Calculus of Variations and Geometric Measure Theory

Variational methods and applications

Spatial hyperbolicity for the system of perfect plasticity - (online)

Jean-François Babadjian (Université Paris Saclay, Département de Mathématiques d'Orsay)

created by paolini on 08 Sep 2021
modified on 14 May 2022

9 sep 2021 -- 11:30   [open in google calendar]


In this work in collaboration with Gilles Francfort, we study the spatial hyperbolic structure of a two-dimensional scalar model of perfect plasticity. Minimizing solutions suffer from two pathologies: the linear growth of the energy leads to singularities in the energy space, while the absence of strict convexity yields non uniqueness of the solutions. Taking advantage of the hyperbolic system associated to this model and under the assumption that the plastic zone has non empty interior, we show rigidity properties of the solutions in that set and, in particular, their constancy along characteristic lines. It allows us to precisely describe the geometric structure of the plastic zone and show partial uniqueness results when it touches the boundary of the domain.