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Networks and Heterogeneous Media (NHM)
 

Globally stable quasistatic evolution in plasticity with softening

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

 
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G. Dal Maso - SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014, Trieste, Italy (email)
Antonio DeSimone - SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste, Italy (email)
M. G. Mora - SISSA-International School for Advanced Studies, Via Beirut 2-4,, 34014, Trieste, Italy (email)
M. Morini - SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014, Trieste, Italy (email)

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.

Keywords:  Quasistatic evolution, rate independent processes, Prandtl-Reuss plasticity, plasticity with softening, shear bands, incremental problems, relaxation, Young measures
Mathematics Subject Classification:  Primary: 74C05; Secondary: 28A33, 74G65, 49J45, 35Q72.

Received: February 2008;      Available Online: June 2008.