Multi-materials with strong interface: Variational modelings

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 . The model is obtained by identifying the Γ-limit of the stored strain energy functional of the physical problem when the thickness 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. AMS subject classifications: 74B15, 74B20 , 49J45 .