Interaction of two circular cylindrical inhomogeneities under antiplane shear

摘要

For the inhomogeneous medium with inclusions orinhomogeneities including fibers, whiskers, particles, cracks,etc.(see Mural l 987), the interaction between inclusions orinhomogeneities is very important in analyzing and investigatingthe following problems: the stress concentration near inclusions orinhomogeneities, the effective properties, the damage mechanismand failure modes etc. For this purpose, the elastic field of theinfinite homogeneous isotropic medium with two circularcylindrical inhomogeneities under the antiplane sheaf stress isinvestigated. The corresponding analytical solution is obtained byusing the conformal mapping and the theorem of analyticcontinuation. Here, two circular cylindrical inhomogeneities areparallel to each others infinitely long along the directionperpendicular to xy-plane and have the radii r1 and r2, respectively.When the matrix, assumed to be infinite in all directions, issubjected to the uniform antiplane shear stress, the presentproblem is the antiplane one.From the results obtained, it can be found that the elastic fielddepends on the shear moduli of individual phases, the geometricparameters of the system and the applied shear stresses at infinity.When one of two circular cylindrical inhomogeneities has thesame shear moduli with matrix, the present expressions candegenerate into the results of Gong and Meguid (1992). Inaddition, numerical results show that the shear moduli of twocircular cylindrical inhomogeneities and the geometric parametersof the system have the important effect on the shear stressdistribution. The presence of two circular cylindricalinhomogeneities makes the stress field between these twoinhomogeneities to have sharper changing tendencies. When twocircular cylindrical inhomogeneities approach each other, theinteraction between these two inhomogeneities is more prominent.