Interaction of Two Circular Cylindrical Inhomogeneities Under Antiplane Shear

Abstract For the inhomogeneous medium with inclusions or inhomogeneities including fibers, whiskers, particles, cracks, etc. (see Mura, 1987), the interaction between inclusions or inhomogeneities is very important in analyzing and investigating the following problems: the stress concentration near inclusions or inhomogeneities, the effective properties, the damage mechanism and failure mode, etc. For this purpose, the elastic field of the infinite homogeneous isotropic medium with two circular cylindrical inhomogeneities under the antiplane shear stress is investigated. The corresponding analytical solution is obtained by using the conformal mapping and the theorem of analytic continuation. Here, two circular cylindrical inhomogeneities are parallel to each other, infinitely long along the direction perpendicular to xy-plane and have the radii rl and r2, respectively. When the matrix, assumed to be infinite in all directions, is subjected to the uniform antiplane shear stress, the present problem is the antiplane one. From the results obtained, it can be found that the elastic field depends on the shear moduli of individual phases, the geometric parameters of the system and the applied shear stresses at infinity. When one of two circular cylindrical inhomogeneities has the same shear moduli with matrix, the present expressions can degenerate into the results of Gong and Meguid (1992). In addition, numerical results show that the shear moduli of two circular cylindrical inhomogeneities and the geometric parameters of the system have the important effect on the shear stress distribution. The presence of two circular cylindrical inhomogeneities makes the stress field between these two inhomogeneities to have sharper changing tendencies. When two circular cylindrical inhomogeneities approach each other, the interaction between these two inhomogeneities is more prominent.