Fast solvers for homogenization problems : fast Fourier transform- and neural network-based approaches

Abstract

The goal of numerics based science is the replication of our tangible reality within computer-aided simulations at least possible deviation from relevant experiments. An ever-growing hardware capability led to an ever-growing resolution of simulations. This increase starts to enable the simulation of material behavior on several length scales and their interaction in computational solid mechanics. From a material physics point of view, the analysis of several lengths scales is of high interest, as many macroscopically observable effects are of microscopic origin. However, despite the massive increase in computational power, full-field simulations across several scales are still uneconomic and time-consuming, preventing them from being applied to a wide range of realistic engineering problems. To relieve said problem, researchers developed homogenization methods and the concept of representative volume elements. The present work deals with numerical homogenization approaches and applies them to several material effects. Particular focus is put on the computation of effective properties as well as their embedding into multiscale simulations.