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

Abstract

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.