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 ...

This paper aims at characteristic failure mechanisms of cohesive frictional materials at two levels of observation: (a) at the macroscale of continuum elastoplasticity, and (b) at the microscale of active microplanes with arbitrary orientation. Thereby, the criteria for the loss of uniqueness and the loss of ellipticity will be discussed for a macroscopic as well as a microplane-based anisotrop...

An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. The forward system is reformulated such that it involves the plastic multiplier and a complementarity condition. In order to derive necessary optimality conditions, a ...

Gradient plasticity at large strains with kinematic hardening is analyzed as quasistatic rate-independent evolution. The energy functional with a frame-indifferent polyconvex energy density and the dissipation are approximated numerically by finite elements and implicit time discretization, such that a computationally implementable scheme is obtained. The non-selfpenetration as well as a possib...

We present in this paper the characterization of the variational structure behind the discrete equations defining the closest-point projection approximation in elastoplasticity. Rate-independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range, the later in the context of isotropic finite strain multiplicative plasticity. Primal variational prin...

This work is concerned with the numerical solution of variational problems in elastoplasticity. Since the whole class of all possible elastoplastic problems is too large for a common treatment, we restrict ourselves to the investigation of problems which are quasi-static, and where strain and displacement are related linearly. Further, the homogeneous and isotropic material should obey the Pran...