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arXiv · 2005.07612

Continuity equation and characteristic flow for scalar Hencky plasticity

Jean-Francois Babadjian·Gilles A. Francfort
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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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Jean-Francois Babadjian, Gilles A. Francfort. 2020-05-15. Continuity equation and characteristic flow for scalar Hencky plasticity. https://arxiv.org/abs/2005.07612

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