Efficient multiscale FE-FFT-based modeling and simulation of macroscopic 
deformation processes with non-linear heterogeneous microstructures

Kochmann, Julian; Ehle, Lisa; Wulfinghoff, Stephan; Mayer, Joachim; Svendsen, Bob; Reese, Stefanie

doi:10.1007/978-3-319-65463-8_7

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Efficient multiscale FE-FFT-based modeling and simulation of macroscopic deformation processes with non-linear heterogeneous microstructures

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Svendsen, Bob
Material Mechanics, Faculty of Georesources and Materials Engineering, RWTH Aachen University, Schinkelstraße 2, D-52062 Aachen, Germany;
Microstructure Physics and Alloy Design, Max-Planck-Institut für Eisenforschung GmbH, Max Planck Society;

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Citation

Kochmann, J., Ehle, L., Wulfinghoff, S., Mayer, J., Svendsen, B., & Reese, S. (2018). Efficient multiscale FE-FFT-based modeling and simulation of macroscopic deformation processes with non-linear heterogeneous microstructures. In P. Wriggers, O. Allix, & J. Soric (Eds.), Lecture Notes in Applied and Computational Mechanics (pp. 129-146). Springer Verlag. doi:10.1007/978-3-319-65463-8_7.

Cite as: https://hdl.handle.net/21.11116/0000-0001-E85E-1

Abstract

The purpose of this work is the prediction of micromechanical fields and the overall material behavior of heterogeneous materials using an efficient and robust two-scale FE-FFT-based computational approach. The macroscopic boundary value problem is solved using the finite element (FE) method. The constitutively dependent quantities such as the stress tensor are determined by the solution of the local boundary value problem. The latter is represented by a periodic unit cell attached to each macroscopic integration point. The local algorithmic formulation is based on fast Fourier transforms (FFT), fixed-point and Newton-Krylov subspace methods (e.g. conjugate gradients). The handshake between both scales is defined through the Hill-Mandel condition. In order to ensure accurate results for the local fields as well as feasible overall computation times, an efficient solution strategy for two-scale full-field simulations is employed. As an example, the local and effective mechanical behavior of ferrit-perlit annealed elasto-viscoplastic 42CrMo4 steel is studied for three-point-bending tests. For simplicity, attention is restricted to the geometrically linear case and quasi-static processes. © Springer International Publishing AG 2018.