A circular inclusion with circumferentially inhomogeneous non-slip interface in plane elasticity

A rigorous solution is presented for a problem associated with a circular i nclusion embedded within an infinite matrix in plane elastostatics. The bon ding at the inclusion-matrix interface is assumed to be imperfect. Specific ally, the jump in the normal displacement is assumed to be proportional to the normal traction with the proportionality parameter taken to be circumfe rentially inhomogeneous. In addition, we assume that displacements in the t angential direction are continuous. This type of interface is generally ref erred to as an inhomogeneous non-slip interface. Using the principle of analytic continuation, the basic boundary-value prob lem for four analytic functions is reduced to a first-order differential eq uation for a single analytic function defined inside the circular inclusion . The resulting closed-form solutions include a finite number of unknown co nstants determined by analyticity requirements and certain other supplement ary conditions. The method is illustrated using several specific examples of a particular c lass of inhomogeneous non-slip interface. The results from these calculatio ns are compared with the corresponding results when the interface imperfect ions are homogeneous. These comparisons indicate that die circumferential v ariation of interface damage has a significant effect on even the average s tresses induced within a circular inclusion.