Uniform fields inside two interacting non-parabolic and non-elliptical inhomogeneities

With the aid of conformal mapping for a doubly connected domain, we prove the existence of internal uniform stress fields inside two interacting elastic inhomogeneities: one of non-parabolic open shape and the other of non-elliptical closed shape, when the matrix is subjected to uniform remote anti-plane and in-plane stresses. The uniformity property is unconditional for anti-plane elasticity but conditional for plane elasticity. The internal uniform stress fields are independent of the specific open and closed shapes of the two inhomogeneities. Typical numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed theory.