Uniform stresses inside two hyperbolic inhomogeneities

We prove that the internal stresses inside two hyperbolic elastic inhomogeneities can indeed remain uniform when the matrix is subjected to uniform remote anti-plane and in-plane stresses. Conditions leading to internal uniform stresses are established rigorously for both anti-plane and plane elasticity. Once these conditions are satisfied, the internal uniform stresses inside the two hyperbolic inhomogeneities are determined explicitly.