Thermo-Elastic Homogenization of TPMS-Based Interpenetrating Phase Composites: A Comparison Between Finite Element and Mechanics of Structure Genome Approaches

Triply periodic minimal surface (TPMS)-based interpenetrating phase composites (IPCs) combine two co-continuous solid phases across a smooth, doubly curved interface, providing a multifunctional design space for tailoring mechanical and thermal properties. This study investigates the effective thermo-elastic and thermal-transport behavior of TPMS-based IPCs using two established homogenization approaches: finite element (FE)-based representative unit cell (RUC) homogenization and mechanics of structure genome (MSG)-based homogenization. Four TPMS topologies—gyroid, diamond (Schwarz D), PMY, and F-rhombic dodecahedron (F-RD)—are considered over TPMS-phase volume fractions ranging from 0.1 to 0.5. Conforming-mesh RUC models are generated using Microgen and analyzed in Abaqus for FE simulations with periodic boundary conditions, and in the in-house CmbsFE code for MSG-based homogenization. The two approaches are cross-verified for predicting effective elastic properties, coefficients of thermal expansion (CTEs), and thermal conductivities, and agree to within 0.3% on identical meshes. On identical meshes the two approaches solve linear systems of the same size, and MSG requires fewer matrix decompositions. The study further examines the influence of TPMS topology and TPMS-phase volume fraction on the multifunctional response of two-phase IPCs, supporting the design and optimization of structural–thermal materials.