Multi-materials with strong interface: Variational modelings

Anne-Laure Bessoud (1) , Francoise Krasucki (1) , Gérard Michaille (1, 2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 UNIMES - Université de Nîmes

We introduce a simplified model for a multi-material made up of two elastic bodies connected by a strong thin material layer whose stiffness grows as 1/ε. The model is obtained by identifying the Γ-limit of the stored strain energy functionalof the physical problem when the thickness ε of the intermediate layer tends to zero. The intermediate layer behaves as a stiffening elastic membrane. Furthermore, in the linear anisotropic case, we establish the strong convergence of the exactsolution toward the solution of the limit problem.

Mots clés: elasticity; multi-materials; multi-scaling; Γ-convergence

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Anne-Laure Bessoud, Francoise Krasucki, Gérard Michaille. Multi-materials with strong interface: Variational modelings. Asymptotic Analysis, 2009, 61, pp.1-19. ⟨10.3233/ASY-2008-0903⟩. ⟨hal-00790347⟩