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Journal Articles Communications on Pure and Applied Mathematics Year : 2021

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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Dates and versions

hal-02594303 , version 1 (15-05-2020)
hal-02594303 , version 2 (19-05-2020)
hal-02594303 , version 3 (19-04-2021)

Identifiers

  • HAL Id : hal-02594303 , version 3

Cite

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