In this paper we present a numerical study of thin layers. This approa
ch can modelise bonding phenomena or interfaces of composite materials
. The considered layers have a hyperelastic behaviour. The study of th
e asymptotic problem, when the thickness and the rigidity parameters o
f 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 an
d thickness of the layers appears in the interface law. By a numerical
study of these problems, we aim to find quantitative conditions on th
e thickness in order to compare the results of the problem with an eff
ective layer and those of the limit problems.