Multi-material topology optimization for nonlinear heat conduction with temperature-dependent properties

With the continuous trend towards miniaturization and high power density in modern engineering systems, thermal management faces unprecedented challenges. Traditional topology optimization based on constant material property assumptions often fails to capture the inherent dependence of material properties on temperature, thereby limiting the design potential in extreme operating environments. In this work, a multi-material topology optimization (TO) framework for steady-state heat conduction considering temperature-dependent material properties (TDMPs) is proposed. By integrating nonlinear finite element analysis with the discrete material optimization (DMO) scheme, a nonlinear heat conduction TO model is constructed. Two optimization objective functions, namely, the minimization of thermal compliance and peak temperature, are investigated to address distinct thermal design requirements. The effectiveness of the proposed method is demonstrated through several two- and three-dimensional numerical examples, including complex and irregular engineering domains. A material switching mechanism is identified from the optimized results, wherein the proposed method autonomously allocates materials with high thermal conductivity based on the local temperature distribution. Furthermore, two numerical approaches are proposed to verify the correctness of the optimized results, and the optimized designs are compared with those obtained from conventional experience-based designs and other multi-material interpolation schemes. The results demonstrate that introducing multiple materials with TDMPs yields physically reasonable designs and superior performance. This observation confirms the potential of the proposed method for thermal design in multifunctional and high-temperature structures.