Hyperbolic structure for a simplified model of dynamical perfect plasticity

TL;DR

This paper compares two approaches to dynamical perfect plasticity, establishing well-posedness, regularity, and equivalence of solutions using hyperbolic boundary conditions and variational methods.

Contribution

It introduces a hyperbolic boundary condition framework for dynamical perfect plasticity and proves well-posedness and solution equivalence in a measure-theoretic setting.

Findings

Established well-posedness of the model

Proved regularity of solutions in short time

Linked variational and hyperbolic formulations

Abstract

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.