ALEX 2018 Workshop: Abstracts

Variational modelling of crystal plasticity - analytical and numerical challenges

Sergio Conti(1) and Georg Dolzmann(2)

(1) Universität Bonn, Institut für angewandte Mathematik (Germany)

(2) Universität Regensburg, Fakultät für Mathematik (Germany)

The variational approach to models in finite plasticity proposed in [6, 3] has inspired a large amount of work in the past 20 years. In this talk, we review one of the many facets of the theory, namely the question of macroscopic or effective theories. In particular, for the classical model energy for one slip system proposed in [3] previous numerical experiments in [1, 2] predict the necessity of second-order order laminates in the relaxation. Recent numerical computations in [4, 5] show that third-order laminates are necessary in order to obtain a complete relaxation formula.

Acknowledgments: This work was partially supported by the Deutsche Forschungsgemeinschaft through the Research Unit FOR 797 “Analysis and computation of microstructure in finite plasticity”, projects CO 304/4-2 (first author) and DO 633/2-2 (second author) and through the Sonderforschungsbereich 1060 “The mathematics of emergent effects”, project A5 (first author)

References

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  • 2 C. Carstensen, S. Conti, and A. Orlando, Mixed analytical-numerical relaxation in finite single-slip crystal plasticity, Cont. Mech. Thermod. 20 (2008), 275–301.
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  • 4 S. Conti and G. Dolzmann, An adaptive relaxation algorithm for multiscale problems and application to nematic elastomers, J. Mech. Phys. Solids 113 (2018), 126–143
  • 5 S. Conti and G. Dolzmann, Numerical study of microstructures in single-slip finite elastoplasticity, submitted.
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