Dissipative boundary conditions and entropic solutions in dynamical perfect plasticity

TL;DR

This paper establishes the well-posedness of a dynamical perfect plasticity model, introducing dissipative boundary conditions and linking variational solutions with entropic-dissipative solutions using hyperbolic and variational methods.

Contribution

It combines calculus of variations and hyperbolic techniques to prove existence, uniqueness, and equivalence of solutions under general conditions for perfect plasticity models.

Findings

Derived a class of dissipative boundary conditions between Dirichlet and Neumann.

Proved existence and uniqueness of solutions for the model.

Established the equivalence between variational and entropic-dissipative solutions.

Abstract

We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic methods. The hyperbolic point of view enables one to derive a class of dissipative boundary conditions, somehow intermediate between homogeneous Dirichlet and Neumann ones. By using variational methods, we show the existence and uniqueness of solutions. Then we establish the equivalence between the original variational solutions and generalized entropic--dissipative ones, derived from a weak hyperbolic formulation for initial--boundary value Friedrichs' systems with convex constraints.