Shape optimization for composite materials and scaffolds

TL;DR

This paper develops a shape optimization framework for designing microstructures in composite materials and scaffolds, focusing on their effective properties and demonstrating practical numerical methods.

Contribution

It introduces a method to compute shape gradients for microstructure optimization, linking shape sensitivity to homogenized material properties.

Findings

Computed Hadamard's shape gradient for microstructure design

Validated the approach with numerical experiments

Enhanced understanding of shape sensitivity in porous media

Abstract

This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge practical interest, for example, for medical applications or for the development of light weight structures in aeronautics. In particular, the optimal design of microstructures leads to fundamental questions for porous media: what is the sensitivity of homogenized coefficients with respect to the shape of the microstructure? We compute Hadamard's shape gradient for the problem of realizing a prescribed effective tensor and demonstrate the applicability and feasibility of our approach by numerical experiments.