Tensile properties of 3D projected 4-polytopes: a new class of mechanical metamaterial

Abstract

In this paper, we explore the mechanical behavior of a new class of mechanical metamaterials based on the 3D projections of 4-dimensional geometries (4-polytopes) subjected to loading in tension. We demonstrate that the specific properties of mechanical metamaterials can be enhanced by more than 4-fold when optimized within a framework powered by an evolutionary algorithm. Optimized metamaterial structures were manufactured using the low-forcestereolithography prototyping technique and mechanically tested in tension. The experimental results show that the best-performing metamaterial structure, the 8-cell (tesseract), has specific yield strength and specific stiffness values in a similar range to those of hexagonal honeycombs tested out-of-plane. Nevertheless, the 8-cell structures are also cubically symmetrical and have the same mechanical properties in three orthogonal axes. The effect of structure is quantified by comparing the tensile strength against the Young's modulus of bulk solid material. We find that the final value of the 8-cell structures exceeds that of the hexagonal honeycomb by 76%. The 5-cell (pentatope) and 16-cell (orthoplex) metamaterials are shown to be more effective in bearing tensile loads than the gyroid structures, while the 24-cell (octaplex) structures exhibit the lowest ratio and possess the least optimal structure-properties relationships. The findings presented in this paper showcase the importance of macro-scale architecture and highlight the potential of 3D projections of 4-polytopes as the basis for a new class of mechanical metamaterials.