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

PAMM, vol. 22

Abstract

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.

Authors 4

1. Christian Gierden corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Straße 1 D-52074 Aachen Germany

   Christian Gierden

   Fax: +49 241 80 22001

   Telephone: +49 241 80 25014

2. Johanna Waimann Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Straße 1 D-52074 Aachen Germany

   Modeling and simulation techniques for systems of polycrystalline materials RWTH Aachen University Mies-van-der-Rohe-Straße 1 D-52074 Aachen Germany

3. Bob Svendsen Aachen Material Mechanics

   Max-Planck-Institut für Nachhaltige Materialien · RWTH Aachen University

   Affiliation as printed

   Material Mechanics RWTH Aachen University Schinkelstraße 2 D-52062 Aachen Germany

   Microstructure Physics and Alloy Design Max-Planck-Institut für Eisenforschung GmbH Max-Planck-Straße 1 D-40237 Düsseldorf Germany

4. Stefanie Reese Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Mies-van-der-Rohe-Straße 1 D-52074 Aachen Germany