Multi-objective design of the multi-phase microstructure for thermal conductivity optimization

In this paper, a new method based on the heat dissipation of microstructure is proposed to predict the thermal conductivity of the material microstructure. This method is shown to be equivalent to the homogenization method both theoretically and numerically. Based on the finite element discretization of the microstructure, the sensitivity analysis for the effective thermal conductivity is carried out and the topology optimization model of the heat-conducting microstructure is built to maximize the different combinations of effective thermal conductivity coefficients related to 2D and 3D multiphase materials. The dual optimization scheme and the quadratic perimeter constraint are used to solve the problem and to control the checkerboard pattern during optimization procedure. Numerical examples show that the design of the microstructure using the heat dissipation is effective and can provide satisfactory design results with respect to material microstructures.