  This paper addresses the well posedness of a dynamical model of perfect
plasticity with mixed boundary conditions for general closed and convex
elasticity sets. The proof relies on an asymptotic analysis of the solution of
a perfect plasticity model with relaxed dissipative boundary conditions
obtained in [7]. One of the main issues consists in extending the measure
theoretic duality pairing between stresses and plastic strains, as well as a
convexity inequality to a more general context where deviatoric stresses are
not necessarily bounded. Complete answers are given in the pure Dirichlet and
pure Neumann cases. For general mixed boundary conditions, partial answers are
given in dimension $2$ and $3$ under additional geometric hypothesis on the
elasticity set and the reference configuration.
