Asymptotic analysis of nonlinear elastic adhesives

Adhesive bonding plays an important role when composite materials are involved. Adhesive joints are subjected to complex states of stress with high stress concentrations and, consequently, their accurate analysis is needed. Due to the large number of elements in the thickness direction, a large number of degrees of freedom is necessary with an increase of the simulation costs. A classical alternative approach consists in modeling the adhesive as a material surface. Various methods have been proposed to identify the appropriate transmission conditions and most of the studies focus on adhesives undergoing small displacements [1-5]. In this communication, we report on a recent work concerning thin adhesives made of the Saint Venant-Kirchhoff material, the simplest hyperelastic material model extending the linear elastic material to the nonlinear regime. Soft and hard cases are considered, meaning that the adhesive is assumed to be softer and harder than the adherents, and the corresponding transmission conditions are obtained. These turn out to be conditions of imperfect contact, prescribing jumps of the displacement and stress fields at the material surface modeling the adhesive