  This paper is devoted to confront two different approaches to the problem of
dynam-ical perfect plasticity. Interpreting this model as a constrained
boundary value Friedrichs' system enables one to derive admissible hyperbolic
boundary conditions. Using variational methods, we show the well-posedness of
this problem in a suitable weak measure theoretic setting. Thanks to the
property of finite speed propagation, we establish a new regularity result for
the solution in short time. Finally, we prove that this variational solution is
actually a solution of the hyperbolic formulation in a suitable
dissipative/entropic sense, and that a partial converse statement holds under
an additional time regularity assumption for the dissipative solutions.
