Modeling the material behavior of heterogeneous materials considering a two‐scale FE–FFT‐based simulation framework

Abstract

In various engineering applications, components subjected to high mechanical or multi‐physical loads such as thermal, thermo‐mechanical, or electro‐thermal loads are predominantly made of metals or composites. These materials are characterized by polycrystalline or multi‐phase microstructures which determine the overall material response. However, since the microscopic material behavior is directly related to the distribution, size, and morphology of the individual grains or phase constituents, precise predictions of the macroscopic material response require simulations of the microstructural behavior. Hence, this work considers a two‐scale finite element (FE) and fast Fourier transform (FFT)‐based simulation framework, which is an efficient alternative to the classical method for the simulation of periodic unit cells. Assuming scale separation, the macroscopic and microscopic boundary value problems are first solved individually and subsequently linked by performing a scale transition in terms of averaging the macroscopic quantities over the corresponding local fields. While the macroscopic solution is computed by means of the finite element method, the microscopic boundary value problem, which is embedded as a periodic unit cell in each macroscopic integration point, is solved using an FFT‐based simulation method. In general, these microscopic simulations allow to model grain‐scale phenomena such as martensitic phase transformation or plastic deformation caused by dislocation glide which can be observed in polycrystalline materials. In this work, we present a two‐scale FE–FFT‐based model to capture the martensitic phase transformations in shape memory alloys. In order to demonstrate the applicability of the model, a numerical example is given.