Inserted: 14 feb 2022
Last Updated: 25 may 2022
Journal: Journal of Convex Analysis
This paper addresses the well posedness of a dynamical model of perfect elasticity 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 Babadjian & Crismale (2021). 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.