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

Dal Maso, G.; DeSimone, A.; Mora, M. G.; Morini, M.

Netw. Heterog. Media 3, No. 3, 567-614 (2008).

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.

MSC:

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)

Keywords:

quasistatic evolution; rate independent processes; Prandtl-reuss plasticity; plasticity with softening; shear bands; incremental problems; relaxation; Young measures