Date/heure
24 octobre 2023
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Elise Bonhomme (Université Paris-Saclay)
Catégorie d'évènement Séminaire Équations aux Derivées Partielles et Applications (Nancy)
Résumé
This talk addresses the question of the interplay between relaxation and irreversibility through
evolution processes in damage mechanics, by inquiring the following question: can the quasi-static
evolution of an elastic material undergoing a process of plastic deformation be derived as the limit
model of a sequence of quasi-static brittle damage evolutions?
This question is motivated by the static analysis led in [1], where the authors have shown
how the brittle damage model introduced by Francfort and Marigo (see [4]) can lead to a model
of (Hencky) perfect plasticity. Problems of damage mechanics being rather described through
evolution processes, it is natural to extend this analysis to quasi-static evolutions, where the inertia
is neglected. We consider the case where the medium is subjected to time-dependent boundary
conditions, in the one-dimensional setting. The idea is to combine the scaling law introduced in [1]
with the quasi-static brittle damage evolution introduced in [3] by Francfort and Garroni, and try
to understand how the irreversibility of the damage process will be expressed in the limit evolution.
Surprisingly, the interplay between relaxation and irreversibility of the damage is not stable
through time evolutions. Indeed, depending on the choice of the prescribed Dirichlet boundary
condition, the effective quasi-static damage evolution obtained may not be of perfect plasticity
type.
References:
[1] J.-F. Babadjian, F. Iurlano, F. Rindler: Concentration versus oscillation effects in brittle damage, Comm.
Pure Appl. Math. 74 (2021) 1803–1854.
[2] G. Dal Maso, A. DeSimone, M. G. Mora: Quasistatic evolution problems for linearly elastic-perfectly plastic
materials, Arch. Ration. Mech. Anal. 180 (2006) no. 2, 237–291.
[3] G. A. Francfort, A. Garroni: A Variational View of Partial Brittle Damage Evolution, Arch. Rational
Mech. Anal 182 (2006) 125–152.
[4] G. A. Francfort, J.-J. Marigo: Revisiting brittle fracture as an energy minimization problem, J. Mech.
Phys. Solids 46 (1998) 1319–1342.