  The problem of quasistatic evolution in small strain associative
elastoplasticity is studied in the framework of the variational theory for
rate-independent processes. Existence of solutions is proved through the use of
incremental variational problems in spaces of functions with bounded
deformation. This provides a new approximation result for the solutions of the
quasistatic evolution problem, which are shown to be absolutely continuous in
time. Four equivalent formulations of the problem in rate form are derived. A
strong formulation of the flow rule is obtained by introducing a precise
definition of the stress on the singular set of the plastic strain.

Analysis of PDEs