Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem

Abstract The equilibrium problem for an elastic body having inhomogeneous inclusion with curvilinear boundaries is considered within the framework of antiplane shear. We assume that there a power-law dependence shear modulus on small parameter characterizing its width. justify passage to limit as vanishes and construct asymptotic model containing thin inclusion. also show that, depending exponent parameter, are five types inclusions: crack, rigid inclusion, ideal contact, crack adhesive interaction faces. strong convergence established family solutions original solution limiting one.