Beyond Global Mechanical Properties: Bioinspired Triply-Periodic Minimal Surface Cellular Solids for Efficient Mechanical Design and Optimization

Abstract

Cellular solids are appealing for load-bearing engineering components due to their remarkable global mechanical properties. However, their complexity makes utilizing them challenging and computationally intensive. Homogenization, a common method for simplifying these structures, replaces heterogeneous media with a material possessing equivalent effective properties. Despite its utility, homogenization introduces challenges, particularly the significant influence of lattice geometry on the method's accuracy and the performance of final optimized designs, which is often overlooked. This study evaluates the efficacy of biologically inspired sheet-based triply-periodic minimal surface (TPMS) lattices in homogenization-based stiffness optimization and benchmarks them against other lattice types. Using tailored probe-based metrics introduced in this study, which measure key relevant attributes such as subtopological homogeneity, load path alignment, resilience to edge effects, and achievable channel clearance, TPMS lattices like gyroids outperform strut-based lattices across all criteria. This results in significantly enhanced end-properties of 3D models optimized through numerical homogenization workflows. The findings emphasize the importance of lattice geometry in homogenization-based optimization and highlight the benefits of TPMS structures in delivering predictable performance with minimal design constraints. Additionally, the metrics developed provide a robust framework for evaluating cellular solid designs, enabling engineers to make more informed lattice design choices in comparable optimization scenarios.