Affiliations: I3M, UMR-CNRS 5149 et LMGC, UMR-CNRS 5508, Université Montpellier 2, Case courier 048, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France. E-mail: bessoud@lmgc.univ-montp2.fr | ACSIOM, I3M, UMR-CNRS 5149, Université Montpellier 2, Case courier 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France. E-mail: krasucki@math.univ-montp2.fr | ACSIOM and AVA, I3M, UMR-CNRS 5149, Université Montpellier 2 et Université de Nîmes, Case courier 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France. E-mail: micha@math.univ-montp2.fr
Abstract: 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 functional of 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 exact solution toward the solution of the limit problem.
