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Computational Mechanics

, Volume 64, Issue 4, pp 1073–1095 | Cite as

On polarization-based schemes for the FFT-based computational homogenization of inelastic materials

  • Matti Schneider
  • Daniel WichtEmail author
  • Thomas Böhlke
Original Paper
  • 133 Downloads

Abstract

We revisit the polarization-based schemes introduced to FFT-based computational homogenization by Eyre–Milton, Michel–Moulinec–Suquet and Monchiet–Bonnet. When applied to nonlinear problems, these polarization-based methods suffer from two handicaps. Firstly, the optimal choice of algorithmic parameters is only known for the linear elastic case. Secondly, in its original version each iteration of the polarization scheme requires solving a nonlinear system of equations for each voxel. We overcome both difficulties for small-strain elastic–viscoplastic materials. In particular, we show how to avoid solving the nonlinear system. As a byproduct, we identify a computationally efficient convergence criterion enabling a fair comparison to gradient-based solvers (like the basic scheme). The convergence behavior of the polarization schemes is compared to the basic scheme of Moulinec–Suquet and fast gradient methods, based on numerical demonstrations.

Keywords

Computational homogenization FFT Douglas–Rachford splitting Elasto-viscoplasticity 

Notes

Acknowledgements

The authors M. Schneider and T. Böhlke acknowledge partial financial support by the German Research Foundation (DFG) within the International Research Training Group “Integrated engineering of continuous–discontinuous long fiber reinforced polymer structures” (GRK 2078). D. Wicht gratefully acknowledges the financial support by the Helmholtz Association of German Research Centers under the framework of the Helmholtz Research School on “Integrated Materials Development for Novel High Temperature Alloys (IMD)”, Grant No. VH-KO-610. We thank the anonymous reviewers for their constructive criticism and R. Lebensohn for providing the value of \({\dot{\gamma }}_0\) in Table 10.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Engineering MechanicsKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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