Design of a neutral elastic inhomogeneity via thermal expansion

A neutral elastic inhomogeneity does not affect the existing stress field when inserted into an elastic body. It has been shown that no such inhomogeneity can exist under the classical assumption of a perfectly bonded interface between the inhomogeneity and the surrounding material. We show that by introducing a suitable temperature field inside the inhomogeneity it is indeed possible to achieve neutrality regardless of the perfect bonding assumption. Specifically, we show that a nonuniform internal temperature field can induce neutrality in an inhomogeneity in the form of an elastic ring with concentric internal and external boundaries of arbitrary shape. Noting that such a temperature field can be identified also in the case of an unpunched inhomogeneity when the inhomogeneity is line-shaped, we further prove that even a flake-shaped inhomogeneity can be made neutral if the thickness of the flake is much smaller than its length. In the case that the elastic body surrounding the unpunched inhomogeneity is subjected to remote hydrostatic loading, the temperature field within the inhomogeneity will remain uniform and independent of the shape of the inhomogeneity. In fact, in this case, the temperature field inside the inhomogeneity depends only on the elastic parameters of the composite and the direction of the remote loading and can be higher or lower than the operating temperature of the composite.