Imperfect interface models for elastic structures bonded by a strain gradient layer: the case of antiplane shear

The problem considered in the present paper has its origins in the description of a laminated structure consisting of an adhesive layer and two adherents. The problem of deformation of the layered structure is described by the coupled model of linear and strain gradient elasticity. Namely, we assume that deformations of both the adhesive layer and adherents obey antiplane shear models, but, at the same time, the adhesive layer is described by the simplified strain gradient elasticity theory (or, in other words, the so-called one-parameter gradient elasticity theory), while the adherents obey the classical elasticity theory. The shear moduli of the adhesive layer and its width depend on a small parameter. We investigate the limiting passage, as this parameter tends to zero. As a result, we find out the five types of limit models with imperfect interfaces in dependence of the parameter exponent. Three of them are the same as in the classical theory, while two of them are new and essentially belong to the strain gradient elasticity.