A Circular Inclusion with Circumferentially Inhomogeneous Non-Slip Interface in Plane Elasticity

Abstract

A rigorous solution is presented for a problem associated with a circular inclusion embedded within an infinite matrix in plane elastostatics. The bonding at the inclusion-matrix interface is assumed to be imperfect. Specifically, the jump in the normal displacement is assumed to be proportional to the normal traction with the proportionality parameter taken to be circumferentially inhomogeneous. In addition, we assume that displacements in the tangential direction are continuous. This type of interface is generally referred to as an inhomogeneous non-slip interface. Using the principle of analytic continuation, the basic boundary-value problem for four analytic functions is reduced to a first-order differential equation for a single analytic function defined inside the circular inclusion. The resulting closed-form solutions include a finite number of unknown constants determined by analyticity requirements and certain other supplementary conditions. The method is illustrated using several specific examples of a particular class of inhomogeneous non-slip interface. The results from these calculations are compared with the corresponding results when the interface imperfections are homogeneous. These comparisons indicate that the circumferential variation of interface damage has a significant effect on even the average stresses induced within a circular inclusion.