Shape optimization of two‐phase inelastic material with microstructure

Proposes a methodology for dealing with the problem of designing a material microstructure the best suitable for a given goal.

The chosen model problem for the design is a two‐phase material, with one phase related to plasticity and another to damage. The design problem is set in terms of shape optimization of the interface between two phases. The solution procedure proposed herein is compatible with the multi‐scale interpretation of the inelastic mechanisms characterizing the chosen two‐phase material and it is thus capable of providing the optimal form of the material microstructure. The original approach based upon a simultaneous/sequential solution procedure for the coupled mechanics‐optimization problem is proposed.

Several numerical examples show a very satisfying performance of the proposed methodology. The latter can easily be adapted to other choices of design variables.

Confirms that one can thus achieve the optimal design of the nonlinear behavior of a given two‐phase material with respect to the goal specified by a cost function, by computing the optimal form of the shape interface between the phases.