Investigation of Energy-Absorbing Properties of a Bio-Inspired Structure

Numerous engineering applications require lightweight structures with excellent absorption capacity. The problem of obtaining such structures may be solved by nature and especially biological structures with such properties. The paper concerns an attempt to develop a new energy-absorbing material using a biomimetic approach. The lightweight structure investigated here is mimicking geometry of diatom shells, which are known to be optimized by nature in terms of the resistance to mechanical loading. The structures mimicking frustule of diatoms, retaining the similarity with the natural shell, were 3D printed and subjected to compression tests. As required, the bio-inspired structure deformed continuously with the increase in deformation force. Finite element analysis (FEA) was carried out to gain insight into the mechanism of damage of the samples mimicking diatoms shells. The experimental results showed a good agreement with the numerical results. The results are discussed in the context of further investigations which need to be conducted as well as possible applications in the energy absorbing structures.


Introduction
Nowadays, light materials are of high interest almost in every branch of industry. Examples of extensively researched materials of light specific weight include high closed porosity foams and open porosity percolated structures. In the case of foams, the metalbased one, especially metal matrix syntactic foams (MMSFs) have become more and more important due to their desired properties (high energy absorbing and damping capability and low density) as well as numerous perspective applications (e.g., automotive) [1][2][3][4][5][6].
A relatively new research line emerging recently is focused on filling out load-bearing elements with light constructs of specific morphology-see for example [7][8][9][10][11][12]. The direction of these experiment is strictly related to their (materials and structures) energyabsorption properties.
The crushing behavior of axially loaded square aluminum extrusions with aluminum foam filler has been investigated by Hanssen et al. [7]. The parameters which were considered by Authors were: loading condition, foam density, extrusion wall strength as well as extrusion wall thickness. The experimental data were used to develop design formulas in order to predict average crush forces for both quasi-static and dynamic loading conditions. Nevertheless, also numerical prediction of the crushing behavior of aluminum foam-filled columns, can be investigated [8]. The finite element modeling developed by Santosa et al., based on available experimental data, clearly showed that crush behavior of the foam-filled column may be correctly predicted. In turn, Toksoy et al. investigated the strengthening effect of commercially available polystyrene foam as a filler for Al tubes [9]. As a result, the existence of an interaction effect which appeared as increase in average crushing load for foam filled tubes, in comparison to results of investigations of the tube and the foam, has been separately confirmed. Further experiments of the mechanisms of interaction effect between the tube and foam has been conducted by Yamada et al. [10]. The internal structure of the foam samples during non-destructive straining was visualized using X-ray computed tomography (XCT). Obtained results showed that interaction effect between the tube and the foam essentially depended on the ratio of the mean crushing force of foam to that of the tube. Similar conclusions, that deformation of the foam-filled tubes is determined by the mean plateau force ratio of tubes to foams, have been obtained by Yang et al. [11]. Yu et al., in order to understand the effect of the foam core on the interaction and the energy absorption of foam-filled tubes, have conducted compressive tests of tubes filled with various cell sizes of Al foams [12]. Obtained results showed that deformation of the foam core is close to the overall deformation when the cell size is fine. Furthermore, the decrease in the cell size causes the increase in the interaction effect which leads to increase in the energy absorption of manufactured structures [12]. The conducted research shows that filling materials in, e.g., aluminum tubes, could effectively improve the deformation as well as absorption capacity of such structures.
The direction as well as efforts in recent studies are directed towards obtaining structures characterized by high crashworthiness and being lightweight at the same time. It seems that these two may compete between each other. However, in nature there is a wide variety of protective strategies developed by organisms which reveal complex structures with sophisticated mechanical properties [13,14]. One of the most studied structures in energy absorption applications, inspired by nature, is the honeycomb structure. Furthermore, the investigations conducted by Ha et al. (2019) showed that a bio-inspired honeycomb sandwich panel (BHSP), based on the microstructure of a woodpecker's beak, exhibits superior energy absorption capability in comparison to the conventional honeycomb sandwich panel [15]. Such properties are related to the wavy character of these structures. Authors investigated the influences of the wave amplitude, wave number as well as core thickness on the energy absorption performance of the BHSPs.
Nevertheless, several solutions based on biomimetic approach have been recently investigated. The mimicking of the coconut tree profile has been proposed by Ha et al. (2018) with the aim of enhancing the energy absorption, minimizing the initial peak crushing force as well as stabilizing the crushing process [16]. Obtained results showed that there were four modes of deformations, the initial peak force was significantly reduced and the undulation load-carrying capacity parameter was minimized. In 2020, Xiang and co-workers provide an effective guideline for designing a foam-filled energy absorber with high energy absorption efficiency mimicking the characteristics of the human skeleton [17]. The proposed structures revealed the higher energy absorption efficiency. Furthermore, the best combination of the filling, which ensures the expected results, was the increasing density of the foams from the inner to the outer tube. Except for the structure, the whole shape may also constitute a bio-inspiration of which a good example is construction of a deformation element in vehicles which absorbs energy in the case of lateral collisions based on diatom frustule (see [18]). The conducted compression tests revealed that the bioinspired crash pads performed better than their technical counterpart. The comprehensive overview of recent advanced in the development of bio-inspired structures for energy absorption applications has been presented by Ha and Lu (2020) [19].
To obtain such a structure, the overwhelming majority of scientists are using the technique of additive manufacturing (AM), which in recent years has become a hot topic. The main advantage of AM, from which arise others, is freedom of design as well as manufacturing. In combination with the increasing accessibility of the technology, honeycombs with dual-material structures [20], structural hierarchy [21][22][23] and graded density [24] may be fabricated. Nevertheless, nature is rich in structures-functionally graded cellular materials worth inspiration as well due to a relatively low-density with high strength, excellent energy absorption and thermal conductivity [25].
The aim of the present paper is to demonstrate a potential use in this context of bioinspired elements resembling the geometry of a shell of a diatom species Didymosphenia geminata [26,27]. Diatoms are ubiquitous microorganisms which are distinguished by unique and highly ornamented frustules (see Figure 1) made of organic silica, with a size which ranges from 2 µm to 5.6 mm [28]. These frustules are known to exhibit a high resistance to mechanical loading-see for example [29][30][31][32]. Since organic silica as such is not considered a high strength material, one may expect that the outstanding resistance to compression of frustules stems from their intricate morphology. Thus in the current research an attempt has been made to verify the possibility of using replication of unique morphology of one of the diatom species in 3D-printed metallic counterparts ("enlarged frustule") as light-high-strength fillers. This objective was fulfilled by compression tests of the print-outs. Additionally, Finite Element analysis of the compression tests was carried out.

Materials
The diatom species which we used in the present case was Didymosphenia geminata ( Figure 1). The structure of its shell was firstly nondestructively visualized using nano X-ray computed tomography (nano-XCT) and transferred into a CAD file which was used as the input for an additive manufacturing technique (3D Selective Laser Melting, SLM). The enlarged counterparts of the nano-XCT visualized frustule were fabricated using spherical CP Ti (Grade 1) powder with a diameter smaller than 45 µm employing a Realizer SLM50 desktop 3D printer (Realizar GmbH, Borchen, Germany). The entire process of obtaining an engineered object has been published in Zglobicka et al. (2019) [27]. The self-similarity of the natural and the engineered objects was demonstrated using X-ray computed tomography (nano-XCT for the diatom frustule and micro-XCT for the engineered Ti object) (see [27]). Dimensions of the printed enlarged-frustule constructs are given in Table 1. geminata [26,27]. Diatoms are ubiquitous microorganisms which are distinguished by unique and highly ornamented frustules (see Figure1) made of organic silica, with a size which ranges from 2 µ m to 5.6 mm [28]. These frustules are known to exhibit a high resistance to mechanical loading-see for example [29][30][31][32]. Since organic silica as such is not considered a high strength material, one may expect that the outstanding resistance to compression of frustules stems from their intricate morphology. Thus in the current research an attempt has been made to verify the possibility of using replication of unique morphology of one of the diatom species in 3D-printed metallic counterparts ("enlarged frustule") as light-high-strength fillers. This objective was fulfilled by compression tests of the print-outs. Additionally, Finite Element analysis of the compression tests was carried out.

Materials
The diatom species which we used in the present case was Didymosphenia geminata ( Figure 1). The structure of its shell was firstly nondestructively visualized using nano Xray computed tomography (nano-XCT) and transferred into a CAD file which was used as the input for an additive manufacturing technique (3D Selective Laser Melting, SLM). The enlarged counterparts of the nano-XCT visualized frustule were fabricated using spherical CP Ti (Grade 1) powder with a diameter smaller than 45 µ m employing a Realizer SLM50 desktop 3D printer (Realizar GmbH, Borchen, Germany). The entire process of obtaining an engineered object has been published in Zglobicka et al. (2019) [27]. The self-similarity of the natural and the engineered objects was demonstrated using X-ray computed tomography (nano-XCT for the diatom frustule and micro-XCT for the engineered Ti object) (see [27]). Dimensions of the printed enlarged-frustule constructs are given in

Methods
Light Microscopy of the printed, engineered object based on the design of frustule of D. geminata. The printed objects were observed using a TAGARNO Prestige digital microscope (Denmark) equipped with objective lenses in the M Plan Apo 10x phase in light microscopy modus. Scanning Electron Microscopy images of the cross sections of printed frustules were obtained using an ultra-high-resolution analytical dual-beam FIB-SEM tool

Methods
Light Microscopy of the printed, engineered object based on the design of frustule of D. geminata. The printed objects were observed using a TAGARNO Prestige digital microscope (Denmark) equipped with objective lenses in the M Plan Apo 10x phase in light microscopy modus. Scanning Electron Microscopy images of the cross sections of printed frustules were obtained using an ultra-high-resolution analytical dual-beam FIB-SEM tool (Scios2 DualBeam, Thermo Fisher Scientific, Waltham, MA, USA) using acceleration voltages of 2 kV for the electrons. During observations, magnifications of 100x and 200x were used.
Compression tests of the printed, engineered object based on the design of a frustule of D. geminata were carried out. Experimental tests were conducted at room temperature with a test machine from MTS Insight Material Testing Systems with an axial loading range ±1 kN and stepless speed control. The applied rate of specimen displacement was l = 0.1 (mm/s).
Finite Element Analysis (FEA) of compression tests of the printed, engineered object was performed using SpaceClaim software (ANSYS Inc., Canonsburg, PA, USA). A 3D model of the ribbed surface was built based on the imported geometry, applying corrections to remove obvious imperfections of the imaging. This model was used to determine the equivalent mechanical properties of the ribbed part. In the modelling of the entire printed frustule, the ribbed part was described using equivalent mechanical properties. Simulations of the compression tests were carried out using bilinear stress-strain curves calculated based on the values for bulk Ti (Table 1). The final mesh consisted of 42,158 finite elements. The load-displacement data obtained in compression tests were obtained assuming elastic deformation of the frustule. The main objective of the simulations was to estimate compression curve.

Results
Photographs of the printed samples of enlarged diatom frustule are given in Figure 2. These photographs show the valve, headpole/footpole and girdle views. Evaluation of geometry of the print-outs revealed some missing fragments of the size in the range 10 mm 2 . These imperfections were regarded as non-essential and possible to avoid in future perfecting of the technology. Values of the weight, surface and volume of the printed frustules are listed in Table 2. This table lists also equivalent density of the frustules as 3D objects. This density of 0.11 g/cm 3 is by an order of a degree lower than that of standard light aluminum foams and lower that the values recently published in [33], where a value of 0.12 g/cm 3 was reported for A-242 alloy foams with over 88% porosity. It can be concluded that the printed frustule can be considered as an ultralight structure.  The low density of the printed frustules stems from three factors: (a) it envelopes relatively large cavity, (b) the frustule features an intricate system of openings (struts and ribs) and (c) micro-porosity of the printed parts. The micro-porosity was revealed in the SEM investigations and is exemplified by images in Figure 3.  The low density of the printed frustules stems from three factors: (a) it envelopes relatively large cavity, (b) the frustule features an intricate system of openings (struts and ribs) and (c) micro-porosity of the printed parts. The micro-porosity was revealed in the SEM investigations and is exemplified by images in Figure 3.
Characteristic dimensions of the printed frustules are provided in Table 3. This table lists values measured for as-printed frustules and for the fully flattened in compression tests.
Photos of the printed, engineered object based on the design of frustule of Didymosphenia geminata after compression testing are shown in Figure 4. The definitions of the respective points of measurements are explained by the arrows numbered from one to seven. Metals 2021, 11, x FOR PEER REVIEW 6 of 11 Characteristic dimensions of the printed frustules are provided in Table 3. This table lists values measured for as-printed frustules and for the fully flattened in compression tests. Photos of the printed, engineered object based on the design of frustule of Didymosphenia geminata after compression testing are shown in Figure 4. The definitions of the respective points of measurements are explained by the arrows numbered from one to seven.   The obtained experimental displacement-force curves are shown in Figure 5A and the respective calculated curve in Figure 5B. A remarkable agreement is observed between the two curves in Figure 5 in the entire range of displacements with the exception of compression by 2.5 mm. This amount of compression corresponds to the moment in which the bottom and upper parts of frustules come in direct contact. From that point onwards, the process of frustule densification starts, which is less precisely accounted for in the FEM simulations. The agreement for the displacements lower than 2.5 mm implies the adopted model of plastic deformation of the printed frustule under compression. In turn, it indicates that the work done by the compression force is accumulated in the compressed material via work hardening phenomena. The obtained experimental displacement-force curves are shown in Figure 5A and the respective calculated curve in Figure 5B. The obtained experimental displacement-force curves are shown in Figure 5A and the respective calculated curve in Figure 5B. A remarkable agreement is observed between the two curves in Figure 5 in the entire range of displacements with the exception of compression by 2.5 mm. This amount of compression corresponds to the moment in which the bottom and upper parts of frustules come in direct contact. From that point onwards, the process of frustule densification starts, which is less precisely accounted for in the FEM simulations. The agreement for the displacements lower than 2.5 mm implies the adopted model of plastic deformation of the printed frustule under compression. In turn, it indicates that the work done by the compression force is accumulated in the compressed material via work hardening phenomena. A remarkable agreement is observed between the two curves in Figure 5 in the entire range of displacements with the exception of compression by 2.5 mm. This amount of compression corresponds to the moment in which the bottom and upper parts of frustules come in direct contact. From that point onwards, the process of frustule densification starts, which is less precisely accounted for in the FEM simulations. The agreement for the displacements lower than 2.5 mm implies the adopted model of plastic deformation of the printed frustule under compression. In turn, it indicates that the work done by the compression force is accumulated in the compressed material via work hardening phenomena.

Discussion
The results presented in the paper show that a printed enlarged version of the diatom can be viewed as an ultra-light structure with a large cavity and two types of pores. Due to the concept adopted in printing, the cavity as such and the openings in the frustules have geometry optimized by the forces of nature. In the literature there are numerous reports confirming exceptional mechanical properties of diatoms and shells-see for example [29][30][31]. These exceptional properties protect diatoms against major predators by imparting high stiffness and resilience [30]. In the present study, we took advantage of these exceptional properties by using it as a template for printing materials with their enlarged values. As a result, tough and resilient structures were obtained, which also contained micro-porosity related to the printing process.
In view of the characteristics of the printed samples given above, generally understood energy absorption seems to an obvious area of their applications. According to the literature, the energy absorption per unit volume is higher in the graded structure in comparison to the uniform structure [34,35].
The Based on obtained results, by integrating the area underneath the curve the following value of the mechanical work was estimated: 1.90 J. With the weight of 0.866 g = 0.000866 kg and volume of 7.87 cm 3 = 0.00787 m 3 , the density of the absorbed (and mostly dissipated) energy is 2194/kg and 241.4 J/m 3 . These values justify further steps needed to use the present results for designing absorbing elements based on the concept adopted here. One line of such development could be filling out such components with a mixture of printed frustules of different size and orientation with expected loadings. The other could be further strengthening of the frustules by filling out their cavities with foams.

Conclusions
According to the literature [37], there are several mechanisms of energy absorption, which depend on the used material: elastomeric foams, plastic or brittle foams, natural, cellular materials or fluid within cells. Recent studies in energy absorption issues are mainly related to foams or thin walled tubes without or with filling in the form of various foams. Results obtained by various research groups show that the strength of the foam core affects the interaction effect. It must be noted that stress-strain curves of metal foams used in absorption applications exhibit a plateau-stress region where deformation proceeds at nearly constant nominal stress, whereas in nonporous metals stress continuously increases with the progress of deformation. The results presented in this manuscript did not allow the observation such a plateau-stress region on the plots, both experimental and theoretical. The obtained results indicate linearly decreasing resistance force and, as a consequence, the absorbed energy is half of that which would be absorbed if the force was constant (plateau region). On the other hand the specific density of the printed structure is extremely low (equivalent density at 0.11 g/cm 3 ), due to the fact that the internal cavity is relatively large and empty.
The structural complexity of the porous structure of the diatom shell may be considered as an anisotropic structure. Such behavior is exhibited within so-called lotus-type porous metals, which have superior specific strength than metal foams. This is because the concentration rarely occurs around the pores when the loading is along the pore direction. It makes lotus-metals promising as functional materials with lightweight structure. Among the applications, sound absorbing, heat sinking and energy absorbing have been mentioned.
Nevertheless, the density of the 3D printed engineered object based on a diatom frustule structure is much lower than that of the same structure with the cavity filled out with any form of foam or rod-type strengthening. Thus, there is a clear space for further investigations as well as improving the structure of interest in terms of the rate of energy absorption by in-printing into the cavity a supporting scaffold.
The consideration of the energy absorption value (2.2 kJ/g) should take into account the structure features as well as void inside the frustule. This preliminary results, with an indication that derivative of the work after displacement is constant, seems to be a good introduction into further research of diatom-inspired energy absorbing structures.
The conducted investigations allowed the attainment of new as well as enrichment of the existing knowledge about behavior of the structured inspired by nature. In future work, we will further study the deformation behavior and energy absorption of bio-inspired structures in various configurations and try to predict their energy absorption capacity.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the further ongoing experiments.