FFT‐based simulation of evolving microstructures utilizing an adapting reduced set of Fourier modes

Abstract

The mechanical behavior of a periodic heterogeneous microstructure may be predicted by using a fast Fourier transform (FFT) based simulation approach. To reduce the computational effort of this method, we introduced a model order reduction (MOR) technique utilizing a reduced set of Fourier modes for the computations in Fourier space. To increase the accuracy of this MOR technique we developed a geometrically adapted sampling pattern for choosing the considered Fourier modes based on the representation of phases within the microstructure. Since the phase distribution of, for example, martensite and austenite in a polycrystalline microstructure evolves with increasing mechanical or thermal loads, the set of considered Fourier modes should also evolve according to the underlying micromechanical fields. We present the accuracy and the adaptability of this adaptive reduced set of Fourier modes by investigating the micromechanical fields of a polycrystal considering such phase transformations.