Generalized tessellations of superellipitcal voids in low porosity architected materials for stress mitigation

Abstract

Stress concentration is a crucial source of mechanical failure in structural elements, especially those embedding voids. This paper examines periodic porous materials with porosity lower than 5%. We investigate their stress distribution under planar multiaxial loading, and presents a family of geometrically optimized void shapes for stress mitigation. We adopt a generalized description for both void geometry and planar tessellation patterns that can handle single and multiple voids of arbitrary void shape at a generic angle. The role of void shape evolution from diamond to rectellipse on the stress-distribution is captured at the edge of voids in a representative volume element (RVE) made of non-equal length periodic vectors. Theoretical derivations, numerical simulations along with experimental validation of the strain field in thermoplastic polymer samples fabricated by laser cutting unveil the role of geometric parameters, e.g. superellipse order, aspect ratio and rotation angle, that minimize stress peak and ameliorate stress distribution around voids. This work extends and complements classical theory by providing fundamental insights into the role that tessellation, void shape and inclination play in the stress distribution of low-porosity architected materials, thus introducing essential guidelines of broad application for stress-minimization and failure mitigation in diverse sectors.