Heuristic structural optimization of two-dimensional filling materials with square-triangular supercells

Cellular filling materials are commonplace in additively manufactured parts to lower the structural weight without detriment to the mechanical properties. This technical note undergoes the heuristic optimization of a two-dimensional metamaterial with repetitive supercells derived from a square frame divided by median and diagonal lines into eight triangles. The inherent quadriaxiality of this layout is ideally suited to resist multiaxial stress fields while enabling size refinement to match the local scale of the component. A step-by-step procedure is developed which optimizes the thickness of the beams along the principal axes of the cell (sidewise and diagonal) according to a fully stressed design concept. Preliminary finite element models, including either bar or beam elements, confirm the theoretical results for a case study. Extension of the optimal approach to three-dimensional geometries is envisioned using a cubic cell that incorporates the present two-dimensional grid on each face of the cube.