Computational Design of Microstructural Composites with Tailored Thermal Conductivity

Abstract

This article presents a numerical procedure to design two-phase periodic microstructural composites with tailored thermal conductivities, which is generalized as a topology optimization problem. The objective function is formulated in a least-square of the difference between the target and effective conductivities. The effective values are derived from homogenization method with periodic boundaries; whereas, the target points locate in the Milton-Kohn bounds. The bound-based interpolation scheme and nonlinear diffusion technique are explored to regularize the original problem for attaining mesh-independent, edge-preserving, and checkerboard-free results. Various microstructures both in 2- and 3-dimensions are presented to demonstrate such a systematic procedure of conductive material design.

Financial support by the Australian Research Council (Project No. DP0558497) is greatly acknowledged.