Abstract
In this paper, we consider the problem of a single elastic inhomogeneity embedded within an infinite elastic matrix in anti-plane shear. In particular, we examine the design of this inhomogeneity to achieve (stress) neutrality when a non-uniform stress field is prescribed in the surrounding matrix. Since it is known that neutral elastic inhomogeneities do not exist when the inhomogeneity is assumed to be perfectly bonded to the matrix, the design method presented here is based on the assumption of an imperfect interface and the appropriate choice of the (single) interface parameter (characterizing the imperfect interface) to achieve the desired neutrality. Specifically, in the case of a homogeneously imperfect interface, it is shown that the circular inhomogeneity is neutral if and only if the prescribed non-uniform stress field in the surrounding matrix belongs to a certain class of polynomial functions. In the case of an inhomogeneously imperfect interface, neutrality is established for circular and elliptic inhomogeneities for specific classes of prescribed states of stress in the surrounding matrix. The results in this paper affirm the feasibility of designing a neutral elastic inhomogeneity by controlling the (imperfect) interface parameter describing the inhomogeneity-matrix interface.