Multi-material topology optimization of thermoelastic structures by an ordered SIMP-based phase field model

This paper presents a phase field approach to multi-material topology optimization of thermo-elastic structures. Based on the ordered Solid Isotropic Material with Penalization (ordered SIMP) model, the phase field variable is interpreted as the normalized density, which is used as the design variable in topology optimization. The material properties are interpolated in each interval of the normalized density. The advantage of ordered SIMP is that the number of design variables does not depend on the number of materials. In the proposed method, phase field evolution is governed by one Allen-Cahn type equation, with the introduction of a multiple-well potential function to take into account multiple material phases. This feature makes the current approach different from previous works, where numerous phase field evolution equations are needed. In contrast to the original ordered SIMP model, which was developed for structures subjected to only mechanical load, the current approach incorporates interpolation schemes to account for both thermal conductivity and thermal stress coefficient. An assessment of the feasibility and performance of the developed method is conducted via various benchmark examples and comparison with available reference results in the literature.