Yield envelope of minimal surface sheet-based stochastic metamaterials under multi-axial loading conditions

There is a growing interest in examining the mechanical characteristics of cellular structures derived from triply periodic minimal surfaces (TPMS) and spinodal decomposition due to advancements in additive manufacturing; however, thorough research on their yield behavior is missing in literature. This research uses finite element analysis to compute elastic and yield characteristics of stochastic TPMS and spinodal cellular structures. Stochastic TPMS cellular structures are generated by stochastically rotating the unit cells inside randomly distributed control volumes using different TPMS topologies, whereas spinodal cellular structures are generated by Gaussian random field (GRF) method. Elastic and yield characteristics of sheet-based stochastic cellular structures are examined numerically under multiple loading conditions, revealing that stochastic Gyroid demonstrates superior properties. Initial yield surfaces are developed for various loading conditions, demonstrating that stochastic cellular structures exhibit identical initial yield surfaces for various loading cases. Extended Hill yield criterion is identified as better capturing the initial yield surfaces of stochastic cellular structures. This study examines the impact of relative density on initial yield surfaces, revealing that these surfaces are independent of relative density. Our findings indicate that TPMS-based stochastic cellular structures can surpass spinodal cellular structures regarding elastic and yield properties when suitable TPMS topology is employed.