Unified multi-material topology optimization of heterogeneous structures for three-phase multi-physics systems

Abstract

While structural topology optimization is a useful tool for multiphysics designs, most existing studies focus on
homogeneous material configurations, with limited attention given to heterogeneous systems. To address this
limitation, this paper proposes a unified topology optimization framework for heterogeneous structures - specifically Functionally Graded Materials (FGMs) - under triply coupled thermal, mechanical, and design-dependent pressure loads. Unlike traditional discrete multi-material approaches, the proposed methodology utilizes the continuous spatial variation of material properties using an explicit power-law interpolation scheme. The model integrates a sequential thermo-mechanical coupling strategy with a Darcy-based representative solid-phase model to evaluate design-dependent pressure fields. This allows for a consistent treatment of the interactions among thermal effects, mechanical responses, and evolving pressure loads. Several numerical examples are presented to verify the accuracy and efficiency of the proposed approach. Furthermore, a comparison demonstrates that FGM designs provide improved structural performance over conventional homogeneous layouts in three-phase multiphysics environments. This shows their applicability in engineering practice