Equilibrium Configurations For Nonhomogeneous Linearly Elastic Materials With Surface Discontinuities

Antonin Chambolle (1, 2, 3) , Vito Crismale (1, 4)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
4 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]

We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises a previous compactness theorem that we proved and employed to show existence of minimisers for the Dirichlet problem for the (homogeneous) Griffith energy.

Mots clés: Generalised special functions of bounded deformation; Brittle fracture; Compactness

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]

Antonin Chambolle, Vito Crismale. Equilibrium Configurations For Nonhomogeneous Linearly Elastic Materials With Surface Discontinuities. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2023, XXIV (3), pp.1575-1610. ⟨10.2422/2036-2145.202006_002⟩. ⟨hal-02667936v2⟩