OPTIMAL DESIGN FOR MULTIMATERIALS

Abstract

We explore how some ideas that have been used before for optimal design problems with two materials through a variational approach, can be extended to cover three or more materials. In particular, we focus on two paradigmatic situations where we consider a linear-in-the-gradient cost functional, and a typical quadratic situation. In both cases, we are able to formulate, quite explicitly, a full relaxation of the problem through which optimal microstructures for the original non-convex problem can be understood.