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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A note on time-dependent DiPerna-Majda

Abstract. A quasistatic evolution problem for a phase transitions model with nonconvex energy density is considered in terms of Young measures. We focus on the particular case of a finite number of phases. The new feature consists in the usage of suitable regularity arguments in order to prove an existence result for the a notion of evolution presenting some improvements with respect to the one defined in [9], for infinitely many phases.