  In this paper, the asymptotic first order analysis, both mathematical and
numerical, of two structures bonded together is presented. Two cases are
considered, the gluing of an elastic structure with a rigid body and the gluing
of two elastic structures. The glue is supposed to be elastic and to have its
stiffness of the same order than those of the elastic structures. An original
numerical method is developed to solve the mechanical problem of stiff
interface at order 1, based on the Nitsche's method. Several numerical examples
are provided to show the efficiency of both the analytical approximation and
the numerical method.
