A multiscale FE-FFT framework for electro-active materials at finite strains

Abstract

The present work addresses the fast-Fourier-transform-based computational homogenization of electro-mechanically coupled materials at finite strains. While the macroscopic boundary value problem is solved with finite elements, the solution at microscale is carried out using fast Fourier transforms (FFT). In the context of the FFT-based solution, we propose a general formulation that employs a fully coupled reference medium resulting in fully coupled preconditioning. In order to arrive at an efficient multiscale setting, we provide an algorithmically consistent macroscopic tangent operator for nonlinear electro-mechanical problems derived from the Lippmann–Schwinger equation. We demonstrate the applicability and accuracy of the formulation with some numerical examples. Here, we also investigate both the fully coupled and uncoupled preconditioning as well as the respective impact on the algorithmic solution. It turns out that while the fully coupled scheme leads to quadratic convergence rates, the uncoupled scheme may allow for shorter computation times under certain boundary conditions.