can be explained as follows:

• Microscopic strain rate: In shock compression, the deformation process involves progressive cell crushing. Experiments show that, since the deformation is highly localized during shock loading, a significant local increase in microscopic strain rate occurs in the base material. The microscopic strain rate is much larger than the macroscopic strain rate (much more so than in dynamic analysis). This phenomenon is characterized by both stretch-dominated and bend-dominated structures, and varies for different architectures, but gives rise to the same effect [50]. This is also related to the fact that, under shock loading, intensive localization of stress and strain produces more local buckling in stretch-dominated architecture, thus resulting in more plastic deformation at the base cell level [156].
• Microinertia phenomena: Although macroinertia plays the main role, microinertia phenomena still exert some influence, since material points on individual base cell structural elements accelerate during row-by-row collapse.

The characteristics of the samples, such as their relative density and dimensions, also play a significant role in determining the behavior of mechanical metamaterials under shock loading. The response of mechanical metamaterials to shock loading depends on pulse duration and intensity. If the pulse duration and intensity are high enough, full densification of the cellular material will be achieved and the pulse transferred to the protected items will increase, since the structures will be fully compressed [158,159]. Consequently, a greater amount of force is transferred to the items requiring protection, sometimes exceeding the impulse itself [159]. Relative density has a significant impact on the response of the structure during shock loading: experiments in [153,155,158] highlight that metamaterials characterized by lower relative densities are more likely to completely crush and diffuse stresses to the items that need to be protected, with their critical velocity for shock initiation ($V_{sc}$) being lower than for other categories, according to Equation (8) [156,160]:

$$V_{sc}={\epsilon }_{d0}\sqrt{{\displaystyle \frac{E_P}{{\rho }_0}}}$$

(8)

where ${\epsilon }_{d0}$ is the densification strain, ${\rho }_0$ is the relative density of the cellular structure prior to the test, and $E_P$ is the linear plastic hardening modulus of the mechanical metamaterial related to the stress–strain relation obtained by a quasi-static test, as shown in Figure 6. This formula was chosen for its straightforward description and implementation, even though more exhaustive formulations can be found in the literature [50,160,161]. The shock initiation velocity can also be predicted by FEM simulations if the settings and boundary conditions are well defined [156,162,163,164].

It is worth pointing out that when the relative density cannot be adjusted, a certain length of the energy absorber must be guaranteed to prevent full densification and the resulting increase in force and stress transmitted to the items to be protected [153,158]. Specifically, the crush absorber must be long enough to dissipate the impact energy through plastic deformation [160].

3.2. Metallic Metamaterials for Energy Absorption: Influence of Parametrization on Mechanical Performance

This section presents different types of base cells and their parametrization. Quantitative data related to Specific Energy Absorption (SEA), yield stress, and elastic modulus will be provided, based on a thorough analysis of scientific papers [133,165,166,167]. It is also important to note that the mechanical response of metamaterials to a specific load depends on the selected base cell and the effects outlined in the previous section. Table 5 and Table 6 present the main base cell topologies and parameterization related to mechanical metamaterials for energy absorption systems. The authors have decided to present the data in table form to help the reader compare different structures. Closed-cell architectures are not analyzed, since their design does not allow for the efficient removal of unmelted powder, which remains stuck inside the structure and affects its overall behavior [168,169,170]. Some additive design strategies [171] can be applied to plate lattices to evacuate entrapped powder [172,173], but these will not be accounted for in the present work for ease of analysis.

Table 5. Plane surface and strut-based lattices base cell representation, parametrization, parameters influence on energy absorption capabilities and qualitative stress–strain response (base cell images generated with the nTop software v5.26.2 [131]).

Base Cell	Parameters Influence on Energy Absorption	References to Stress–Strain Curve
Hexagonal honeycomb [174]	h: In out-of-plane compression the energy needed to buckle the structure increases with thickness. However, the frequency of ripples in buckled walls becomes lower. This means the structure is less efficient in absorbing energy [175,176].	[17,177]
	l: Lower base cell size allows us to increase the energy needed to deform the honeycomb structure during out-of-plane compression since the bearing ability of the metamaterial increases [178]. The size of the base cell has a significant impact on energy absorption capabilities of in-plane loading of honeycomb [179,180]: by maintaining constant both the thickness (h) and the cell wall angle ($\beta$), the energy absorption capability decreases as more oscillations starts to occur in the plateau region of stress–strain curve.
	$\beta$: Has a significant impact on honeycomb energy absorption capabilities. In particular, considering out-of-plane compression and the same relative density, an increment in crushing force and the overall energy absorbed can be noted if $\beta$ decreases [175]. Considering in-plane compression along x-axis and the same relative density, experiments showed that densification strain remains the same, but the crushing strength decreases as $\beta$ increases [177]. However, this effect is significantly reduced as the impact velocity increases since inertia effects start to play a predominant role [177]. When loaded in the in-plane y-direction, experiments [177,181,182] show that the energy absorption increases as $\beta$ increases until it reachs the value of 45°. After this point an increase in $\beta$ will result in a decrease in the energy absorbed [177].
In-plane re-entrant Honeycomb [183]	h: An increment of this parameter affects mainly the deformation modes and loading condition when load is applied in the x-direction, increasing the onset densification strain [184].	Load in y direction [153]. Load in x direction [185]. The literature has examined the re-entrant honeycomb properties, focusing primarily on the in-plane direction (even if the out-of-plane direction exhibit some unique properties such as synclastic [186] and anti-penetration behavior [187]). This direction exhibits distinctive properties, including a negative Poisson ratio that can expressed as [182,188]: ${\upsilon }_{xy}= -{\displaystyle \frac{{\epsilon }_1}{{\epsilon }_2}}=-{\displaystyle \frac{{\cos }^2\theta }{\left(\frac{h}{l}+sin\theta \right)sin\theta }}$
	l: An increase in this factor will produce, in the in-plane loading direction, a decrease in the mean plateau stress, while the other parameters remain constant. This behavior can be explained by the higher flexural momentum that appears on nodes [189]
	t: Thick-wall cells are characterized by a more stable and symmetrical auxetic behavior related to thin-walls structures which exhibit a less stable and effective once [153]. Moreover, an increase in thickness will produce a decrease in the densification strain (${\epsilon }_{d0})$, but an increase in the mean plateau stress [153].
	$\theta$: Zhang and Yang focused on how the wall angle influences the re-entrant honeycomb response in the in-plane compression [188] by having a constant h/l ratio (=2) and t to assess specifically how mechanical properties are affected by $\theta$. They found that the maximum stress of the re-entrant honeycomb decreases non-linearly with θ when the structure is loaded in y direction [188]. Similar behavior can be observed when they are loaded in the x-direction [186,189,190]; hence, an increase in θ lead to a more compliant behavior of the structures leading to lower peak and plateau stresses.
BCC(Z) lattice structure [191]	l: Lower strut length is responsible for the higher yield/plateau stress of the metamaterial, but does not affect the elastic modulus of the structure [192,193].	[193]
	d: Experiments found that the strut diameter significantly influences the Elastic modulus of the metamaterial generated by BCC base cells [194]. Moreover, a higher strut diameter is always related to a higher local yield stress since the structure is able to withstand higher forces [195]; hence, plateau stress will be higher and more energy can be absorbed in absolute terms (an optimum should be searched related to the weight).
	Z struts: BCC structure exhibits high structural compliance. This means that they are characterized by lower bearing capacity and deformation/stress that are more concentrated at nodes [196]. The use of Z struts allows them to have a higher bearing capacity, since the introduction of structural elements aligned to the load (it also introduces a certain level of anisotropy). Moreover, this introduces a different strut connection from which the material tends to respond more like a stretch-dominated structure than a bend dominated once. Z-struts can be implemented with different thickness [193]: this allows us to tune the bearing response and the switch to stretch-dominated allowing for the final architecture to absorb the highest amount of energy.
FCC(Z) lattice structure [191,192,193]	l: A higher cell dimension is associated with an increase in bending moment to which nodes are subjected [197].
	d: Similar BCC structures [197,198].
	Z struts: FCC structure exhibits higher structural stiffness than BCC once. Otherwise, they are still under-stiff to create an isostatic structure and hence they are characterized by a bend-dominated behavior from which deformation/stress concentration at nodes arises [196]. The use of Z struts, as for BCC, allows them to have a higher bearing and energy absorption capabilities [193].
Octet-truss [199]	l: A shorter length always determines an increase in the capacity of the structures to absorb more energy [199]. This phenomenon is related to the lower distance between nodes that postpones the insurgence of buckling phenomena on struts [200].	Macro-oscillations in the stress–strain response are related to the collapse of individual layers of unit cells, while micro-oscillations are related to local buckling and collapse at struts level [199]
	d: Gilchrist et al. [201] highlighted that a small strut diameter is responsible for a sudden drop in compressive stress after the failure initiation with the initial buckling of the rods. This drop is less evident when the diameter increases. Moreover, a lower strut diameter causes a certain peakiness in the plateau region, since buckling is highly localized, resulting in considerable stress oscillation. This behavior is less pronounced with a higher strut diameter, as rod buckling is more evenly distributed. As for BCC(Z) and FCC(Z), an increase in diameter is always associated with increased stiffness and higher rigidity [202].
Rhombic Dodecahedron [203]	l: By leaving the other parameters constant and changing only the strut length, it was observed [204] that a higher yield strength but a similar plateau was obtained [205,206].	[206]
	d: As seen for BCC(Z), FCC(Z), and Octet-truss, the plateau stress and the energy absorption capability of the structure increase as the strut diameter increases [207].
	$2\alpha$: The analysis of the angle will be conducted only for parameter $\alpha$, since the others can be simply obtained by constraining strut length. Experiments [203,205,206] revealed that a low value of α results in the loads applied to the strut being distributed in such a way as to increase the bending component of the load while decreasing the compressive component when an external load is applied in the z direction. For a value of $\alpha$ higher than 45° or for loading in the X direction (and $\alpha$ lower than 45°), the stress distribution is characterized by a more prominent axial compression; this means that struts are more likely to buckle than to bend around node giving the structure a higher bearing capacity [203,206].
Miura-ori base cell [208,209] SeG Miura-ori base cell [210]	$2L=2 a \sqrt{1-{\sin }^2\theta {\sin }^2\gamma }$	Loading curve in x,y,z [210]. The following assumption are related to multiple literature references and must be declined to the Miura-ori. Studies [208,209,210,211,212,213,214] demonstrate the following: ▪ $\alpha \uparrow$ and $\theta \downarrow$: increase the force reaction to a compressive load. ▪ $2S, 2L, H\uparrow$ decreases the densification strain. Moreover, the response of Miura-ori architecture is characterized by a high level of anisotropy [210].
	$V=b{\displaystyle \frac{1}{\sqrt{1+{\cos }^2\theta {\tan }^2\gamma }}}$
	$2S=2 b{\displaystyle \frac{cos\theta tan\gamma }{\sqrt{1+{\cos }^2\theta {\tan }^2\gamma }}}$
	t $\to$ increasing thickness will increase the force needed to deform the structure and will decrease the on-set densification strain.
	$H=a sin\theta sin\gamma$
	$tan\xi =cos\theta tan\gamma$
	$sin\psi =sin\theta sin\gamma$

Table 5. Plane surface and strut-based lattices base cell representation, parametrization, parameters influence on energy absorption capabilities and qualitative stress–strain response (base cell images generated with the nTop software v5.26.2 [131]).

Base Cell	Parameters Influence on Energy Absorption	References to Stress–Strain Curve
Hexagonal honeycomb [174]	h: In out-of-plane compression the energy needed to buckle the structure increases with thickness. However, the frequency of ripples in buckled walls becomes lower. This means the structure is less efficient in absorbing energy [175,176].	[17,177]
	l: Lower base cell size allows us to increase the energy needed to deform the honeycomb structure during out-of-plane compression since the bearing ability of the metamaterial increases [178]. The size of the base cell has a significant impact on energy absorption capabilities of in-plane loading of honeycomb [179,180]: by maintaining constant both the thickness (h) and the cell wall angle ($\beta$), the energy absorption capability decreases as more oscillations starts to occur in the plateau region of stress–strain curve.
	$\beta$: Has a significant impact on honeycomb energy absorption capabilities. In particular, considering out-of-plane compression and the same relative density, an increment in crushing force and the overall energy absorbed can be noted if $\beta$ decreases [175]. Considering in-plane compression along x-axis and the same relative density, experiments showed that densification strain remains the same, but the crushing strength decreases as $\beta$ increases [177]. However, this effect is significantly reduced as the impact velocity increases since inertia effects start to play a predominant role [177]. When loaded in the in-plane y-direction, experiments [177,181,182] show that the energy absorption increases as $\beta$ increases until it reachs the value of 45°. After this point an increase in $\beta$ will result in a decrease in the energy absorbed [177].
In-plane re-entrant Honeycomb [183]	h: An increment of this parameter affects mainly the deformation modes and loading condition when load is applied in the x-direction, increasing the onset densification strain [184].	Load in y direction [153]. Load in x direction [185]. The literature has examined the re-entrant honeycomb properties, focusing primarily on the in-plane direction (even if the out-of-plane direction exhibit some unique properties such as synclastic [186] and anti-penetration behavior [187]). This direction exhibits distinctive properties, including a negative Poisson ratio that can expressed as [182,188]: ${\upsilon }_{xy}= -{\displaystyle \frac{{\epsilon }_1}{{\epsilon }_2}}=-{\displaystyle \frac{{\cos }^2\theta }{\left(\frac{h}{l}+sin\theta \right)sin\theta }}$
	l: An increase in this factor will produce, in the in-plane loading direction, a decrease in the mean plateau stress, while the other parameters remain constant. This behavior can be explained by the higher flexural momentum that appears on nodes [189]
	t: Thick-wall cells are characterized by a more stable and symmetrical auxetic behavior related to thin-walls structures which exhibit a less stable and effective once [153]. Moreover, an increase in thickness will produce a decrease in the densification strain (${\epsilon }_{d0})$, but an increase in the mean plateau stress [153].
	$\theta$: Zhang and Yang focused on how the wall angle influences the re-entrant honeycomb response in the in-plane compression [188] by having a constant h/l ratio (=2) and t to assess specifically how mechanical properties are affected by $\theta$. They found that the maximum stress of the re-entrant honeycomb decreases non-linearly with θ when the structure is loaded in y direction [188]. Similar behavior can be observed when they are loaded in the x-direction [186,189,190]; hence, an increase in θ lead to a more compliant behavior of the structures leading to lower peak and plateau stresses.
BCC(Z) lattice structure [191]	l: Lower strut length is responsible for the higher yield/plateau stress of the metamaterial, but does not affect the elastic modulus of the structure [192,193].	[193]
	d: Experiments found that the strut diameter significantly influences the Elastic modulus of the metamaterial generated by BCC base cells [194]. Moreover, a higher strut diameter is always related to a higher local yield stress since the structure is able to withstand higher forces [195]; hence, plateau stress will be higher and more energy can be absorbed in absolute terms (an optimum should be searched related to the weight).
	Z struts: BCC structure exhibits high structural compliance. This means that they are characterized by lower bearing capacity and deformation/stress that are more concentrated at nodes [196]. The use of Z struts allows them to have a higher bearing capacity, since the introduction of structural elements aligned to the load (it also introduces a certain level of anisotropy). Moreover, this introduces a different strut connection from which the material tends to respond more like a stretch-dominated structure than a bend dominated once. Z-struts can be implemented with different thickness [193]: this allows us to tune the bearing response and the switch to stretch-dominated allowing for the final architecture to absorb the highest amount of energy.
FCC(Z) lattice structure [191,192,193]	l: A higher cell dimension is associated with an increase in bending moment to which nodes are subjected [197].
	d: Similar BCC structures [197,198].
	Z struts: FCC structure exhibits higher structural stiffness than BCC once. Otherwise, they are still under-stiff to create an isostatic structure and hence they are characterized by a bend-dominated behavior from which deformation/stress concentration at nodes arises [196]. The use of Z struts, as for BCC, allows them to have a higher bearing and energy absorption capabilities [193].
Octet-truss [199]	l: A shorter length always determines an increase in the capacity of the structures to absorb more energy [199]. This phenomenon is related to the lower distance between nodes that postpones the insurgence of buckling phenomena on struts [200].	Macro-oscillations in the stress–strain response are related to the collapse of individual layers of unit cells, while micro-oscillations are related to local buckling and collapse at struts level [199]
	d: Gilchrist et al. [201] highlighted that a small strut diameter is responsible for a sudden drop in compressive stress after the failure initiation with the initial buckling of the rods. This drop is less evident when the diameter increases. Moreover, a lower strut diameter causes a certain peakiness in the plateau region, since buckling is highly localized, resulting in considerable stress oscillation. This behavior is less pronounced with a higher strut diameter, as rod buckling is more evenly distributed. As for BCC(Z) and FCC(Z), an increase in diameter is always associated with increased stiffness and higher rigidity [202].
Rhombic Dodecahedron [203]	l: By leaving the other parameters constant and changing only the strut length, it was observed [204] that a higher yield strength but a similar plateau was obtained [205,206].	[206]
	d: As seen for BCC(Z), FCC(Z), and Octet-truss, the plateau stress and the energy absorption capability of the structure increase as the strut diameter increases [207].
	$2\alpha$: The analysis of the angle will be conducted only for parameter $\alpha$, since the others can be simply obtained by constraining strut length. Experiments [203,205,206] revealed that a low value of α results in the loads applied to the strut being distributed in such a way as to increase the bending component of the load while decreasing the compressive component when an external load is applied in the z direction. For a value of $\alpha$ higher than 45° or for loading in the X direction (and $\alpha$ lower than 45°), the stress distribution is characterized by a more prominent axial compression; this means that struts are more likely to buckle than to bend around node giving the structure a higher bearing capacity [203,206].
Miura-ori base cell [208,209] SeG Miura-ori base cell [210]	$2L=2 a \sqrt{1-{\sin }^2\theta {\sin }^2\gamma }$	Loading curve in x,y,z [210]. The following assumption are related to multiple literature references and must be declined to the Miura-ori. Studies [208,209,210,211,212,213,214] demonstrate the following: ▪ $\alpha \uparrow$ and $\theta \downarrow$: increase the force reaction to a compressive load. ▪ $2S, 2L, H\uparrow$ decreases the densification strain. Moreover, the response of Miura-ori architecture is characterized by a high level of anisotropy [210].
	$V=b{\displaystyle \frac{1}{\sqrt{1+{\cos }^2\theta {\tan }^2\gamma }}}$
	$2S=2 b{\displaystyle \frac{cos\theta tan\gamma }{\sqrt{1+{\cos }^2\theta {\tan }^2\gamma }}}$
	t $\to$ increasing thickness will increase the force needed to deform the structure and will decrease the on-set densification strain.
	$H=a sin\theta sin\gamma$
	$tan\xi =cos\theta tan\gamma$
	$sin\psi =sin\theta sin\gamma$

Table 6. Curve surface lattices base cell representation, equation, parameters influence energy absorption capabilities and qualitative stress–strain response (base cell images generated with the nTop software v5.26.2 [131]).

Base Cell	Equation and Peculiar Properties	References to Stress–Strain Curve
TPMS Gyroid Sheet	$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-T<\cos \left(\omega x\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega y\right)+\cos \left(\omega y\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega z\right)+\cos \left(\omega z\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega x\right)<+T$ where         $\omega =2\pi /L$ $L$ is the unit cell length (cubic bounding box length of the unit cell). If $L\downarrow$ the structures are more prone to distribute load by stressing the structural elements by tension-compression giving rise to a certain oscillation of the plateau region. Contrarily, if $L\uparrow$ structural elements of the base cell deform by folding [213,214,215,216,217]. $T$ is the cell iso-value. In particular, when $\mathrm{t}\downarrow$ the plateau region is characterized by a certain amount of oscillation since gyroid base cells are more prone to buckling during load application. Contrarily, if $\mathrm{t}\uparrow$ the buckling phenomena is less effective, and the structure is more compliant giving rise to a more distended plateau more similar to the one of bend dominated architectures [213,218].	Stress–strain curves reported in [213,219]. The architecture shows practically isotropic properties.
TPMS Gyroid Skeletal	$\cos \left(\omega x\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega y\right)+\cos \left(\omega y\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega z\right)+\cos \left(\omega z\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega x\right)>+T$         $\cos \left(\omega x\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega y\right)+\cos \left(\omega y\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega z\right)+\cos \left(\omega z\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega x\right)<-T$ where         $\omega =2\pi /L$ $L$ is the unit cell length (cubic bounding box length of the unit cell). If $L\downarrow$ so is the densification strain (${\epsilon }_{d0}\downarrow$), however the plateau stress is higher [220]. T is the cell iso-value. Samples characterized by a higher T are subjected to a significant stress fluctuation in the plateau region, which is related to the stress enhancement caused by the walls crushing against each other and the deformation restarting in a more favorable zone. This behavior is less pronounced when the iso-value is reduced [221]. Furthermore, an increase in T is associated with an increase in the elastic modulus of the metamaterial and the mean plateau stress [221,222].	Stress–strain curves [220]. As can be clearly seen, the skeletal gyroid architecture exhibits practically isotropic properties.
TPMS Diamond Sheet	$-T<\cos \left(\omega x\right) cos\left(\omega y\right)\cos \left(\omega z\right)-\sin \left(\omega x\right) sin\left(\omega y\right)\sin \left(\omega z\right)<+T$ where         $\omega =2\pi /L$ $L$ is the unit cell length. A decrease in the unit cell length means generally an increase in the energy absorbed since the enhancement related to the increase the plateau strength is generally higher than the lowering effect correlated with a lower densification strain $({\epsilon }_{d0}\downarrow )$ [220,223,224]. T is the cell iso-value. An increase in T will result in an intensification in the rigidity of the architected structure and compressive properties [197]. Thes iso-value effect starts to be more pronounced as the unit base cell length increases [223].	Stress–strain curves [220].
TPMS Diamond Skeletal	$\cos \left(\omega x\right) cos\left(\omega y\right)\cos \left(\omega z\right)-\sin \left(\omega x\right) sin\left(\omega y\right)\sin \left(\omega z\right)>+T$          $\cos \left(\omega x\right) cos\left(\omega y\right)\cos \left(\omega z\right)-\sin \left(\omega x\right) sin\left(\omega y\right)\sin \left(\omega z\right)<-T$ where         $\omega =2\pi /L$ $L$ is the unit cell length. Same consideration valid for the sheet TPMS Diamond. In the case of Skeletal diamond, bigger cells are characterized by the appearance of a certain fluctuation in the initial stage of the plateau region since structural elements of the base cell are more prone to collapse instability [220]. T is the cell iso-value. Some issues already discussed for TPMS Diamond Sheet.
TPMS Primitive Sheet	$-T<\mathit{cos}\left(\omega x\right)\mathit{cos}\left(\omega y\right)\mathit{cos}\left(\omega z\right)<+T$ where         $\omega =2\pi /L$ $L$ is the unit cell length. Unlike the other architectures, it has been demonstrated that smaller cells $(L\downarrow )$ show more compliance and tend to collapse before larger cells [225]. T is the cell iso-value. An increase in the cell iso-value will result in an increase in metamaterial stiffness, yield stress and plateau stress and a lowering in the densification strain [226]. Designers should always aim to the right trade off to obtain the best performance given a certain circumstance.	Stress–strain curves [226].
TPMS Primitive Skeletal	$\mathit{cos}\left(\omega x\right)\mathit{cos}\left(\omega y\right)\mathit{cos}\left(\omega z\right)>+T$         $\mathit{cos}\left(\omega x\right)\mathit{cos}\left(\omega y\right)\mathit{cos}\left(\omega z\right)<-T$ where         $\omega =2\pi /L$ $L$ is the unit cell length. An increase in base cell dimension will produce an increase in elastic modulus, yield stress and plateau stress of the metamaterial [227]. T is the cell iso-value. No data has been found in the literature discussing this topic. Surely, researchers around the world will fix this gap in the next years.	Stress–strain curves [228].

Table 6. Curve surface lattices base cell representation, equation, parameters influence energy absorption capabilities and qualitative stress–strain response (base cell images generated with the nTop software v5.26.2 [131]).

Base Cell	Equation and Peculiar Properties	References to Stress–Strain Curve
TPMS Gyroid Sheet	$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-T<\cos \left(\omega x\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega y\right)+\cos \left(\omega y\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega z\right)+\cos \left(\omega z\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega x\right)<+T$ where         $\omega =2\pi /L$ $L$ is the unit cell length (cubic bounding box length of the unit cell). If $L\downarrow$ the structures are more prone to distribute load by stressing the structural elements by tension-compression giving rise to a certain oscillation of the plateau region. Contrarily, if $L\uparrow$ structural elements of the base cell deform by folding [213,214,215,216,217]. $T$ is the cell iso-value. In particular, when $\mathrm{t}\downarrow$ the plateau region is characterized by a certain amount of oscillation since gyroid base cells are more prone to buckling during load application. Contrarily, if $\mathrm{t}\uparrow$ the buckling phenomena is less effective, and the structure is more compliant giving rise to a more distended plateau more similar to the one of bend dominated architectures [213,218].	Stress–strain curves reported in [213,219]. The architecture shows practically isotropic properties.
TPMS Gyroid Skeletal	$\cos \left(\omega x\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega y\right)+\cos \left(\omega y\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega z\right)+\cos \left(\omega z\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega x\right)>+T$         $\cos \left(\omega x\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega y\right)+\cos \left(\omega y\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega z\right)+\cos \left(\omega z\right) \mathrm{s}\mathrm{i}\mathrm{n}\left(\omega x\right)<-T$ where         $\omega =2\pi /L$ $L$ is the unit cell length (cubic bounding box length of the unit cell). If $L\downarrow$ so is the densification strain (${\epsilon }_{d0}\downarrow$), however the plateau stress is higher [220]. T is the cell iso-value. Samples characterized by a higher T are subjected to a significant stress fluctuation in the plateau region, which is related to the stress enhancement caused by the walls crushing against each other and the deformation restarting in a more favorable zone. This behavior is less pronounced when the iso-value is reduced [221]. Furthermore, an increase in T is associated with an increase in the elastic modulus of the metamaterial and the mean plateau stress [221,222].	Stress–strain curves [220]. As can be clearly seen, the skeletal gyroid architecture exhibits practically isotropic properties.
TPMS Diamond Sheet	$-T<\cos \left(\omega x\right) cos\left(\omega y\right)\cos \left(\omega z\right)-\sin \left(\omega x\right) sin\left(\omega y\right)\sin \left(\omega z\right)<+T$ where         $\omega =2\pi /L$ $L$ is the unit cell length. A decrease in the unit cell length means generally an increase in the energy absorbed since the enhancement related to the increase the plateau strength is generally higher than the lowering effect correlated with a lower densification strain $({\epsilon }_{d0}\downarrow )$ [220,223,224]. T is the cell iso-value. An increase in T will result in an intensification in the rigidity of the architected structure and compressive properties [197]. Thes iso-value effect starts to be more pronounced as the unit base cell length increases [223].	Stress–strain curves [220].
TPMS Diamond Skeletal	$\cos \left(\omega x\right) cos\left(\omega y\right)\cos \left(\omega z\right)-\sin \left(\omega x\right) sin\left(\omega y\right)\sin \left(\omega z\right)>+T$          $\cos \left(\omega x\right) cos\left(\omega y\right)\cos \left(\omega z\right)-\sin \left(\omega x\right) sin\left(\omega y\right)\sin \left(\omega z\right)<-T$ where         $\omega =2\pi /L$ $L$ is the unit cell length. Same consideration valid for the sheet TPMS Diamond. In the case of Skeletal diamond, bigger cells are characterized by the appearance of a certain fluctuation in the initial stage of the plateau region since structural elements of the base cell are more prone to collapse instability [220]. T is the cell iso-value. Some issues already discussed for TPMS Diamond Sheet.
TPMS Primitive Sheet	$-T<\mathit{cos}\left(\omega x\right)\mathit{cos}\left(\omega y\right)\mathit{cos}\left(\omega z\right)<+T$ where         $\omega =2\pi /L$ $L$ is the unit cell length. Unlike the other architectures, it has been demonstrated that smaller cells $(L\downarrow )$ show more compliance and tend to collapse before larger cells [225]. T is the cell iso-value. An increase in the cell iso-value will result in an increase in metamaterial stiffness, yield stress and plateau stress and a lowering in the densification strain [226]. Designers should always aim to the right trade off to obtain the best performance given a certain circumstance.	Stress–strain curves [226].
TPMS Primitive Skeletal	$\mathit{cos}\left(\omega x\right)\mathit{cos}\left(\omega y\right)\mathit{cos}\left(\omega z\right)>+T$         $\mathit{cos}\left(\omega x\right)\mathit{cos}\left(\omega y\right)\mathit{cos}\left(\omega z\right)<-T$ where         $\omega =2\pi /L$ $L$ is the unit cell length. An increase in base cell dimension will produce an increase in elastic modulus, yield stress and plateau stress of the metamaterial [227]. T is the cell iso-value. No data has been found in the literature discussing this topic. Surely, researchers around the world will fix this gap in the next years.	Stress–strain curves [228].

Table 6 differs slightly from Table 5 because TPMS structures are defined by a mathematical equation involving the definition of a mean zero curvature surface from which the sheet and skeletal architectures are obtained. Specifically, the two types of architecture are defined by how space is filled in relation to an offset region obtained from the original surface. Adding material inside the offset region generates a sheet architecture, while adding material outside generates a skeletal architecture [229]. The behavior of the TPMS structure is a topic of ongoing discussion: some scientists argue that the sheet-based structure exhibits stretch-dominated behavior, while the skeletal structure exhibits bend-dominated behavior [220]. Other scientists claim the opposite [226]. This review will present the former approach, as the authors found it to be more compelling. It should be noted that Table 5 and Table 6 do not only show data relating to the metallic base material. Such data has been included to demonstrate that prototype structures can be 3D-printed in polymeric material to gain an initial understanding of how the base cell (and, more generally, geometry) affects the stress–strain response. Therefore, initial validation of the mesoscopic response can be performed to determine whether the designed structure is suitable for a given application. Some qualitative properties of the metamaterial can be obtained from the curve. Between the peaks, stress oscillation in the plateau region is of fundamental importance: when it comes to impact phenomena, it is important not only to design metamaterials that can absorb a certain amount of energy, but also to ensure that the transmitted force remains below a certain threshold to avoid damaging protected objects or people. To illustrate this concept, 2D cellular architectures, as shown in Figure 8, are used as an example [230].

It is important to note that 2D cells with part of their geometry parallel to the direction of the uniaxial compressive load become unstable, creating peaks and valleys in the plateau area. The number of peaks corresponds to the number of rows in the cellular arrangement. Each peak can be considered a stress impulse that will be transmitted to any objects or persons that need to be protected during impact phenomena [230]. Therefore, they are acceptable, provided that they exhibit an intensity that is sufficiently low to be harmless. In quantitative terms, the choice of base cell and its parametrization is strictly correlated with certain parameters, from which the different mechanical responses of the designed architecture can be deduced.

Mechanical metamaterials for energy absorption systems can analyzed by the following aspects:

• RD (relative density): Relative density is defined as the density of the cellular specimen on the density of its bulk counterpart (as expressed in Equation (9)) and it is a measure of the level of porosity of the metamaterial investigated [50,133,223]:

  $$RD={\displaystyle \frac{{\rho }_{MM}}{{\rho }_S}}={\displaystyle \frac{\frac{m_{specimen}}{V_{bulk}}}{\frac{m_{bulk}}{V_{bulk}}}}={\displaystyle \frac{m_{specimen}}{m_{bulk}}}$$

  (9)

  where ${\rho }_{MM}$ is the metamaterial density, ${\rho }_S$ is the base material density, $m_{specimen}$ is the metamaterial mass, $m_{bulk}$ is the base material bulk volume mass, and $V_{bulk}$ is the volume of the equivalent bulk related to the metamaterial.
• E_MM (mechanical metamaterial elastic modulus): Elastic modulus can be calculated by first approximation, as shown in Equations (1) and (3), but the use of these formula needs the determination of C constant. For new structures, most of the time, E_MM is determined experimentally by identifying the linear relation characterizing the pre-collapse stage of the metamaterial stress strain curve (Figure 5).
• ${\sigma }_{Y_{MM}}$ (mechanical metamaterial yield strength): As can be clearly seen in Figure 5, the yield strength is a fundamental parameter. This parameter can be calculated combining Equations (2) and (4), but it is generally defined by an experimental test, as shown in the literature [231,232].
• ${\sigma }_{pl}$ (mechanical metamaterial mean plateau stress): The mean plateau stress can be considered to be a measure of the metamaterial capacity to absorb large amount of energy. Indeed, it is evident that an increase in plateau stress invariably leads to an increase in energy absorption if the deformation remains constant; hence, a high mean plateau stress is a good quantitative indicator of a good capacity to absorb energy, and can be calculated as shown in Equation (10) [50]:

  $${\sigma }_{pl}={\displaystyle \frac{U_{pl}}{{\epsilon }_{d0}-{\epsilon }_{c0}}}$$

  (10)

  where $U_{pl}$ is the plastic energy absorbed by the sample in the plateau stage (presented in Equation (5)), while ε_d0 and ε_c0 correspond to the onset densification strain and the collapse initiation strain, respectively (Figure 5a).
• SEA (Specific Energy Absorption) is a criterion used to measure the energy absorbed ($U_{pl}$) by each unit of mass. It is an essential indicator of the ability of structures to absorb energy and determine the efficiency of a certain architecture. This factor has a significant influence on the performance-to-weight ratio and is the main parameter considered for applications in which weight reduction is essential, such as the aerospace sector, defense, and motorsports. SEA can be calculated using the mathematical equation expressed in Equation (11) [17,233]:

  $$SEA={\displaystyle \frac{U_{pl}}{{\rho }_{MM}}}$$

  (11)

  where $U_{pl}$ is the plastic energy absorbed by the sample in the plateau stage (presented in Equation (5)) and ${\rho }_{MM}$ is the metamaterial density.

Table 7 summarizes the behavior of different base cells and materials according to the aforementioned parameters. Furthermore, the same base cell with different materials is presented in Table 7 to clarify the mechanical properties of certain structures. This is to enable the design of the best possible mechanical metamaterial for energy absorption systems for a defined application. To complement the quantitative analysis of metamaterials for energy absorption, Figure 9 illustrates the properties that characterize two-dimensional cellular architectures [234].

Table 7. Comparison of the main mechanical properties for energy absorption structures based on different base material, cell topologies, and relative density.

Base Material	Base Material HT	Base Cell	Base Cell Relative Density (RD)	EMM (GPa)	${\mathit{\sigma }}_{{\mathit{Y}}_{\mathit{M}\mathit{M}}}$ (MPa)	${\mathit{\sigma }}_{\mathit{p}\mathit{l}}$ (MPa)	$\mathit{SEA}\left(\frac{\mathbf{k}\mathbf{J}}{\mathbf{k}\mathbf{g}}\right)$	Strain Rate	Ref.
β-Ti5553	Stress relieve annealing in tube vacuumed furnace backfilled with Argon (300 °C-1 h)	Octet truss	6.64%	/	/	17.5	32	0.001${\mathrm{s}}^{-1}$	[70]
Ti6Al4V	as-built state	Rhombic Dodecahedron	12.9%	0.346	15.87	10.7	12.96	0.001 ${\mathrm{s}}^{-1}$	[235]
		Rhombic Dodecahedron	16.4%	0.247	13.27	11.1	11.34
	as-built state	Octet truss	1.4%	/	/	/	10.27	1000 ${\mathrm{s}}^{-1}$	[236]
		Octet truss	5.7%	/	/	/	3.47
		Octet truss	12.7%	/	/	/	3.23
	as-built state	Gyroid sheet	65%	7.6 ± 0.6	/	375.3 ± 7.7	33.12	0.001 ${\mathrm{s}}^{-1}$	[237]
		Primitive sheet	65%	6.4 ± 0.2	/	260.9 ± 3.3	23.71
		BCC	65%	4.7 ± 0.1	/	185.9 ± 8.4	17.85
	Heat treated at 950 °C × 2 h + furnace cooling	Gyroid sheet	65%	7.5 ± 0.4	/	389.3 ± 2.8	51.02
		Primitive sheet	65%	6.7 ± 0.3	/	250.7 ± 6.5	41.53
		BCC	65%	4.8 ± 0.1	/	222.4 ± 4.1	28.97
	as-built state	BCC	11.9%	0.924	/	/	5	1000 ${\mathrm{s}}^{-1}$	[238]
		FCC	26.2%	6.779	/	/	11
	as-built state	FCCZ	12.4%	/	/	/	22.1	0.001 ${\mathrm{s}}^{-1}$	[239]
	Heat treated at 950 °C × 2 h + furnace cooling	FCCZ	12.4%	/	/	/	16.9	0.001 ${\mathrm{s}}^{-1}$
		FCCZ	12.4%	/	/	/	18.84	1 ${\mathrm{s}}^{-1}$
		FCCZ	12.4%	/	/	/	24.6	312.5 ${\mathrm{s}}^{-1}$
	Stress relieve annealing (820 °C × 2 h air environment + air cooling)	Gyroid sheet	54%	8.46 ± 0.43	181 ± 3	/	/	0.001 ${\mathrm{s}}^{-1}$	[240]
		Gyroid sheet	62%	6.81	108	/	/
		Gyroid sheet	67%	5.69	94	/	/
		Diamond Sheet	52.7%	10.22 ± 0.31	199 ± 3	/	/
		Diamond Sheet	56.4%	9.37	159	/	/
		Diamond Sheet	62.2%	7.59	134	/	/
	Heat treated 800 °C × 2 h in vacuum furnace	Gyroid sheet	10%	2.015 ± 0.1	49.689 ± 0.2	/	74.11	0.001 ${\mathrm{s}}^{-1}$	[241]
		Gyroid sheet	20%	4.146 ± 0.02	117.940 ± 4.0	/	75.49
		Gyroid sheet	30%	5.301 ± 0.1	222.411 ± 3.4	/	62.87
		Gyroid sheet	40%	6.083 ± 0.02	335.597 ± 2.9	/	103.68
		Gyroid sheet	50%	6.471 ± 0.004	494.397 ± 2.9	/	28.94
AlSi10Mg	as-built state	FCC	27.25%	/	37.4	/	3.26	750 ${\mathrm{s}}^{-1}$	[242]
		FCC	27.25%	/	37.59	/	3.43	1100 ${\mathrm{s}}^{-1}$
	as-built state	Rhombic Dodecahedron	19%	/	/	7.97	15.79	0.001${\mathrm{s}}^{-1}$	[243]
		Rhombic Dodecahedron	19%	/	/	10.49	13.40	806 ${\mathrm{s}}^{-1}$
	as-built state	Octet truss	20%	1.2 ± 0.02	/	26.55 ± 2.65	31.59	0.001 ${\mathrm{s}}^{-1}$	[244]
		Octet truss	30%	1.6 ± 0.02	/	49.07 ± 2.76	30.89
		Octet truss	40%	2.79 ± 0.04	/	74.31 ± 12.89	30.03
		Octet truss	50%	3.26 ± 0.01	/	122.91 ± 2.44	36.78
	as-built state	BCC	20%	1.23 ± 0.04	/	29.49 ± 0.38	27.96
		BCC	30%	1.58 ± 0.02	/	48.67 ± 5.5	27.37
		BCC	40%	2.76 ± 0.03	/	68.79 ± 13.6	35.86
		BCC	50%	3.24 ± 0.04	/	109.84 ± 2.35	49.17
	as-built state	Gyroid Sheet	20%	1.22 ± 0.01	/	27.38 ± 0.99	59.57
		Gyroid Sheet	30%	1.52 ± 0.04	/	61.77 ± 6.26	59.05
		Gyroid Sheet	40%	2.47 ± 0.02	/	86.03 ± 0.61	51.44
		Gyroid Sheet	50%	3.00 ± 0.03	/	130.31 ± 2.2	59.12
	Solution heat treatment (525 °C × 2 h) + water cooling + artificial aging (175 °C × 8 h) + water cooling	Gyroid Sheet	35%	/	/	64.27	32.91	0.001 ${\mathrm{s}}^{-1}$	[245]
		Gyroid Skeletal	35%	/	/	36.27	18.55
		Diamond Sheet	35%	/	/	73.44	37.54
		Diamond Skeletal	35%	/	/	44.55	22.82
	as-built state	Gyroid sheet	14.3%	/	/	/	11.89	140 ${\mathrm{s}}^{-1}$	[215]
	as-built state	BCCZ	15.4%	0.389	20.22	/	3.01	0.001 ${\mathrm{s}}^{-1}$	[246]
	Solution heat treatment (460 × 2 h) + water quenching	BCCZ	15.4%	0.208	11.93	/	14.67
	Solution heat treatment (500 × 2 h) + water quenching	BCCZ	15.4%	0.225	14.30	/	17.15
	Solution heat treatment (540 × 2 h) + water quenching	BCCZ	15.4%	0.239	14.59	/	16.87
	Solution heat treatment (460 × 2 h) + water quenching + artificial aging (180 °C × 6 h) + water quenching	BCCZ	15.4%	0.225	12.46	/	15.59
	Solution heat treatment (500 × 2 h) + water quenching + artificial aging (180 °C × 6 h) + water quenching	BCCZ	15.4%	0.351	17.11	/	12.37
	Solution heat treatment (540 × 2 h) + water quenching + artificial aging (180 °C × 6 h) + water quenching	BCCZ	15.4%	0.339	17.57	/	11.26
	Stress relieve annealing (300 °C × 2 h in vacuumed furnace)	Gyroid Sheet	30%	0.997	58.75	/	15.22	0.001 ${\mathrm{s}}^{-1}$	[247]
		Gyroid Sheet	50%	1.189	77.78	/	19.63
		Diamond Sheet	30%	1.046	64.69	/	16.74
		Diamond Sheet	50%	1.431	84.58	/	23.42
		Primitive Sheet	30%	0.832	54.63	/	7.33
		Primitive sheet	50%	1.302	79.49	/	14.5
AISI 316L	Heat treated at 900 °C × 2–4 h in a vacuumed furnace filled with Ar+ furnace cooling	Rhombic Dodecahedron	5%	0.045	0.92	/	1.15	0.001 ${\mathrm{s}}^{-1}$	[248]
		Octet truss	5%	0.121	1.98	/	1.93
	as-built state	Octet truss	20.2%	7.43	29.09	/	6.24	0.001 ${\mathrm{s}}^{-1}$	[249]
		Octet truss	31.8%	13.57	47.10	/	8.06
		Octet truss	5%	0.747	/	5.68	4.08	0.001 ${\mathrm{s}}^{-1}$ (+25% at 1000 ${\mathrm{s}}^{-1}$)	[200]
		Octet truss	10%	2.01	/	13.68	4.94
		Octet truss	20%	12.52	/	42.19	7.82
		Octet truss	30%	13.50	/	82.67	10.26
		Octet truss	40%	18.36	/	130.28	12.22
		Octet truss	50%	23.00	/	192.20	17.84
		BCC	10.57%	0.132	3.86 ± 0.75	4.61 ± 0.57	0.14	220 ${\mathrm{s}}^{-1}$	[250]
		BCCZ	11.93%	0.562	11.36 ± 0.36	11.08 ± 0.31	0.26
		FCC	8.71%	0.319	7.02 ± 0.31	7.31 ± 0.46	0.30
		FCCZ	9.93%	0.776	16.64 ± 1.02	15.44 ± 1.11	0.49
		FCCZ	12.4%	/	/	/	15.4	0.001 ${\mathrm{s}}^{-1}$	[239]
		SeG Miura (y)	30.7%	/	/	32.7	2.83	0.001 ${\mathrm{s}}^{-1}$	[210]
		SeG Miura (y)	18.9%	/	/	6.2	1.13
	as-built state	Octet truss	10%	0.982	29.54	/	4.78	0.001 ${\mathrm{s}}^{-1}$	[251]
		Octet truss	25%	3.019	98.62	/	9.86
		Gyroid Sheet	10%	1.104	32.92	/	7.44
		Gyroid Sheet	25%	3.365	122.01	/	13.15
		Gyroid Skeletal	10%	0.508	16.46	/	4.09
		Gyroid Skeletal	25%	2.373	98.14	/	9.40
		Diamond Sheet	10%	2.026	38.04	/	8.94
		Diamond Sheet	25%	3.261	136.10	/	14.43
		Diamond Skeletal	10%	0.373	8.23	/	0.70
		Diamond Skeletal	25%	2.867	100.47	/	6.41
		Primitive Sheet	10%	0.961	24.10	/	5.48
		Primitive Sheet	25%	3.185	122.26	/	13.14
	as-built state	Gyroid Sheet	36%	/	88.71	145.46	31.41	0.001 ${\mathrm{s}}^{-1}$	[252]
		Gyroid Sheet	36%	/	161.66	176.41	37.65	2000 ${\mathrm{s}}^{-1}$
		Gyroid Sheet	36%	/	190.37	203.56	41.31	3000 ${\mathrm{s}}^{-1}$
		Gyroid Sheet	36%	/	216.68	248.82	47.05	4000 ${\mathrm{s}}^{-1}$
CpTi	as-built state	Gyroid Sheet	35.52%	/	79.73 ± 2.7	/	17.5 ± 2.3	0.001 ${\mathrm{s}}^{-1}$	[253]
Scalmalloy®	as-built state	BCC	1.26%	/	4.43	/	5.87	75 ${\mathrm{s}}^{-1}$	[254]
		BCC	1.20%	/	4.7	/	8.85	1393 ${\mathrm{s}}^{-1}$
		BCC	0.924%	/	3.44	/	7.04	3000 ${\mathrm{s}}^{-1}$
		BCCZ	0.905%	/	4.19	/	7.78	1393 ${\mathrm{s}}^{-1}$
Ta	as-built state	BCC	20%	0.59	9.83	13.67	20.08	0.001 ${\mathrm{s}}^{-1}$	[255]
		Gyroid Skeletal	15%	1.114	18.8 ± 0.6	25.7 ± 0.7	6.29	0.001 ${\mathrm{s}}^{-1}$	[256]
		Rhombic dodecahedron	30%	1.78 ± 0.11	44.4 ± 2.53	/	4.33	0.001 ${\mathrm{s}}^{-1}$	[257]
Inconel 625	as-built state	BCC	12.3%	0.493	7.28	/	8.48	0.001 ${\mathrm{s}}^{-1}$	[258]
			5.7%	0.056	1.64	/	3.09
			3.3%	0.026	0.50	/	1.85
		BCCZ	13.8%	0.836	16.94	/	17.1
			6.4%	0.640	4.07	/	5.66
			3.6%	0.393	1.85	/	3.14
		FCC	9.5%	0.702	8.89	/	12.2
			4.4%	0.156	2.15	/	4.97
			2.5%	0.052	0.86	/	3.01
		FCCZ	10.4%	1.130	16.97	/	17.8
			4.8%	0.719	4.83	/	7.37
			2.9%	0.498	2.15	/	4.17

Table 7. Comparison of the main mechanical properties for energy absorption structures based on different base material, cell topologies, and relative density.

Base Material	Base Material HT	Base Cell	Base Cell Relative Density (RD)	EMM (GPa)	${\mathit{\sigma }}_{{\mathit{Y}}_{\mathit{M}\mathit{M}}}$ (MPa)	${\mathit{\sigma }}_{\mathit{p}\mathit{l}}$ (MPa)	$\mathit{SEA}\left(\frac{\mathbf{k}\mathbf{J}}{\mathbf{k}\mathbf{g}}\right)$	Strain Rate	Ref.
β-Ti5553	Stress relieve annealing in tube vacuumed furnace backfilled with Argon (300 °C-1 h)	Octet truss	6.64%	/	/	17.5	32	0.001${\mathrm{s}}^{-1}$	[70]
Ti6Al4V	as-built state	Rhombic Dodecahedron	12.9%	0.346	15.87	10.7	12.96	0.001 ${\mathrm{s}}^{-1}$	[235]
		Rhombic Dodecahedron	16.4%	0.247	13.27	11.1	11.34
	as-built state	Octet truss	1.4%	/	/	/	10.27	1000 ${\mathrm{s}}^{-1}$	[236]
		Octet truss	5.7%	/	/	/	3.47
		Octet truss	12.7%	/	/	/	3.23
	as-built state	Gyroid sheet	65%	7.6 ± 0.6	/	375.3 ± 7.7	33.12	0.001 ${\mathrm{s}}^{-1}$	[237]
		Primitive sheet	65%	6.4 ± 0.2	/	260.9 ± 3.3	23.71
		BCC	65%	4.7 ± 0.1	/	185.9 ± 8.4	17.85
	Heat treated at 950 °C × 2 h + furnace cooling	Gyroid sheet	65%	7.5 ± 0.4	/	389.3 ± 2.8	51.02
		Primitive sheet	65%	6.7 ± 0.3	/	250.7 ± 6.5	41.53
		BCC	65%	4.8 ± 0.1	/	222.4 ± 4.1	28.97
	as-built state	BCC	11.9%	0.924	/	/	5	1000 ${\mathrm{s}}^{-1}$	[238]
		FCC	26.2%	6.779	/	/	11
	as-built state	FCCZ	12.4%	/	/	/	22.1	0.001 ${\mathrm{s}}^{-1}$	[239]
	Heat treated at 950 °C × 2 h + furnace cooling	FCCZ	12.4%	/	/	/	16.9	0.001 ${\mathrm{s}}^{-1}$
		FCCZ	12.4%	/	/	/	18.84	1 ${\mathrm{s}}^{-1}$
		FCCZ	12.4%	/	/	/	24.6	312.5 ${\mathrm{s}}^{-1}$
	Stress relieve annealing (820 °C × 2 h air environment + air cooling)	Gyroid sheet	54%	8.46 ± 0.43	181 ± 3	/	/	0.001 ${\mathrm{s}}^{-1}$	[240]
		Gyroid sheet	62%	6.81	108	/	/
		Gyroid sheet	67%	5.69	94	/	/
		Diamond Sheet	52.7%	10.22 ± 0.31	199 ± 3	/	/
		Diamond Sheet	56.4%	9.37	159	/	/
		Diamond Sheet	62.2%	7.59	134	/	/
	Heat treated 800 °C × 2 h in vacuum furnace	Gyroid sheet	10%	2.015 ± 0.1	49.689 ± 0.2	/	74.11	0.001 ${\mathrm{s}}^{-1}$	[241]
		Gyroid sheet	20%	4.146 ± 0.02	117.940 ± 4.0	/	75.49
		Gyroid sheet	30%	5.301 ± 0.1	222.411 ± 3.4	/	62.87
		Gyroid sheet	40%	6.083 ± 0.02	335.597 ± 2.9	/	103.68
		Gyroid sheet	50%	6.471 ± 0.004	494.397 ± 2.9	/	28.94
AlSi10Mg	as-built state	FCC	27.25%	/	37.4	/	3.26	750 ${\mathrm{s}}^{-1}$	[242]
		FCC	27.25%	/	37.59	/	3.43	1100 ${\mathrm{s}}^{-1}$
	as-built state	Rhombic Dodecahedron	19%	/	/	7.97	15.79	0.001${\mathrm{s}}^{-1}$	[243]
		Rhombic Dodecahedron	19%	/	/	10.49	13.40	806 ${\mathrm{s}}^{-1}$
	as-built state	Octet truss	20%	1.2 ± 0.02	/	26.55 ± 2.65	31.59	0.001 ${\mathrm{s}}^{-1}$	[244]
		Octet truss	30%	1.6 ± 0.02	/	49.07 ± 2.76	30.89
		Octet truss	40%	2.79 ± 0.04	/	74.31 ± 12.89	30.03
		Octet truss	50%	3.26 ± 0.01	/	122.91 ± 2.44	36.78
	as-built state	BCC	20%	1.23 ± 0.04	/	29.49 ± 0.38	27.96
		BCC	30%	1.58 ± 0.02	/	48.67 ± 5.5	27.37
		BCC	40%	2.76 ± 0.03	/	68.79 ± 13.6	35.86
		BCC	50%	3.24 ± 0.04	/	109.84 ± 2.35	49.17
	as-built state	Gyroid Sheet	20%	1.22 ± 0.01	/	27.38 ± 0.99	59.57
		Gyroid Sheet	30%	1.52 ± 0.04	/	61.77 ± 6.26	59.05
		Gyroid Sheet	40%	2.47 ± 0.02	/	86.03 ± 0.61	51.44
		Gyroid Sheet	50%	3.00 ± 0.03	/	130.31 ± 2.2	59.12
	Solution heat treatment (525 °C × 2 h) + water cooling + artificial aging (175 °C × 8 h) + water cooling	Gyroid Sheet	35%	/	/	64.27	32.91	0.001 ${\mathrm{s}}^{-1}$	[245]
		Gyroid Skeletal	35%	/	/	36.27	18.55
		Diamond Sheet	35%	/	/	73.44	37.54
		Diamond Skeletal	35%	/	/	44.55	22.82
	as-built state	Gyroid sheet	14.3%	/	/	/	11.89	140 ${\mathrm{s}}^{-1}$	[215]
	as-built state	BCCZ	15.4%	0.389	20.22	/	3.01	0.001 ${\mathrm{s}}^{-1}$	[246]
	Solution heat treatment (460 × 2 h) + water quenching	BCCZ	15.4%	0.208	11.93	/	14.67
	Solution heat treatment (500 × 2 h) + water quenching	BCCZ	15.4%	0.225	14.30	/	17.15
	Solution heat treatment (540 × 2 h) + water quenching	BCCZ	15.4%	0.239	14.59	/	16.87
	Solution heat treatment (460 × 2 h) + water quenching + artificial aging (180 °C × 6 h) + water quenching	BCCZ	15.4%	0.225	12.46	/	15.59
	Solution heat treatment (500 × 2 h) + water quenching + artificial aging (180 °C × 6 h) + water quenching	BCCZ	15.4%	0.351	17.11	/	12.37
	Solution heat treatment (540 × 2 h) + water quenching + artificial aging (180 °C × 6 h) + water quenching	BCCZ	15.4%	0.339	17.57	/	11.26
	Stress relieve annealing (300 °C × 2 h in vacuumed furnace)	Gyroid Sheet	30%	0.997	58.75	/	15.22	0.001 ${\mathrm{s}}^{-1}$	[247]
		Gyroid Sheet	50%	1.189	77.78	/	19.63
		Diamond Sheet	30%	1.046	64.69	/	16.74
		Diamond Sheet	50%	1.431	84.58	/	23.42
		Primitive Sheet	30%	0.832	54.63	/	7.33
		Primitive sheet	50%	1.302	79.49	/	14.5
AISI 316L	Heat treated at 900 °C × 2–4 h in a vacuumed furnace filled with Ar+ furnace cooling	Rhombic Dodecahedron	5%	0.045	0.92	/	1.15	0.001 ${\mathrm{s}}^{-1}$	[248]
		Octet truss	5%	0.121	1.98	/	1.93
	as-built state	Octet truss	20.2%	7.43	29.09	/	6.24	0.001 ${\mathrm{s}}^{-1}$	[249]
		Octet truss	31.8%	13.57	47.10	/	8.06
		Octet truss	5%	0.747	/	5.68	4.08	0.001 ${\mathrm{s}}^{-1}$ (+25% at 1000 ${\mathrm{s}}^{-1}$)	[200]
		Octet truss	10%	2.01	/	13.68	4.94
		Octet truss	20%	12.52	/	42.19	7.82
		Octet truss	30%	13.50	/	82.67	10.26
		Octet truss	40%	18.36	/	130.28	12.22
		Octet truss	50%	23.00	/	192.20	17.84
		BCC	10.57%	0.132	3.86 ± 0.75	4.61 ± 0.57	0.14	220 ${\mathrm{s}}^{-1}$	[250]
		BCCZ	11.93%	0.562	11.36 ± 0.36	11.08 ± 0.31	0.26
		FCC	8.71%	0.319	7.02 ± 0.31	7.31 ± 0.46	0.30
		FCCZ	9.93%	0.776	16.64 ± 1.02	15.44 ± 1.11	0.49
		FCCZ	12.4%	/	/	/	15.4	0.001 ${\mathrm{s}}^{-1}$	[239]
		SeG Miura (y)	30.7%	/	/	32.7	2.83	0.001 ${\mathrm{s}}^{-1}$	[210]
		SeG Miura (y)	18.9%	/	/	6.2	1.13
	as-built state	Octet truss	10%	0.982	29.54	/	4.78	0.001 ${\mathrm{s}}^{-1}$	[251]
		Octet truss	25%	3.019	98.62	/	9.86
		Gyroid Sheet	10%	1.104	32.92	/	7.44
		Gyroid Sheet	25%	3.365	122.01	/	13.15
		Gyroid Skeletal	10%	0.508	16.46	/	4.09
		Gyroid Skeletal	25%	2.373	98.14	/	9.40
		Diamond Sheet	10%	2.026	38.04	/	8.94
		Diamond Sheet	25%	3.261	136.10	/	14.43
		Diamond Skeletal	10%	0.373	8.23	/	0.70
		Diamond Skeletal	25%	2.867	100.47	/	6.41
		Primitive Sheet	10%	0.961	24.10	/	5.48
		Primitive Sheet	25%	3.185	122.26	/	13.14
	as-built state	Gyroid Sheet	36%	/	88.71	145.46	31.41	0.001 ${\mathrm{s}}^{-1}$	[252]
		Gyroid Sheet	36%	/	161.66	176.41	37.65	2000 ${\mathrm{s}}^{-1}$
		Gyroid Sheet	36%	/	190.37	203.56	41.31	3000 ${\mathrm{s}}^{-1}$
		Gyroid Sheet	36%	/	216.68	248.82	47.05	4000 ${\mathrm{s}}^{-1}$
CpTi	as-built state	Gyroid Sheet	35.52%	/	79.73 ± 2.7	/	17.5 ± 2.3	0.001 ${\mathrm{s}}^{-1}$	[253]
Scalmalloy®	as-built state	BCC	1.26%	/	4.43	/	5.87	75 ${\mathrm{s}}^{-1}$	[254]
		BCC	1.20%	/	4.7	/	8.85	1393 ${\mathrm{s}}^{-1}$
		BCC	0.924%	/	3.44	/	7.04	3000 ${\mathrm{s}}^{-1}$
		BCCZ	0.905%	/	4.19	/	7.78	1393 ${\mathrm{s}}^{-1}$
Ta	as-built state	BCC	20%	0.59	9.83	13.67	20.08	0.001 ${\mathrm{s}}^{-1}$	[255]
		Gyroid Skeletal	15%	1.114	18.8 ± 0.6	25.7 ± 0.7	6.29	0.001 ${\mathrm{s}}^{-1}$	[256]
		Rhombic dodecahedron	30%	1.78 ± 0.11	44.4 ± 2.53	/	4.33	0.001 ${\mathrm{s}}^{-1}$	[257]
Inconel 625	as-built state	BCC	12.3%	0.493	7.28	/	8.48	0.001 ${\mathrm{s}}^{-1}$	[258]
			5.7%	0.056	1.64	/	3.09
			3.3%	0.026	0.50	/	1.85
		BCCZ	13.8%	0.836	16.94	/	17.1
			6.4%	0.640	4.07	/	5.66
			3.6%	0.393	1.85	/	3.14
		FCC	9.5%	0.702	8.89	/	12.2
			4.4%	0.156	2.15	/	4.97
			2.5%	0.052	0.86	/	3.01
		FCCZ	10.4%	1.130	16.97	/	17.8
			4.8%	0.719	4.83	/	7.37
			2.9%	0.498	2.15	/	4.17

4. Advanced Lattice Configuration to Enhance Energy Absorption

The following section will analyze the methodologies that can be implemented to improve the energy absorption of previously analyzed mechanical structural designs. The section is divided into three e sub-sections. The first focuses on optimizing the structural parameters of mechanical components, the second focuses on optimizing basic material properties using microstructural orientation texturing techniques, and the third approach examined metal composite structures to optimise their energy absorption capability.

4.1. Enhancement of Energy Absorption Through Optimization of Structural Elements

4.1.1. Structural Grading

The first attempts to produce a graded structure were performed to study the energy absorption performance of metallic foams. Analytical studies [263,264] highlighted that a graded architecture can positively influence both the peak stress reached during deformation (related to the maximum force transmitted to items that need to be protected) and the overall energy absorbed. However, the challenges associated with generating a foam that meets the specified nominal grading criteria [265], coupled with the modest performance enhancement observed, have led scientists to abandon this approach. The advent of additive manufacturing has sparked renewed interest in this option, as it enables the design of graded architectures with predictable mechanical behavior [266]. Various grading methodologies have been investigated and are presented in Figure 10.

Studies on foams and metamaterials based on the size of the bounding box of the base cell [264] have demonstrated that the mechanical performance of metamaterials is affected in different ways under dynamic shock loading.

Figure 10a–d shows the four different architectures investigated (impact end on the left side of the represented samples). The results show that all of the grading strategies are characterized by lower energy absorption than the uniform architecture. This behavior can be explained by the lower velocity discontinuity generated by the middle–low, middle–high, and negative architectures [155], whereas for the positive architecture, as in the quasi-static regime, it is due to the lower bearing capacity of the larger cells [266,267,268]. It should be noted that the performance of the positive grading architecture is only slightly lower than that of the uniform architecture. Furthermore, it demonstrated a significant decrease in the maximum stress achieved, offering the best compromise between energy absorption capability and maximum stress reduction, as also resulted from Panesar and Plocher’s work [269].

Studies on cellular materials performed by Karagozova et al. [263] concerning thickness grading demonstrated that positive grading (Figure 10g) is preferable to negative grading (Figure 10h) when load is applied along the grading direction. This conclusion is based on observations from analytical and finite element analyses showing an increase in transmitted force at the fixed end when negative grading is applied. Furthermore, positive grading is characterized by lower peak stress in the initial deformation stage. Since a higher density at the fixed end leads to larger stresses during wave reflection, graded mechanical metamaterials should be designed to prevent wave reflection and efficiently absorb energy within the primary compaction wave [50,263]. The resulting stress–strain response is characterized by a step-like plateau stage, where each step represents the crushing of cells within a specific thickness range [243,270,271,272]. The middle–low strategy (Figure 10e) further enhances the effectiveness of thickness grading by generating wider layers of the same thickness through a symmetrical density distribution [271]. In contrast, the middle–high strategy (Figure 10h) shows an increased risk of catastrophic failure or earlier onset densification, resulting in a lower energy absorption capacity [273]. When load is applied perpendicular to the grading direction, bend-dominated architectures demonstrate enhanced energy absorption properties compared to stretch-dominated ones. Applying load perpendicular to the grading direction enhances the energy absorption properties of bend-dominated architectures and stretch-dominated ones.

Starting from bend-dominated mechanical metamaterials, they exhibit similar deformation behavior but different stress concentrations (primarily distributed in cells characterized by lower relative densities) related to the uniform (non-graded) once [270]. This results in a certain difference in mechanical properties, which result in enhanced E_MM, ${\sigma }_{pl}$, and $SEA$, since the contribution to elastic modulus and mechanical strength is characterized by an exponential trend with respect to density (as can be seen from Equations (10) and (11)), although the contribution of each individual layer to the relative density is determined by a linear relationship [270]. Therefore, graded mechanical metamaterials can be designed to further enhance mechanical properties by applying the strongest grading approaches to increase the number of struts with a greater density while leaving the overall relative density unaltered.

Similarly to bend-dominated architectures, stretch-dominated architectures are characterized by higher stresses generated in their thicker structural elements under equivalent strain, which increases force absorption before failure and requires higher loads to achieve the same deformation [243,273]. This effect has a less prominent beneficial impact on stretch-dominated surface lattices, whereas it has a stronger effect on strut-based lattices. In stretch-dominated lattice structures, increasing the thickness reduces the slenderness ratio of the struts, thereby increasing the critical buckling load [273] and enhancing the strength and energy absorption capability of the metamaterial. It is worth mentioning that, with linear grading strategies, the results show that, in some cases, the improvements in energy absorption are not high enough to justify the increase in manufacturing complexity needed to fabricate non-uniform parts. Non-linear grading approaches have not yet been considered, but they could represent an interesting area of research to explore in the coming years (even though some preliminary studies have been conducted [274]).

The grading strategies discussed up to this point are applied to the entire specimen at a macro level and can be applied to all base cell architectures presented in previous chapters. Other strategies can be implemented at strut level [275,276,277].

4.1.2. Structural Hybridization

In addition to the use of functionally graded designs, many researchers have recently shifted their focus to the analysis of multi-topology energy absorption structures, leading to the rise in mechanical metamaterial hybridization. This approach has proven to be effective in tailoring lattice deformation and failure modes to enhance the specific properties of mechanical metamaterials [278]. These novel hybrid structures demonstrated high energy absorption with no significant damage, enhanced response to shock loading, and a triggered deformation generated by the different cells used and their parametrization [278,279,280]. After a careful literature analysis on hybridized structures, the authors concluded that these novel architectures can be categorized into two main hybridization strategies, as represented in Figure 11.

These categories are further described as follows:

• Base cell transition along the specimen: This approach is generated by describing a transition function between different base cell geometries [229,281,282]. Figure 11a,b shows two typical transitions in a hybrid mechanical metamaterial consisting of longitudinal-linear and radial hybridization functions. It has been demonstrated that, by selecting the appropriate cell arrangement and parametrization [278], a stable plateau can be achieved without stress jumps occurring, thereby enhancing the energy absorption capabilities. As demonstrated by Novak et al. [283], this behavior is related to the fact that deformation starts from the less stiff topology and then gradually propagates to the more rigid one, leading to greater energy absorption capacity related to un-hybridized structures. Lattice parameters during hybridization of different base cells along a certain direction must be properly tuned to avoid sudden failure in the transition-hybridization zone (HZ) [266,281,284,285,286]. One efficient way to overcome this issue is to tune the mass distribution using a sufficiently high relative density. Cell mismatch can be reduced by adjusting the shape and dimensions of the base cells [254,259,260] or by using a stochastic geometry generalization approach [127,287,288,289].
• Base cell topology hybridization: This approach involves combining two different topologies in a single architecture, as shown in Figure 11c [250]. It should be noted that cell topology hybridization affects the elastic modulus and stress wave dissipation and decreases base cell anisotropy. In particular, combining stretch- and bend-dominated architectures increases impact time and delays failure, enabling more energy to be absorbed during plastic deformation [130,290,291].

4.2. Optimizing the Properties of the Base Material by Fine-Tuning and Controlling the LPBF Process

Epitaxial growth is a characteristic phenomenon of additive manufacturing, since it is a thermodynamically favored condition during the process itself. The size and extension of the columnar grains formed during epitaxial growth are strictly interconnected with the thickness of the structural elements and the process parameters [292]. This is because the thermal history and partial remelting of the prior layer (which depend strictly on the thickness) generate a certain latent heat that affects the cooling rate and thermal dissipation vector of the newly melted material. Thick specimens are characterized by a higher latent heat due to the extensive reheating and remelting generated by their higher volume compared to thin specimens [292]. Grain growth in the Z direction remains higher than growth in the in-plane direction, since neighboring grains constrain growth in the XY direction [293]. The effective grain size used to predict material behavior can be expressed in the Z-direction as the length of the elongated grain, while the in-plane direction is considered the transverse dimension of the elongated grain. Therefore, based on the Hall–Patch relation [294], properties considered under a load parallel to the build plate exhibit higher values than properties considered under a load in the building direction.

Although thicker samples have higher thermal inertia, typical cooling rates in fusion-based additive manufacturing processes are high enough to generate residual stress due to constrained thermal strain/contraction during solidification. This phenomenon is responsible for the generation of Geometrically Necessary Dislocations (GNDs) [292,295], which can hinder dislocation motion, resulting in the higher strength of the base material and a certain loss of ductility. GNDs have been reported to be more prevalent in thinner structures due to their higher cooling rates [292,295], as shown in Figure 12a.

In recent years, a great deal of research effort has been dedicated to tuning the base material properties of additively manufactured parts during the printing process. The aim of this is to control both the generated structural geometry and the microstructure in order to obtain the most advanced and optimized properties from the generated architecture. Many approaches can be followed to achieve this, such as using nanoparticles to stabilize the solidification process and promote the formation of equiaxed grains [253], manipulating the solidification process through powder coating [296], and shaping the beam spatially by controlling the distribution of the heating source’s power density [297]. The latter solution was found to be particularly cost-effective and efficient for tuning base material properties.

The following laser beam shapes have been considered, besides the classical Gaussian sources:

• Bessel beam: Tumkur et al. [298,299] has demonstrated enhanced capabilities in create better surfaces and lower porosity. Moreover, this beam shape can be used to mitigate the intrinsic meltpool thermal gradient, creating a more uniform cooling rate and lower residual stress.
• Donut/ring beam: Many studies [297,300,301] demonstrated that using a donut shape laser beam increases the production window, allowing us to tune the cooling rate and temperature gradient such that equiaxed grain can be obtained rather than elongated one [302,303].

Therefore, it is clear that using a laser other than a Gaussian laser allows for better control of the microstructure, as shown in other studies [304,305,306,307]. One peculiar aspect is the ability to generate customized textures [66,297,308], which can improve mechanical and energy absorption performance, as demonstrated by Hazeli et al. [309,310]. Specifically, the research focused on how variations in cell topology, cell size, and microstructures influence performance. It was demonstrated that larger cells are more susceptible to microstructural changes due to their higher grain count [309]. Furthermore, specific base cells exhibit a non-strict dependence on microstructural changes, as their deformation is closely related to geometric effects such as buckling, node cracking, and macroscopic shear [309]. For mechanical metamaterials influenced by microstructural change, it was observed that a substantial enhancement in mechanical properties can be achieved by orienting the grains (texturing) within the structural element, optimizing their alignment with the applied load and increasing both yielding and post-yielding behavior [310], as shown in Figure 12b. It should be noted that the implementation of a specific texture does not invariably result in an enhancement of metamaterial properties. As illustrated in Figure 12b, the application of a cubic texture leads to an augmentation of energy absorption properties for the BCC cell [311]. However, applying the same texture to a cubic lattice structure (see Figure 12c) results in reduced energy absorption performance and increased isotropy [311]. The efficacy of this approach depends on the specific loading case scenario. If the expected load is applied in multiple directions, it is recommended that isotropy is obtained through texture-based cell optimization or metamaterial topology optimization.

Figure 12. (a) Effect of structural elemental dimensions and cooling rates on dislocation density in metamaterials (adapted from [295]): smaller struts are characterized by a higher dislocation density which increases the strength of the base material. (b) Cube-engineered texture effect on BCC base cell shows an increase in energy absorption performance obtained through optimized crystal structure orientation to the load from which a more efficient stress distribution is generated. (c) Cube-engineered texture effect on a cubic base cell metamaterial shows a small decrease in energy absorption performance, but an increase in isotropy of the structure (adapted from [312]).

Figure 12. (a) Effect of structural elemental dimensions and cooling rates on dislocation density in metamaterials (adapted from [295]): smaller struts are characterized by a higher dislocation density which increases the strength of the base material. (b) Cube-engineered texture effect on BCC base cell shows an increase in energy absorption performance obtained through optimized crystal structure orientation to the load from which a more efficient stress distribution is generated. (c) Cube-engineered texture effect on a cubic base cell metamaterial shows a small decrease in energy absorption performance, but an increase in isotropy of the structure (adapted from [312]).

4.3. Metal Porous Structures Saturated with Polymeric/Metallic Matrix: The Rise of Interpenetrating Phase Composites

Composites are a class of materials that can enhance the performance capabilities of standard, separate components. A well-known example is carbon-fiber-reinforced polymeric epoxy resin. In this case, the resin holds the carbon fibers together, enabling them to work efficiently and achieve optimized performance. The same principle can be applied to metamaterials for energy absorption systems. Here, the reinforcement is characterized by a printed metallic architecture. The matrix can be varied to achieve the desired performance and deformation behavior. This novel class of materials is known as an interpenetrating phase composite (IPC) and demonstrated exceptional performance despite a slight increase in weight [312]. These composite mechanical metamaterials are obtained by infiltration, whereby a polymeric or metallic matrix is melted in a preform containing the metallic reinforcement architecture. Depending on the viscosity of the matrix, the infiltration process can be assisted by positive/negative pressure [313,314,315], sonication [316], or centrifugal casting [317] to avoid the formation of gas pores. Regarding the metallic mechanical metamaterials produced by LPBF, two main classes of IPC can be distinguished: metal–polymer IPC (MP-IPC), and metal–metal IPC (MM-IPC).

Concerning MM-IPCs, different types of behaviors can be obtained depending on the crystallographic nature and mechanical performance of the matrix and reinforcement. While a significant enhancement in impact energy absorption performance has been highlighted in IPCs with the same crystallographic structure and different mechanical properties (i.e., Al matrix reinforced with AISI316L structures [318]), the best result is obtained while creating IPCs with brittle reinforcement and ductile matrix. This is the case of the W-reinforced Cu matrix [319,320], since copper enables load transfer and prevents catastrophic failures in W architectures by retaining the integrity of the structure, as shown in Figure 13a. These two behaviors combined allow for an increase of 20% in deformation to be withstood, leading to a significant increase in the specific energy absorbed. The metallurgical characteristics of the interface and the mechanical behavior of the IPC are not the main focus of this paper. However, it should be noted that the formation of intermetallic phases can improve energy absorption performance by creating an interpenetrating metallurgical structure at the interface, as demonstrated by the NiTi-Al IPC [321].

The fabrication of MP-IPCs is typically less complex than that of MM-IPCs, and the performance of the IPC still invariably exceeds that of its constituent elements when considered collectively, as well as when evaluated independently [322]. In particular, the difference in stiffness between the matrix and the reinforcement plays a pivotal role: concerning this, Novak et al. [323,324] demonstrated that a silicon infill is slightly effective in increasing the Specific Energy Absorption while an epoxy one is able to increase it by more than 30%, as shown in Figure 13b. Elastomeric infills are primarily used for dumping applications and are more effective with compliant metallic reinforcement [312]. Conversely, strong polymers are better suited to forming MP-IPC, where mechanical performance needs to be optimized. The optimal ratio of stiffness between the matrix and reinforcement, as well as the optimal volume fraction of matrix and reinforcement, varies depending on the type of material and architecture used in the fabrication of MP-IPC, and must be studied and identified for each case.

Figure 13. (a) Energy absorption increment in MM-IPC Cu-W. The effectiveness of the Cu matrix in holding the cracked W reinforcement and avoiding catastrophic failure is highlighted in green and yellow (adapted from [320]). Cracks form and propagate in W, but the W-Cu interphase remains solid and structurally strong. (b) Increase in energy absorption performance in MP-IPC composed of a 316L diamond structure infilled with epoxy resin (adapted from [324]).

Figure 13. (a) Energy absorption increment in MM-IPC Cu-W. The effectiveness of the Cu matrix in holding the cracked W reinforcement and avoiding catastrophic failure is highlighted in green and yellow (adapted from [320]). Cracks form and propagate in W, but the W-Cu interphase remains solid and structurally strong. (b) Increase in energy absorption performance in MP-IPC composed of a 316L diamond structure infilled with epoxy resin (adapted from [324]).

5. Summary and Future Outlook

Mechanical metamaterials for energy absorption are one of the main topics currently analyzed by researchers around the world. The scope of this review was to introduce readers to the field of LPBF-manufactured metal metamaterials by providing an overview of the stages involved in designing an optimized structure. This review provides an in-depth correlated analysis of the relationship between the base material and the topology, examining the ‘beyond’ and ‘in-between’ properties of metastructures. It offers a detailed understanding of the various root causes that contribute to specific mechanical behavior, as illustrated by the Ishikawa diagram in Figure 14.

Drawing on the extensive scientific literature analyzed concerning metals and alloys as base materials, as well as novel discoveries and numerical experimental analyses on mechanical metamaterials, the following conclusions can be drawn:

• Different metals and heat treatments can have a significant impact on the performance of metamaterials. A necessary compromise between strength and toughness is required to achieve a high level of energy absorption in the plateau region. LPBF allows for the laser shape, process parameters, and heat treatments to be tuned in order to adjust the microstructural topology and generate microstructural features that maximize energy absorption.
• The selection and parametrization of the base cell determine the geometric response of the designed absorption systems. The review defines three classes of metamaterial: beam-based, curved-surface lattice, and plane-surface lattice. These can be further differentiated by their inherent response to an applied load in bend- and stretch-dominated architectures. Bend-dominated architectures are particularly prone to deformation, but are characterized by lower crushing stress. In contrast, stretch-dominated architecture can bear a higher load, offering higher resistance at the expense of lower plasticity. This means that the plateau stage for these different topologies is completely different and can be optimized based on the application. All cell configurations can be improved further by applying advanced design strategies. Base cell grading and hybridization, as well as the generation of composite structures in which metallic mechanical metamaterials act as reinforcement, have been shown to effectively reduce peak load transfer and/or increase energy absorption effectively. Since its implementation in industrial contexts is relatively straightforward, IPC has been identified as the most robust option. However, it is important to note that its functionality can degrade at elevated temperatures. This is attributed to the delicate balance between the elastic moduli of the constituent components and the metals and polymers involved in the process. This balance can be disrupted, potentially leading to instability and material degradation at high temperatures. The processes of dislocation tuning and laser manipulation are of particular interest, as they facilitate the generation of microstructural features that can be directly obtained in as-built samples. The efficacy of the aforementioned structures has been demonstrated through their ability to enhance energy absorption and isotropy in specific structures, achieved by generating a tuned texture. Furthermore, the capacity to generate tuned textures in different regions of the metamaterial could, in the near future, result in a variety of mechanical responses depending on stress localization (fine tuning). Without adequate control, however, the process may be difficult to regulate and may not be fully developed or characterized. It is important to recognize that there is no superior methodology, as they are all inherently dependent on the materials used, the material base cell, and the applied load. Therefore, it is essential to thoroughly understand the environment in which metamaterials will be employed in order to achieve the desired performance. It is also possible to apply all of the methods simultaneously to achieve perfect, optimized performance.

It is therefore evident that identifying a compromise between strength and deformation, with a view to optimizing performance, remains the primary challenge in the design of metal structures for shock absorption. The ongoing enhancement of LPBF processes, the emergence of novel materials such as high-entropy alloys, and the conception of sophisticated, advanced frameworks are set to substantially improve shock absorption capabilities in the coming years.

The perspective offered by this work is not only valuable for academic research, but it also has the potential to inform the industrial field. Particularly valuable is the experience maturate in aerospace, in which the application of metallic metamaterials for energy absorption has been demonstrated to be effective in multiple design fields. Between them, satellite shielding from space debris and rover protections in the landing systems used in the Mars and lunar missions are noteworthy. Moreover, with the advent of space travel and recoverable vectors, crushable energy absorption systems could play a pivotal role both in assuring safety and increasing reliability in systems characterized by impulse loading. The importance of protection from impulse loading in future fission and fusion nuclear plants is well documented. The transient operation of these machines, coupled with the high environmental and pressure conditions to which the materials are exposed, necessitates the development of engineered structures capable of withstanding any potential events and ensuring optimal safety. The application of metamaterials, which has already become prevalent in the biomedical industry, is now receiving increased attention in the design of humanoid robotic and animal-like drones that operate in hazardous environments. In all of the aforementioned cases, it is imperative to ensure an adequate response to impulse loading in order to safeguard people, instrumentation, and advanced sensors. This is performed to guarantee the maximum survival rate, mission success, and extended operational lifespan.

In order to ensure the effective implementation of metallic metamaterials in industrial contexts, it is imperative that a comprehensive and profound understanding of the operational conditions under consideration is obtained. In order to ascertain whether metallic metamaterials can be considered an effective and cost-efficient solution within the given project constraints and performance criteria, it is imperative that a focused and precise perspective is maintained. This is attributable to the necessity of the manufacturing process, guaranteeing optimal quality, a requisite that is concomitant with the elevated expense typically associated with conventional processes. Currently, the LPBF process is the only production method capable of efficiently manufacturing metallic mechanical metamaterials offering the required dimensional tolerance and resolution at relatively low cost. However, issues that limit its printing volumes constrain its industrial scalability, resulting in protracted production times. Advancements in the production processes of laser powder direct energy deposition (LP-DED), wire arc additive manufacturing (WAAM), and molten metal deposition (MMD) will undoubtedly facilitate the large-scale production of shock-absorbing metamaterials in the near future. This will be achieved while ensuring optimal quality and reduced delivery times. It is important to note that these processes will be characterized by a different cooling rate of the metal during manufacture. This necessitates developing and investigating the implications of this at the material level, as well as investigating its effect on the performance of the final geometries. Nevertheless, all considerations relating to the properties derived purely from geometries remain valid and can be scaled for these processes.