zbMATH — the first resource for mathematics

Globally stable quasistatic evolution in plasticity with softening. (English) Zbl 1156.74308
Summary: 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.

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
28A33 Spaces of measures, convergence of measures
74G65 Energy minimization in equilibrium problems in solid mechanics
49J45 Methods involving semicontinuity and convergence; relaxation
35Q72 Other PDE from mechanics (MSC2000)
Full Text: DOI Link