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Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

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Abstract

We provide a global existence result for the time-continuous elastoplasticity problem using the energetic formulation. For this, we show that the geometric nonlinearities arising from the multiplicative decomposition of the strain can be controlled via polyconvexity and a priori stress bounds in terms of the energy density. While temporal oscillations are controlled via energy dissipation, the spatial compactness is obtained via regularizing terms involving gradients of the internal variables.

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Authors and Affiliations

  1. IADM, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Andreas Mainik

  2. Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

  3. Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489, Berlin, Germany

    Alexander Mielke

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  1. Andreas Mainik
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  2. Alexander Mielke
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Correspondence to Alexander Mielke.

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Communicated by R. Kohn.

Dedicated to Sir John Ball on the occasion of his 60th birthday.

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Mainik, A., Mielke, A. Global Existence for Rate-Independent Gradient Plasticity at Finite Strain. J Nonlinear Sci 19, 221–248 (2009). https://doi.org/10.1007/s00332-008-9033-y

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  • DOI: https://doi.org/10.1007/s00332-008-9033-y

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