Interface Problems in Viscoplasticity and Plasticity

Abstract

This paper is concerned with three-dimensional interface (or transmission) problems in solid mechanics which consist of the (quasi-static) equilibrium condition and a first order evolution inclusion in a bounded Lipschitz domain $\Omega $ and the homogeneous linear elasticity problem in an unbounded exterior domain $\Omega _2 $. The evolution problem in $\Omega $ models viscoplasticity and Prandtl–Reus plasticity with hardening as well as perfect plasticity. The exterior part of the interface problem is rewritten in terms of boundary integral operators using the Poincare–Steklov operator. This symmetric coupling approach takes the total system of the Calderon projector into account. Then, existence and uniqueness results are obtained in a mixed variational formulation.