Numerical study of soft adhesively bonded joints in finite elasticity

In this paper we present a numerical study of thin layers. This approach can modelise bonding phenomena or interfaces of composite materials. The considered layers have a hyperelastic behaviour. The study of the asymptotic problem, when the thickness and the rigidity parameters of the layer tend to zero, yields a limit problem with an interface law on the surface to which the layer shrinks. The limit problem keeps in memory the mechanical and geometrical properties of the layers in the sense that the relative behaviour of the limit values of stiffness and thickness of the layers appears in the interface law. By a numerical study of these problems, we aim to find quantitative conditions on the thickness in order to compare the results of the problem with an effective layer and those of the limit problems.