Computational Mechanics

, Volume 61, Issue 6, pp 751–764 | Cite as

Efficient and accurate two-scale FE-FFT-based prediction of the effective material behavior of elasto-viscoplastic polycrystals

  • Julian Kochmann
  • Stephan Wulfinghoff
  • Lisa Ehle
  • Joachim Mayer
  • Bob Svendsen
  • Stefanie Reese
Review Paper


Recently, two-scale FE-FFT-based methods (e.g., Spahn et al. in Comput Methods Appl Mech Eng 268:871–883, 2014; Kochmann et al. in Comput Methods Appl Mech Eng 305:89–110, 2016) have been proposed to predict the microscopic and overall mechanical behavior of heterogeneous materials. The purpose of this work is the extension to elasto-viscoplastic polycrystals, efficient and robust Fourier solvers and the prediction of micromechanical fields during macroscopic deformation processes. Assuming scale separation, the macroscopic problem is solved using the finite element method. The solution of the microscopic problem, which is embedded as a periodic unit cell (UC) in each macroscopic integration point, is found by employing fast Fourier transforms, fixed-point and Newton–Krylov methods. The overall material behavior is defined by the mean UC response. In order to ensure spatially converged micromechanical fields as well as feasible overall CPU times, an efficient but simple solution strategy for two-scale simulations is proposed. As an example, the constitutive behavior of 42CrMo4 steel is predicted during macroscopic three-point bending tests.


FE-FFT Two-scale Polycrystals Crystal plasticity Efficient 



We thank Dennis Kochmann for helpful discussions on many algorithmic aspects of this work. Financial support of Subprojects M03 and C02 of the Transregional Collaborative Research Center SFB/TRR 136 by the German Science Foundation (DFG) is gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Julian Kochmann
    • 1
  • Stephan Wulfinghoff
    • 1
  • Lisa Ehle
    • 2
  • Joachim Mayer
    • 2
  • Bob Svendsen
    • 3
    • 4
  • Stefanie Reese
    • 1
  1. 1.Institute of Applied MechanicsRWTH Aachen UniversityAachenGermany
  2. 2.Central Facility for Electron MicroscopyRWTH Aachen UniversityAachenGermany
  3. 3.Material MechanicsRWTH Aachen UniversityAachenGermany
  4. 4.Microstructure Physics and Alloy DesignMax-Planck-Institut für Eisenforschung GmbHDüsseldorfGermany

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