Abstract

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

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