The present paper deals with the derivation of a higher order theory of interface models. In particular, it is studied the problem of two bodies joined by an adhesive interphase for which "soft" and "hard" linear elastic constitutive laws are considered. For the adhesive, interface models are determined by using two different methods. The first method is based on the matched asymptotic expansion technique, which adopts the strong formulation of classical continuum mechanics equations (compatibility, constitutive and equilibrium equations). The second method adopts a suitable variational (weak) formulation, based on the minimization of the potential energy. First and higher order interface models are derived for soft and hard adhesives. In particular, it is shown that the two approaches, strong and weak formulations, lead to the same asymptotic equations governing the limit behavior of the adhesive as its thickness vanishes. The governing equations derived at zero order are then put in comparison with the ones accounting for the first order of the asymptotic expansion, thus remarking the influence of the higher order terms and of the higher order derivatives on the interface response. Moreover, it is shown how the elastic properties of the adhesive enter the higher order terms. The effects taken into account by the latter ones could play an important role in the nonlinear response of the interface, herein not investigated. Finally, two simple applications are developed in order to illustrate the differences among the interface theories at the different orders

a b s t r a c tThe mechanical problem of two elastic bodies separated by a thin elastic film is studied here. The stiffness of the three bodies is assumed to be similar. The asymptotic behavior of the film as its thickness tends to zero is studied using a method based on asymptotic expansions and energy minimization. Several cases of interphase material symmetry are studied (from isotropy to triclinic symmetry). In each case, non-local relations are obtained relating the jumps in the displacements and stress vector fields at order one to these fields at order zero.

This study deals with a linear elastic body consisting of two solids connected by a thin adhesive interphase with a small thickness e. The three parts have similar elastic moduli.It is proposed to model the limit behavior of the interphase when e ! 0. It has been established [1], using matched asymptotic expansions, that at order zero, the interphase reduces to a perfect interface, while at order one, the interphase behaves like an imperfect interface, with a transmission condition involving the displacement and the traction vectors at order zero. The perfect interface model is exactly recovered using a C-convergence argument. At a higher order, a new model of imperfect interface is obtained by studying the properties of a suitable (weakly converging) sequence of equilibrium solutions. Some analytical examples are given to illustrate the results obtained.

The paper is concerned with the derivation of a general imperfect interface law in a linear multiphysics framework for a composite, constituted by two solids, separated by a thin adhesive layer. The analysis is performed by means of the asymptotic expansions technique. After defining a small parameter ε, which will tend to zero, associated with the thickness and the constitutive coefficients of the intermediate layer, we characterize three different limit models and their associated limit problems: the soft interface model, in which the constitutive coefficients depend linearly on ε; the hard interface model, in which the constitutive properties are independent of ε; the rigid interface model, in which they depend on 1 ε. The asymptotic expansion method is reviewed by taking into account the effect of higher order terms and by defining a general multiphysics interface law which comprises the above aforementioned models.

This paper deals with necessary conditions and sufficient conditions for a weak local minimum of the energy of a hyperelastic body. We consider anisotropic bodies of arbitrary shape, subject to prescribed displacements on a given portion of the boundary. As an example, we consider the uniaxial stretching of a cylinder, in the two cases of compressible and incompressible material. In both cases we find that there is a continuous path across the natural state, made of local energy minimizers. For the Blatz-Ko compressible material and for the Mooney-Rivlin incompressible material, explicit estimates of the minimizing path are given and compared with those available in the literature.