Tensile Properties of 3D-Projected 4-Polytopes: A New Class of Mechanical Metamaterial

In this article, we research the tensile behavior mechanical metamaterial based on the 3D projections of 4D geometries (4-polytopes). The specific properties of these mechanical metamaterials can be enhanced by more than fourfold when optimized within a framework powered by an evolutionary algorithm. We 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. 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 metamaterial tensile strength against the Young's modulus of constituent solid material. We find that the strength-to-modulus 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 under tensile loading than gyroid structures, while 24-cell (octaplex) structures display 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 metamaterial.