Globally stable quasistatic evolution in plasticity with softening

G. Dal Maso; Antonio DeSimone; M. G. Mora; M. Morini; G. Dal Maso; Antonio DeSimone; M. G. Mora; M. Morini

doi:10.3934/nhm.2008.3.567

Networks and Heterogeneous Media

2008, Volume 3, Issue 3: 567-614. doi: 10.3934/nhm.2008.3.567

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Globally stable quasistatic evolution in plasticity with softening

1.
SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014, Trieste
2.
SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste
3.
SISSA-International School for Advanced Studies, Via Beirut 2-4,, 34014, Trieste

Received: 01 February 2008
Primary: 74C05; Secondary: 28A33, 74G65, 49J45, 35Q72.

We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each time interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.
- Quasistatic evolution,
- rate independent processes,
- Prandtl-Reuss plasticity,
- plasticity with softening,
- shear bands,
- incremental problems,
- relaxation,
- Young measures
Citation: G. Dal Maso, Antonio DeSimone, M. G. Mora, M. Morini. Globally stable quasistatic evolution in plasticity with softening[J]. Networks and Heterogeneous Media, 2008, 3(3): 567-614. doi: 10.3934/nhm.2008.3.567

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Abstract

We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each time interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.
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