Slow decay of end effects in layered structures with an imperfect interface

An asymptotic analysis of a layered structure with an imperfect interface subject to an anti-plane shear deformation and non-homogeneous Dirichlet end conditions is presented in this paper. Two layers of isotropic materials are bonded via a middle interface layer (adhesive joint), which is thin and soft; effectively, this can be described as a discontinuity surface for the displacement. Model fields are constructed to compensate for the error produced by the asymptotic solution for the case when the layered structure is subject to non-homogeneous Dirichlet end conditions. Numerical examples and analytical estimates are presented to illustrate the slow decay of the `boundary-layer' fields.