Linearization for finite plasticity under dislocation-density tensor regularization


Finite-plasticity theories often feature nonlocal energetic contributions in the plastic variables. By introducing a length-scale for plastic effects in the picture, these nonlocal terms open the way to existence results (Mainik and Mielke in J Nonlinear Sci 19(3):221–248, 2009). We focus here on a reference example in this direction, where a specific energetic contribution in terms of dislocation-density tensor is considered (Mielke and Müller in ZAMM Z Angew Math Mech 86:233–250, 2006). When external forces are small and dissipative terms are suitably rescaled, the finite-strain elastoplastic problem converges toward its linearized counterpart. We prove a \(\Gamma \)-convergence result making this asymptotics rigorous, both at the incremental level and at the level of quasistatic evolution.

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US gratefully acknowledges the support of the Vienna Science and Technology Fund (WWTF) through under Project MA14-009 and of the Austrian Science Fund (FWF) under Project F 65. RS gratefully acknowledges the Erwin Schrödinger Institute for financial support.

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Correspondence to Ulisse Stefanelli.

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Scala, R., Stefanelli, U. Linearization for finite plasticity under dislocation-density tensor regularization. Continuum Mech. Thermodyn. (2020).

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  • Finite plasticity
  • Linearization
  • \(\Gamma \)-convergence
  • Incremental problem