Optimal design of heterogeneous materials

This article reviews recent inverse techniques that we have devised to optimize the structure and macroscopic properties of heterogeneous materials such as composite materials, porous media, colloidal dispersions, and polymer blends. Optimization methods provide a systematic means of designing materials with tailored properties and microstructures for a specific application. This article focuses on two inverse problems that are solved via optimization techniques: (a) the topology optimization procedure used to design heterogeneous materials and (b) stochastic optimization methods employed to reconstruct or construct microstructures.