A Neutral Isotropic Elastic Ellipsoidal Inhomogeneity with a Spring-Type Imperfect Interface

Summary We study the design of an imperfectly bonded neutral isotropic elastic ellipsoidal inhomogeneity that does not disturb the prescribed uniform normal stresses in an isotropic elastic matrix. The imperfect inhomogeneity-matrix interface is modeled by a spring-type imperfect interface characterized by a single imperfect interface function. The same degree of interface imperfection is realized in both the normal and tangential directions. The two loading parameters and the imperfect interface function are determined by solving a resulting cubic equation for each one of the three types of elastic constants of the composite. All three roots of the cubic equation are permissible provided that the Young’s modulus (for the first two types) or the Poisson’s ratio (for the third type) of the inhomogeneity is higher or lower than that corresponding to the matrix. The design of a neutral superellipsoidal or paraboloidal elastic inhomogeneity with another kind of spring-type interface that does not sustain shear traction under a prescribed uniform hydrostatic stress field in the matrix is also achieved.