Continuity Equation and Characteristic Flow for Scalar Hencky Plasticity

Abstract

We investigate uniqueness issues for a continuity equation arising out of the simplest model for plasticity, Hencky plasticity. The associated system is of the form curl (µσ ) = 0 where µ is a nonnegative measure and σ a two-dimensional divergence free unit vector field. After establishing the Sobolev regularity of that field, we provide a precise description of all possible geometries of the characteristic flow, as well as of the associated solutions.1. Introduction 2. Notation and preliminaries 3. Hencky plasticity 4. Sobolev regularity of the stress 5. Rigidity properties of the solutions 6. Geometry of the solutions Appendix. Bibliography