Asymptotic analysis of an adhesive joint with mismatch strain

This paper proposes the study of the equilibrium problem, where two elastic bodies are bonded to a thin elastic film under mismatch strain conditions resulting in a state of residual stress. The asymptotic behavior of the film/adherent system is modeled as the film thickness tends to zero, using a method based on asymptotic expansions and energy minimization procedures. This method yields a family of non-local imperfect interface laws, which define a jump in the displacement and the traction vector fields. The amplitudes of the jumps turn out to be correlated with the state of residual stress and the elastic properties of the materials. As an example, the interface law is calculated at order zero in the case of a pure homogeneous mismatch strain and a thin isotropic film consisting of Blatz-Ko material.