Efficient topology optimization using compatibility projection in micromechanical homogenization

TL;DR

This paper introduces a discrete adjoint method tailored for Fourier-based homogenization solvers using compatibility projection, enabling efficient topology optimization of composite and metamaterial structures with voids.

Contribution

It develops a novel discrete adjoint approach compatible with Fourier-based solvers, enhancing efficiency in topology optimization involving complex material behaviors.

Findings

Efficient gradient computation for Fourier-based homogenization.

Successful optimization of composite and auxetic metamaterials.

Effective modeling of void regions with zero stiffness.

Abstract

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas Fourier-based solvers have recently shown large efficiency gains for homogenization problems. In this paper, we derive the discrete adjoint method for Fourier-based solvers that employ compatibility projection. We demonstrate the method on the optimization of composite materials and auxetic metamaterials, where void regions are modelled with zero stiffness.