A Vanishing Viscosity Approach to Quasistatic Evolution in Plasticity with Softening

By Gianni Dal Maso, Antonio DeSimone, Maria Giovanna Mora, Massimiliano Morini. 2006

88 citations recorded by the source corpus.

We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analyse a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.

Subfields: Biomedical Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f8e1f0277b7d1201615a99dc09354e0f30ee518b

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In Biomedical Engineering

In Computational Theory and Mathematics

Citations in the corpus

Γ-limits and relaxations for rate-independent evolutionary problems (2008, background): “Related evolutionary systems for Young measures, also in the rate-dependent case, are discussed in [5,11,12,23,24,28,29,42].”
The Variational Approach to Fracture (2008, background): “An attempt at reconciling relaxation and irreversibility was recently made in [51] and in [39] in the much more pliant contexts of damage evolution and plasticity with softening respectively.”
BV SOLUTIONS AND VISCOSITY APPROXIMATIONS OF RATE-INDEPENDENT SYSTEMS ∗ (2009, unknown): “We refer the reader to [27] for rate-independent problems with convex energies and discontinuous inputs, and, in more specific applied contexts, to [16] for elastoplasticity with softening, to [19] for general material models with nonconvex elastic energies, to [17] for a non-associative plasticity ”