Antiplane shear deformations of an anisotropic elliptical inhomogeneity with imperfect or viscous interface

Abstract

AbstractBased on the Lekhnitskii‐Eshelby approach of two‐dimensional anisotropic elasticity, a semi‐analytical solution is derived for the problem associated with an anisotropic elliptical inhomogeneity embedded in an infinite anisotropic matrix subjected to remote uniform antiplane shear stresses. In this research, the linear spring type imperfect bonding conditions are imposed on the inhomogeneity‐matrix interface. We use a different approach than that developed by Shen et al. (2000) to expand the function encountered during the analysis for an imperfectly bonded interface. Our expansion method is in principle based on Isaac Newton's generalized binomial theorem. The solution is verified, both theoretically and numerically, by comparison with existing solution for a perfect interface. It is observed that the stress field inside an anisotropic elliptical inhomogeneity with a homogeneously imperfect interface is intrinsically nonuniform. The explicit expression of the nonuniform stress field within the inhomogeneity is presented. The nonuniform stress field inside the inhomogeneity is also graphically illustrated. A difference in internal stress distribution between a composite composed of anisotropic constituents and a composite composed of isotropic constituents is also observed. We finally extend the solution derived for a linear spring type imperfect interface to address an elliptical inhomogeneity with a viscous interface described by the linear law of rheology. It is observed that the stress field inside an elliptical inhomogeneity with a viscous interface is nonuniform and time‐dependent.