Interaction of two circular cylindrical inhomogeneities under anti-plane shear

A simple and effective method is used to derive the elastic field of the infinite homogeneous isotropic medium with two circular cylindrical inhomogeneities under the anti-plane shear. The analytical solution is obtained by using the conformal mapping and the theorem of analytic continuation. When two circular cylindrical inhomogeneities are tangent to each other and/or they are holes and/or rigid inhomogeneities, the corresponding specific cases are also considered in this paper. Finally, numerical results are illustrated to apply the present results to composite materials.