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Keywords = shell-based lattice

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13 pages, 4687 KB  
Article
Non-Close-Packed Isotropic Responsive Magnetic Photonic Crystal Microspheres
by Lejian Zhao, Jie Zhu, Maocheng Sun, Wei Luo, Huiru Ma and Jianguo Guan
Nanomaterials 2026, 16(9), 556; https://doi.org/10.3390/nano16090556 - 1 May 2026
Viewed by 1477
Abstract
Magnetic photonic crystal microspheres (MPCMs) have emerged as a versatile platform for intelligent sensing and display applications, owing to their integration of magnetic actuation with structural coloration. However, their practical implementation is limited by a fundamental structural constraint: most reported MPCMs adopt anisotropic [...] Read more.
Magnetic photonic crystal microspheres (MPCMs) have emerged as a versatile platform for intelligent sensing and display applications, owing to their integration of magnetic actuation with structural coloration. However, their practical implementation is limited by a fundamental structural constraint: most reported MPCMs adopt anisotropic architectures, resulting in angle-dependent optical responses that require continuous magnetic alignment to maintain uniform coloration. Herein, we propose a different structural paradigm based on non-close-packed, optically isotropic MPCMs. Driven by electrostatic repulsion in solutions, monodisperse Fe3O4@tannic acid (TA) core–shell nanoparticles spontaneously assemble into non-close-packed amorphous colloidal arrays, also known as photonic glasses, which are subsequently immobilized within stimuli-responsive polymer networks via emulsification-assisted thermal polymerization. By integrating poly(2-hydroxyethyl methacrylate-co-N-vinylpyrrolidone) (HEMA–NVP) or poly(N-isopropylacrylamide) (PNIPAM) as responsive matrices, the resulting MPCMs exhibit sensitive solvent- or thermo-dependent optical responses. Crucially, structural isotropy ensures angle-independent coloration, eliminating the need for continuous magnetic alignment during optical readout. As evidenced by the unchanged structural color and reflection peak under various magnetic field orientations, this design effectively decouples optical sensing from magnetic actuation. The intrinsic free volume of the non-close-packed architecture allows for isotropic lattice expansion and contraction, leading to broad spectral tunability. Collectively, this work establishes a promising design framework for magnetic photonic microsensors. Full article
(This article belongs to the Section Nanophotonics Materials and Devices)
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15 pages, 1736 KB  
Article
Static Local Lattice Distortion in BCC Refractory High-Entropy Alloys: A DFT Study of NbTaTiV, TiZrNbMo, and HfZrNbMo
by Tijana Đorđević, Ana Kalinić and Dejan Pjević
Metals 2026, 16(4), 412; https://doi.org/10.3390/met16040412 - 9 Apr 2026
Viewed by 792
Abstract
Local lattice distortion (LLD) arising from atomic size mismatch is an important structural feature of body-centered cubic (BCC) refractory high-entropy alloys (RHEAs). Reported LLDs are often difficult to compare across alloys because studies use different definitions and reference lattices. In this paper, we [...] Read more.
Local lattice distortion (LLD) arising from atomic size mismatch is an important structural feature of body-centered cubic (BCC) refractory high-entropy alloys (RHEAs). Reported LLDs are often difficult to compare across alloys because studies use different definitions and reference lattices. In this paper, we computed a consistent static DFT baseline for width-based LLD descriptors for three equimolar quaternary BCC RHEAs: NbTaTiV, TiZrNbMo, and the sparsely reported HfZrNbMo. The alloys were modeled as 128-atom special quasi-random structures and fully relaxed using density functional theory (DFT). Two complementary descriptors were evaluated from the relaxed geometries using a consistently defined reference lattice: a displacement-based metric derived from atomic off-site displacements and a shell-resolved bond length broadening metric for the first and second coordination shells. The resulting LLD descriptors have the lowest values for NbTaTiV, intermediate values for TiZrNbMo, and the highest for HfZrNbMo. Element-resolved analysis shows that individual species contribute differently to the overall distortion, information that is not captured by global descriptors alone. The pretrained MACE machine learning interatomic potential is assessed as a pre-relaxation step prior to DFT relaxation, as well as for screening candidate lattice parameters for HfZrNbMo. Full article
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43 pages, 41959 KB  
Article
Synthesis, Static and Dynamic Characterization of Novel Triply Periodic Minimal Surface Lattices
by Federico Casucci, Enrico Tosoratti, Mohamadreza Afrasiabi and Pier Paolo Valentini
Modelling 2026, 7(2), 43; https://doi.org/10.3390/modelling7020043 - 24 Feb 2026
Viewed by 901
Abstract
This study introduces a new synthesis algorithm for triply periodic minimal surfaces based on determining the equilibrium configuration of elastic membranes constrained at their boundaries. Beyond the methodology itself and its computational efficiency, the scientific relevance of this work lies in the 66 [...] Read more.
This study introduces a new synthesis algorithm for triply periodic minimal surfaces based on determining the equilibrium configuration of elastic membranes constrained at their boundaries. Beyond the methodology itself and its computational efficiency, the scientific relevance of this work lies in the 66 surfaces with these characteristics that it enabled to generate. Leveraging their continuous and highly regular geometry, these surfaces were used to define novel shell-based lattices, the mechanical behavior of which was investigated numerically and experimentally through both static and dynamic analyses. The computational models demonstrated high predictive accuracy, with numerical results deviating by less than 10% from the experimental data. Across the new geometries, the surface-area-to-volume ratio ranged from 1.8 to 4.8 cm−1. At infill coefficients of 10%, 20%, and 30%, the structures exhibited a wide range of stiffness and anisotropic behaviors, with equivalent elastic modulus spanning from 0.02% to 25% that of the base material and Zener indices from 4.67×102 to 11.8. Ultimately, the study revealed a clear influence of cell geometry on stress concentration and modal response. Full article
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18 pages, 3889 KB  
Article
Influence of Structural Height on the Thermo-Hydraulic Performance of a Water-Cooled Gyroid Heat Sink
by Mohamad Ziad Saghir and Mohammad Mansur Rahman
Fluids 2026, 11(2), 57; https://doi.org/10.3390/fluids11020057 - 19 Feb 2026
Viewed by 525
Abstract
The triply periodic minimal surface structure is receiving significant attention amongst the engineering community. The advantage of using such a structure is its ability to provide lightweight cooling to surfaces. In this paper, attention is drawn to a gyroid structure composed of a [...] Read more.
The triply periodic minimal surface structure is receiving significant attention amongst the engineering community. The advantage of using such a structure is its ability to provide lightweight cooling to surfaces. In this paper, attention is drawn to a gyroid structure composed of a shell network and a solid network, with a porosity of 0.7. Three different flow rates, using water as the circulating fluid, are experimentally applied to cool a square surface with a base of 37.5 mm and a height of 12.7 mm. It was found that this structure provided a high cooling rate, achieving a Nusselt number around 100 with a solid lattice and 160 for a shell lattice. It is also noted that the TPMS area plays a significant role, thereby increasing the cooling rate. When the TPMS height is 90% of the initial height of 12.7 mm, the performance of both structures is found to be well accepted. Pressure drop is reduced, and the heat performance is improved. The circulating flow above the structure marginally reduced the pressure drop. The performance evaluation criteria for the shell network ranged from 95 < PEC to < 225, and for the solid network from 125 < PEC to < 155. The optimization method has been applied across the entire height range using response surface methodology. It is found that the optimum TPMS height is for an aspect ratio of 95.1%. Full article
(This article belongs to the Special Issue Thermal Fluids: Theory and Applications)
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24 pages, 12828 KB  
Article
Surrogate-Model Prediction of Mechanical Response in Architected Ti6Al4V Cylindrical TPMS Metamaterials
by Mansoureh Rezapourian, Ali Cheloee Darabi, Mohammadreza Khoshbin, Siegfried Schmauder and Irina Hussainova
Metals 2025, 15(12), 1372; https://doi.org/10.3390/met15121372 - 15 Dec 2025
Cited by 1 | Viewed by 1267
Abstract
A Machine Learning (ML)-based surrogate modeling framework is presented for mapping structure–property relationships in architected Ti6Al4V cylindrical TPMS metamaterials subjected to quasi-static compression. A Python–nTop pipeline automatically generated 3456 cylindrical shell lattices (Gyroid, Diamond, Split-P), and ABAQUS/Explicit simulations with a Johnson–Cook failure model [...] Read more.
A Machine Learning (ML)-based surrogate modeling framework is presented for mapping structure–property relationships in architected Ti6Al4V cylindrical TPMS metamaterials subjected to quasi-static compression. A Python–nTop pipeline automatically generated 3456 cylindrical shell lattices (Gyroid, Diamond, Split-P), and ABAQUS/Explicit simulations with a Johnson–Cook failure model for Ti6Al4V quantified their mechanical response. From 3024 valid designs, key mechanical properties targets including elastic modulus (E), yield stress (Y), ultimate strength (U), plateau stress (PL), and energy absorption (EA) were extracted alongside geometric descriptors such as surface area (SA), surface-area-to-volume ratio (SA/VR), and relative density (RD). A multi-output surrogate model (feedforward neural network) trained on the simulated set accurately predicts these properties directly from seven design parameters (thickness; unit cell counts in X, Y, and Z directions; unit cell orientation; height; diameter), enabling rapid property estimation across large design spaces. Topology-dependent trends indicate that Split-P exhibits the highest strength, energy absorption, and total SA, and shows the largest variation in SA/VR; Gyroid exhibits the lowest SA with a moderate SA/VR; and Diamond is the most compliant lattice and maintains a higher SA/VR than Gyroid despite lower SA. RD increases with both SA and SA/VR across all topologies. The framework provides a reusable computational tool for architectured lattices, enabling quick prescreening of implant designs without repeated finite-element analyses. Full article
(This article belongs to the Special Issue Application of Machine Learning in Metallic Materials)
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13 pages, 2233 KB  
Article
Interfacial Defect Suppression and Enhanced Optical Properties in InP Quantum Dots via Two-Step ZnSe Shelling Strategy
by Jaehyeong Yoo, Sung-Yoon Joe and Jae-Hyeon Ko
Materials 2025, 18(17), 4172; https://doi.org/10.3390/ma18174172 - 5 Sep 2025
Viewed by 1672
Abstract
This study investigates the interfacial structural origin of enhanced optical performance in InP-based quantum dots (QDs) employing a 2-step ZnSe shelling strategy. By comparing InP/ZnSe/ZnS QDs synthesized via 1-step and 2-step shelling methods using identical InP cores, we demonstrate that the 2-step approach [...] Read more.
This study investigates the interfacial structural origin of enhanced optical performance in InP-based quantum dots (QDs) employing a 2-step ZnSe shelling strategy. By comparing InP/ZnSe/ZnS QDs synthesized via 1-step and 2-step shelling methods using identical InP cores, we demonstrate that the 2-step approach results in improved core–shell lattice matching, more favorable carrier dynamics, and enhanced thermal stability. These enhancements are attributed to the formation of an initial thin ZnSe interfacial layer, which facilitates uniform shell growth and suppresses interfacial defect formation. High-resolution transmission electron microscopy and elemental mapping via energy-dispersive X-ray spectroscopy analyses confirm the improved crystallinity and reduced oxygen-related trap states in the 2-step samples. The findings highlight the critical role of interfacial control in determining QD performance and establish the 2-step ZnSe shelling strategy as an effective route to achieving structurally and optically robust QD emitters for advanced optoelectronic applications. Full article
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25 pages, 8085 KB  
Article
Neural Network-Based Prediction of Compression Behaviour in Steel–Concrete Composite Adapter for CFDST Lattice Turbine Tower
by Shi-Chao Wei, Hao Wen, Ji-Zhi Zhao, Yu-Sen Liu, Yong-Jun Duan and Cheng-Po Wang
Buildings 2025, 15(17), 3103; https://doi.org/10.3390/buildings15173103 - 29 Aug 2025
Viewed by 1176
Abstract
The prestressed concrete-filled double skin steel tube (CFDST) lattice tower has emerged as a promising structural solution for large-capacity wind turbine systems due to its superior load-bearing capacity and economic efficiency. The steel–concrete composite adapter (SCCA) is a key component that connects the [...] Read more.
The prestressed concrete-filled double skin steel tube (CFDST) lattice tower has emerged as a promising structural solution for large-capacity wind turbine systems due to its superior load-bearing capacity and economic efficiency. The steel–concrete composite adapter (SCCA) is a key component that connects the upper tubular steel tower to the lower lattice segment, transferring axial loads. However, the compressive behaviour of the SCCA remains underexplored due to its complex multi-shell configuration and steel–concrete interaction. This study investigates the axial compression behaviour of SCCAs through refined finite element simulations, identifying diagonal extrusion as the typical failure mode. The analysis clarifies the distinct roles of the outer and inner shells in confinement, highlighting the dominant influence of outer shell thickness and concrete strength. A sensitivity-based parametric study highlights the significant roles of outer shell thickness and concrete strength. To address the high cost of FE simulations, a 400-sample database was built using Latin Hypercube Sampling and engineering-grade material inputs. Using this dataset, five neural networks were trained to predict SCCA capacity. The Dropout model exhibited the best accuracy and generalization, confirming the feasibility of physics-informed, data-driven prediction for SCCAs and outperforming traditional empirical approaches. A graphical prediction tool was also developed, enabling rapid capacity estimation and design optimization for wind turbine structures. This tool supports real-time prediction and multi-objective optimization, offering practical value for the early-stage design of composite adapters in lattice turbine towers. Full article
(This article belongs to the Section Building Structures)
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25 pages, 4087 KB  
Review
Progress in High-Entropy Alloy-Based Microwave Absorbing Materials
by Chengkun Ma and Yuying Zhang
Symmetry 2025, 17(8), 1286; https://doi.org/10.3390/sym17081286 - 10 Aug 2025
Cited by 4 | Viewed by 4058
Abstract
The rational design of high-performance microwave absorbers with broadband coverage, superior attenuation, and environmental durability is critical for addressing challenges in both defense and civilian technologies. High-entropy alloys (HEAs) exhibit atomic-scale asymmetric arrangements, demonstrating exceptional potential for microwave absorption through their unique lattice [...] Read more.
The rational design of high-performance microwave absorbers with broadband coverage, superior attenuation, and environmental durability is critical for addressing challenges in both defense and civilian technologies. High-entropy alloys (HEAs) exhibit atomic-scale asymmetric arrangements, demonstrating exceptional potential for microwave absorption through their unique lattice distortion, high entropy, sluggish diffusion, and “cocktail effect”. This critical review article provides an overview of the progress made in the development and understanding of HEA-based microwave absorbing materials. Initially, the microwave dissipation mechanisms for HEAs were analyzed, where atomic-scale distortions enhance polarization loss and broaden resonance bandwidth. Subsequently, key synthesis techniques like mechanical alloying and carbothermal shock are discussed, highlighting non-equilibrium processing for phase engineering. Building on these foundations, the discussion then progresses to evaluate four principal material design approaches: (1) compositionally-tuned powders, (2) multifunctional core–shell structures, (3) phase-controlled architectures, and (4) two-dimensional/porous configurations, each demonstrating distinct performance advantages. Finally, the discussion concludes by addressing current challenges in quantitative property modeling and industrial scalability while outlining future directions, including machine learning-assisted design and flexible integration, providing comprehensive guidance for developing next-generation high-performance microwave absorbing materials. Full article
(This article belongs to the Section Engineering and Materials)
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38 pages, 9771 KB  
Article
Global Research Trends in Biomimetic Lattice Structures for Energy Absorption and Deformation: A Bibliometric Analysis (2020–2025)
by Sunny Narayan, Brahim Menacer, Muhammad Usman Kaisan, Joseph Samuel, Moaz Al-Lehaibi, Faisal O. Mahroogi and Víctor Tuninetti
Biomimetics 2025, 10(7), 477; https://doi.org/10.3390/biomimetics10070477 - 19 Jul 2025
Cited by 8 | Viewed by 4033
Abstract
Biomimetic lattice structures, inspired by natural architectures such as bone, coral, mollusk shells, and Euplectella aspergillum, have gained increasing attention for their exceptional strength-to-weight ratios, energy absorption, and deformation control. These properties make them ideal for advanced engineering applications in aerospace, biomedical devices, [...] Read more.
Biomimetic lattice structures, inspired by natural architectures such as bone, coral, mollusk shells, and Euplectella aspergillum, have gained increasing attention for their exceptional strength-to-weight ratios, energy absorption, and deformation control. These properties make them ideal for advanced engineering applications in aerospace, biomedical devices, and structural impact protection. This study presents a comprehensive bibliometric analysis of global research on biomimetic lattice structures published between 2020 and 2025, aiming to identify thematic trends, collaboration patterns, and underexplored areas. A curated dataset of 3685 publications was extracted from databases like PubMed, Dimensions, Scopus, IEEE, Google Scholar, and Science Direct and merged together. After the removal of duplication and cleaning, about 2226 full research articles selected for the bibliometric analysis excluding review works, conference papers, book chapters, and notes using Cite space, VOS viewer version 1.6.20, and Bibliometrix R packages (4.5. 64-bit) for mapping co-authorship networks, institutional affiliations, keyword co-occurrence, and citation relationships. A significant increase in the number of publications was found over the past year, reflecting growing interest in this area. The results identify China as the most prolific contributor, with substantial institutional support and active collaboration networks, especially with European research groups. Key research focuses include additive manufacturing, finite element modeling, machine learning-based design optimization, and the performance evaluation of bioinspired geometries. Notably, the integration of artificial intelligence into structural modeling is accelerating a shift toward data-driven design frameworks. However, gaps remain in geometric modeling standardization, fatigue behavior analysis, and the real-world validation of lattice structures under complex loading conditions. This study provides a strategic overview of current research directions and offers guidance for future interdisciplinary exploration. The insights are intended to support researchers and practitioners in advancing next-generation biomimetic materials with superior mechanical performance and application-specific adaptability. Full article
(This article belongs to the Special Issue Nature-Inspired Science and Engineering for Sustainable Future)
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19 pages, 2558 KB  
Article
Development of Patient-Specific Lattice Structured Femoral Stems Based on Finite Element Analysis and Machine Learning
by Rashwan Alkentar, Sándor Manó, Dávid Huri and Tamás Mankovits
Crystals 2025, 15(7), 650; https://doi.org/10.3390/cryst15070650 - 15 Jul 2025
Cited by 3 | Viewed by 1985 | Correction
Abstract
Hip implant optimization is increasingly receiving attention due to the development of manufacturing technology and artificial intelligence interaction in the current research. This study investigates the development of hip implant stem design with the application of lattice structures, and the utilization of the [...] Read more.
Hip implant optimization is increasingly receiving attention due to the development of manufacturing technology and artificial intelligence interaction in the current research. This study investigates the development of hip implant stem design with the application of lattice structures, and the utilization of the MATLAB regression learner app in finding the best predictive regression model to calculate the mechanical behavior of the implant’s stem based on some of the design parameters. Many cases of latticed hip implants (using 3D lattice infill type) were designed in the ANSYS software, and then 3D printed to undergo simulations and lab experiments. A surrogate model of the implant was used in the finite element analysis (FEA) instead of the geometrically latticed model to save computation time. The model was then generalized and used to calculate the mechanical behavior of new variables of hip implant stem and a database was generated for surgeon so they can choose the lattice parameters for desirable mechanical behavior. This study shows that neural networks algorithms showed the highest accuracy with predicting the mechanical behavior reaching a percentage above 90%. Patients’ weight and shell thickness were proven to be the most affecting factors on the implant’s mechanical behavior. Full article
(This article belongs to the Special Issue Celebrating the 10th Anniversary of International Crystallography)
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15 pages, 2499 KB  
Article
Constructing Sulfur Vacancy-Rich NiCo2S4@MoS2 Core@shell Heterostructure via Interface Engineering for Enhanced HER Electrocatalysis
by Ziteng Song, Yuan Liu, Peng Yin, Jie Dai, Yingying Xu, Rongming Wang and Sibin Duan
Nanomaterials 2025, 15(14), 1061; https://doi.org/10.3390/nano15141061 - 9 Jul 2025
Cited by 6 | Viewed by 1893
Abstract
The rational design of heterointerfaces with optimized charge dynamics and defect engineering remains pivotal for developing advanced non-noble metal-based electrocatalysts for water splitting. A comparative study of NiCo2S4–MoS2 heterostructures was conducted to elucidate the impact of interfacial architecture [...] Read more.
The rational design of heterointerfaces with optimized charge dynamics and defect engineering remains pivotal for developing advanced non-noble metal-based electrocatalysts for water splitting. A comparative study of NiCo2S4–MoS2 heterostructures was conducted to elucidate the impact of interfacial architecture and defect engineering on hydrogen evolution reaction (HER) performance. A core@shell NiCo2S4@MoS2 heterostructure was synthesized via a facile hydrothermal growth method, inducing lattice distortion and strong interfacial coupling, while supported NiCo2S4/MoS2 heterostructures were prepared by ultrasonic-assisted deposition. A detailed structural and spectroscopic characterization and theoretical calculation demonstrated that the core@shell configuration promotes charge redistribution across the NiCo2S4–MoS2 interface and generates abundant sulfur vacancies, thereby increasing the density of electroactive sites. Electrochemical measurements reveal that NiCo2S4@MoS2 markedly outperforms the supported heterostructure, single-component NiCo2S4, and MoS2 when serving as the HER catalyst in acid solution. These findings establish a dual-optimization strategy—combining interfacial design with vacancy modulation—that provides a generalizable paradigm for the deliberate design of high-efficiency non-noble metal-based electrocatalysts for water splitting reactions. Full article
(This article belongs to the Special Issue Nanostructured Materials for Electrocatalysis)
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22 pages, 52232 KB  
Review
Structural Regulation of Advanced Platinum-Based Core-Shell Catalysts for Fuel Cell Electrocatalysis
by Xiaqing Wang, Panpan Du, Kun Cheng, Xing Hua, Ming Xie, Yuyu Li, Yun Zheng, Yingying Wang, Chaoran Pi and Shiming Zhang
Minerals 2025, 15(3), 235; https://doi.org/10.3390/min15030235 - 26 Feb 2025
Cited by 4 | Viewed by 4217
Abstract
Platinum (Pt), a precious metal extracted from minerals, plays an important role as a catalyst in energy conversion and storage devices. However, Pt is expensive and a limited resource, so it is crucial to maximize its utilization. In the electrocatalytic process, the improvement [...] Read more.
Platinum (Pt), a precious metal extracted from minerals, plays an important role as a catalyst in energy conversion and storage devices. However, Pt is expensive and a limited resource, so it is crucial to maximize its utilization. In the electrocatalytic process, the improvement of its utilization is contingent on enhancing its mass and specific activities, a goal that can be significantly realized through the deposition of a Pt-based shell layer on a nanosubstrate material, thereby producing a core-shell structure. This review gives an important overview on the characteristics of Pt-based core-shell catalysts, the structural regulation of the core-shell, and its effects on the electrocatalytic performance. The core-shell structure can significantly increase the ratio of surface Pt atoms per unit mass of Pt particles. Moreover, the lattice mismatch between the core material and the platinum shell can generate strain, which can modulate the magnitude of the adsorption-desorption force of the platinum-based shell layer on the active intermediates, and thus contribute to the modulation of the catalytic performance. In addition to the aforementioned characteristics, the electrocatalytic performance of Pt-based core-shell catalysts is significantly influenced by the core and shell structures. The core-shell structures have unique advantages over other types of catalysts, leading to the development of advanced Pt-based catalysts. Full article
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21 pages, 30504 KB  
Article
Bending Performance of Diamond Lattice Cylindrical Shells
by Sheng Li, Laiyu Liang, Ping Yang, Shaoan Li and Yaozhong Wu
Materials 2025, 18(2), 272; https://doi.org/10.3390/ma18020272 - 9 Jan 2025
Cited by 7 | Viewed by 1393
Abstract
The Diamond lattice cylindrical shell (Diamond LCS) was proposed by a mapping approach based on the triply periodic minimal surfaces (TPMS). The finite element models were built and their accuracy was verified by experimental results. Parameter studies were carried out to investigate the [...] Read more.
The Diamond lattice cylindrical shell (Diamond LCS) was proposed by a mapping approach based on the triply periodic minimal surfaces (TPMS). The finite element models were built and their accuracy was verified by experimental results. Parameter studies were carried out to investigate the effect of geometric and loading parameters on the bending properties of the Diamond LCSs by the finite element model. The results show that Diamond LCS has a stable “V” deformation pattern under a three-point bending load. In the range of relative density (RD) = 15–30%, the higher the RD, the better the lateral bending performance of the Diamond LCS structure. The larger the variation radial coefficient, the higher the lateral load-carrying capacity of the structure. The smaller the loading angle of the punch, the better the lateral bending performance of the Diamond LCS structure. However, if the loading angle is too small, the structure is prone to large torsional deformation, and the deformation tends to destabilize. The increase in punch diameter effectively improves the deformation pattern and bending energy absorption characteristics of the structure. The smaller the span of the cylindrical support, the better the bending energy absorption characteristics of the structure. Full article
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43 pages, 25488 KB  
Review
High Mechanical Performance of Lattice Structures Fabricated by Additive Manufacturing
by Yuhua Li, Deyu Jiang, Rong Zhao, Xin Wang, Liqiang Wang and Lai-Chang Zhang
Metals 2024, 14(10), 1165; https://doi.org/10.3390/met14101165 - 12 Oct 2024
Cited by 78 | Viewed by 22043
Abstract
Lattice structures show advantages in mechanical properties and energy absorption efficiency owing to their lightweight, high strength and adjustable geometry. This article reviews lattice structure classification, design and applications, especially those based on additive manufacturing (AM) technology. This article first introduces the basic [...] Read more.
Lattice structures show advantages in mechanical properties and energy absorption efficiency owing to their lightweight, high strength and adjustable geometry. This article reviews lattice structure classification, design and applications, especially those based on additive manufacturing (AM) technology. This article first introduces the basic concepts and classification of lattice structures, including the classification based on topological shapes, such as strut, surface, shell, hollow-strut, and so on, and the classification based on the deformation mechanism. Then, the design methods of lattice structure are analyzed in detail, including the design based on basic unit, mathematical algorithm and gradient structure. Next, the effects of different lattice elements, relative density, material system, load direction and fabrication methods on the mechanical performance of AM-produced lattice structures are discussed. Finally, the advantages of lattice structures in energy absorption performance are summarized, aiming at providing theoretical guidance for further optimizing and expanding the engineering application potential of lattices. Full article
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17 pages, 2707 KB  
Article
Analytical Solutions of Symmetric Isotropic Spin Clusters Using Spin and Point Group Projectors
by Shadan Ghassemi Tabrizi and Thomas D. Kühne
Magnetism 2024, 4(3), 183-199; https://doi.org/10.3390/magnetism4030013 - 5 Jul 2024
Cited by 2 | Viewed by 2713
Abstract
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters [...] Read more.
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters with spatial symmetry, analytical solutions exist, and a few Heisenberg systems have been solved in closed form. This paper presents a simple, generally applicable approach to analytically solve isotropic spin clusters, based on adapting the basis to both total spin and point group symmetry to factor the Hamiltonian matrix into sufficiently small blocks. We demonstrate applications to small rings and polyhedra, some of which are straightforward to solve by successive spin-coupling for Heisenberg terms only; additional interactions, such as biquadratic exchange or multi-center terms necessitate symmetry adaptation. Full article
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