Non-convex, ringing-free, FFT-accelerated solver using an incremental approximate energy functional

TL;DR

This paper introduces a novel FFT-accelerated solver that effectively handles non-convex micromechanical homogenization problems, eliminating ringing artifacts and enabling the use of advanced iterative methods like trust-region and LBFGS.

Contribution

It develops a modified trust region solver for non-convex problems and integrates it into a ringing-free FFT-accelerated scheme using an approximate incremental energy functional.

Findings

Successfully handles non-convex problems such as continuum damage.

Eliminates ringing artifacts in FFT-accelerated micromechanical simulations.

Enables use of modern iterative solvers in FFT schemes.

Abstract

Fourier-accelerated micromechanical homogenization has been developed and applied to a variety of problems, despite being prone to ringing artifacts. In addition, the majority of Fourier-accelerated solvers applied to FFT-accelerated schemes only apply to convex problems. We here introduce a that allows to employ modern efficient and non-convex iterative solvers, such as trust-region solvers or LBFGS in a FFT-accelerated scheme. These solvers need the explicit energy functional of the system in their standard form. We develop a modified trust region solver, capable of handling non-convex micromechanical homogenization problems such as continuum damage employing the approximate incremental energy functional. We use the developed solver as the solver of a ringing-free FFT-accelerated solution scheme, namely the projection based scheme with finite element discretization.