Quasiconvex envelope for a model of finite elastoplasticity with one active slip system and linear hardening

Abstract

An explicit characterization of the quasiconvex envelope of the condensed energy in a model for finite elastoplasticity is presented, both in two and in three spatial dimensions. A variational formulation of plasticity, which is appropriate for the first time step in a time discrete formulation of the evolution problem, is used, and it is assumed that only one slip system is active. The model includes a nonlinear elastic energy, which is invariant under SO(n), and an effective plastic contribution which is quadratic in the slip parameter. The quasiconvex envelope arises via the formation of first-order laminates.

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Acknowledgements

This work was partially supported by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 1060 “The mathematics of emergent effects”, Project A5.

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Correspondence to Sergio Conti .

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Communicated by Andreas Öchsner.

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Conti , S., Dolzmann, G. Quasiconvex envelope for a model of finite elastoplasticity with one active slip system and linear hardening. Continuum Mech. Thermodyn. 32, 1187–1196 (2020). https://doi.org/10.1007/s00161-019-00825-8

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Keywords

  • Quasiconvexity
  • Relaxation
  • Elastoplasticity