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This paper addresses the well posedness of a dynamical model of perfectplasticity with mixed boundary conditions for general closed and convexelasticity sets. The proof relies on an asymptotic analysis of the solution ofa perfect plasticity model with relaxed dissipative boundary conditionsobtained in [7]. One of the main issues consists in extending the measuretheoretic duality pairing between stresses and plastic strains, as well as aconvexity inequality to a more general context where deviatoric stresses arenot necessarily bounded. Complete answers are given in the pure Dirichlet andpure Neumann cases. For general mixed boundary conditions, partial answers aregiven in dimension $2$ and $3$ under additional geometric hypothesis on theelasticity set and the reference configuration.

Mixed boundary conditions as limits of dissipative boundary conditions in dynamic perfect plasticity