In this work we develop a rigorous mathematical analysis of variational problems describing the quasistatic evolutionary problems in plasticity. The common feature of the problems under consideration is the variational energy formulation, where the mathematical difficulties arise due to the presence of a term with a linear growth in the symmetric part of the gradient of the unknown vector-valued functions in a volumetric case, or on the Hessian of the unknown scalar function in two-dimensional problems for plates. In the applications these functions represent displacement fields of a body...
