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September  2008, 3(3): 567-614. doi: 10.3934/nhm.2008.3.567

Globally stable quasistatic evolution in plasticity with softening

G. Dal Maso 1, , Antonio DeSimone 2, , M. G. Mora 3, and  M. Morini 1,

1. 

SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014, Trieste, Italy
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, Italy

Received  February 2008 Published  June 2008

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.
Keywords: Quasistatic evolution, Young measures, rate independent processes, relaxation, plasticity with softening, shear bands, incremental problems, Prandtl-Reuss plasticity.
Mathematics Subject Classification: Primary: 74C05; Secondary: 28A33, 74G65, 49J45, 35Q7.
Citation: G. Dal Maso, Antonio DeSimone, M. G. Mora, M. Morini. Globally stable quasistatic evolution in plasticity with softening. Networks and Heterogeneous Media, 2008, 3 (3) : 567-614. doi: 10.3934/nhm.2008.3.567
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