Cubically symmetric mechanical metamaterials projected from 4th dimensional geometries reveal high specific properties in shear

Reduced density significantly compromises the mechanical properties of ordinary materials as their structural components undergo bending when subjected to shear loading. In this paper, we present an emerging class of cubically symmetric mechanical metamaterial, based on 3-space geometrical shadows of 4th dimensional geometries (4-polytopes) that are optimised for high shear resistance and minimised weight. We show that by employing a genetic algorithm-based optimisation framework, the mechanical metamaterials can achieve an increase of more than 40-fold in their specific shear properties. Experimental results reveal that the metamaterial structure with the highest specific shear resistance, the 5-cell (pentatope), exhibits specific shear stiffness that is almost 2-fold higher than that of a gyroid, while the 8-cell (tesseract) structure exhibits the highest specific shear yield strength that is 2.4 times higher than that of a hexagonal honeycomb tested in the out-of-plane direction. The dataset relates to the publication "Cubically symmetric mechanical metamaterials projected from 4th dimensional geometries reveal high specific properties in shear" (https://doi.org/10.31224/3035) by the same authors.

低密度会显著劣化常规材料的力学性能，因为在受剪切载荷作用时，其结构组分会发生弯曲变形。本文提出了一类新型立方对称力学超材料，其设计基于四维多胞体（4-polytopes）在三维空间的几何投影，该类超材料针对高抗剪切性能与最小化质量进行了优化。研究表明，通过采用基于遗传算法的优化框架，该类力学超材料的比剪切性能可提升40倍以上。实验结果显示，比抗剪切性能最优的五胞体（5-cell，pentatope）结构，其比剪切刚度几乎比gyroid高出近2倍；而8-cell（四维超正方体，tesseract）结构的比剪切屈服强度最高，在面外测试方向下较六边形蜂窝高出2.4倍。本数据集关联于同一作者团队发表的论文《基于四维几何投影的立方对称力学超材料展现优异比剪切性能》（Cubically symmetric mechanical metamaterials projected from 4th dimensional geometries reveal high specific properties in shear, https://doi.org/10.31224/3035）。