Calculus of Variations and Geometric Measure Theory

Concentration versus oscillation effects in brittle damage

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

created on 17 Nov 2020
modified on 26 Nov 2020

26 nov 2020 -- 14:30   [open in google calendar]

WADE (Webinar in Analysis and Differential Equations)--Paris time


This talk is concerned with the asymptotic analysis of a variational model of brittle damage, when the damaged zone concentrates into a set of zero Lebesgue measure, and, at the same time, the stiffness of the damaged material becomes arbitrarily small. In a particular non-trivial regime, concentration leads to a limit energy with linear growth as typically encountered in perfect plasticity. While the singular part of the limit energy can be easily described, the identification of the bulk part of the limit energy requires a subtler analysis of the interplay between concentration and oscillation properties of the displacements. This is a joint work with F. Iurlano and F. Rindler.