# 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 $\rm{ curl\;}(\mu\sigma)=0$ where $\mu$ is a nonnegative measure and $\sigma$ 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.
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Journal articles

https://hal.archives-ouvertes.fr/hal-02594303
Submitted on : Monday, April 19, 2021 - 3:07:23 PM
Last modification on : Tuesday, May 4, 2021 - 3:37:07 AM

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• HAL Id : hal-02594303, version 3

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Jean-François Babadjian, Gilles A. Francfort. Continuity equation and characteristic flow for scalar Hencky plasticity. Communications on Pure and Applied Mathematics, Wiley, 2021. ⟨hal-02594303v3⟩

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