FFT-based simulation using a reduced set of frequencies adapted to the underlying microstructure

Abstract

Instead of the classical finite element (FE) based microstructure simulation, a Fast Fourier transform (FFT) based microstructure simulation, introduced by Moulinec and Suquet (1994, 1998), also enables the computation of highly resolved microstructural fields. In this context, the microscopic boundary value problem is captured by the Lippmann-Schwinger equation and solved by using Fast Fourier transforms (FFT) and fixed-point iterations. To decrease the computational effort of the fixed-point solver, Kochmann et al. (2019) introduced a model order reduction (MOR) technique based on solving the Lippmann-Schwinger equation in Fourier space with a reduced set of frequencies. Thereby, the accuracy of this MOR technique depends on the number of used frequencies and the choice of frequencies that are considered within the simulation. Instead of the earlier proposed fixed (Kochmann et al., 2019) or geometrically adapted (Gierden et al., 2021b) sampling patterns, we propose a sampling pattern which is updated after each load step based on the current strain. To show the precision of such a strain-based sampling pattern, an elasto-plastic two-phase composite microstructure is investigated.