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An elastic harmonic inclusion near a rigid harmonic inclusion loaded by a couple

We use conformal mapping techniques to solve the inverse problem concerned with an elastic non-elliptical harmonic inclusion in the vicinity of a rigid non-elliptical harmonic inclusion loaded by a couple when the surrounding matrix is subjected to remote uniform stresses. Both a size-independent complex loading parameter and a size-dependent real loading parameter are introduced as part of the solution procedure. The stress field inside the elastic inclusion is uniform and hydrostatic; the interfacial normal and tangential stresses as well as the hoop stress on the matrix side are uniform along each one of the two inclusion–matrix interfaces. The tangential stress along the interface of the elastic inclusion (free of external loading) vanishes, whereas that along the interface of the rigid inclusion (loaded by the couple) does not. A novel method is proposed to determine the area of the rigid inclusion.