Linearized plasticity is the evolutionary $\Gamma$-limit of finite plasticity

Alexander Mielke; Ulisse Stefanelli

doi:10.4171/jems/381

JournalsjemsVol. 15, No. 3pp. 923–948

Linearized plasticity is the evolutionary $Γ$ -limit of finite plasticity

Alexander Mielke
Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
Ulisse Stefanelli
Università di Pavia, Italy

$Linearized plasticity is the evolutionary $\Gamma$-limit of finite plasticity cover$

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Abstract

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via $Γ$ -convergence for rate-independent processes that energetic solutions of the quasi-static finite-strain elastoplasticity system converge to the unique strong solution of linearized elastoplasticity.

Cite this article

Alexander Mielke, Ulisse Stefanelli, Linearized plasticity is the evolutionary $Γ$ -limit of finite plasticity. J. Eur. Math. Soc. 15 (2013), no. 3, pp. 923–948

DOI 10.4171/JEMS/381