MATHEMATICAL ANALYSIS OF NONLINEAR BONDED JOINT MODELS
Within the framework of nonlinear elasticity, we consider the problem of two adherents joined along their common surface by a thin soft adhesive. Two stored energy functions are considered: the stored energy function of Saint Venant–Kirchhoff and the stored energy function of Ciarlet–Geymonat. Using the asymptotic expansion method, the limit energy associated to each of these stored energy functions is obtained. The aim of this paper is to give a rigorous mathematical analysis of the formally derived limit problem. We show that the limit problem associated to the Saint Venant–Kirchhoff case admits at least one solution and the limit problem associated to the Ciarlet–Geymonat case admits exactly one solution. An analytical comparison in the one-dimensional case and a three-dimensional numerical application are also presented.