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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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
Keywords
- Energetic rate-independent systems
- Energetic solution
- Finite-strain elastoplasticity
- Multiplicative decomposition of the strain
- Lie group of plastic strain
- Dissipation distance
- Nonlocal theory via gradient terms