Neutrality of a coated anisotropic spherical inhomogeneity under a uniform hydrostatic stress field

We study the neutrality of a coated spherical inhomogeneity when the surrounding matrix is subjected to a uniform remote hydrostatic stress distribution. Both the inhomogeneity and the coating are composed of the most general spherically uniform linear anisotropic elastic materials permitting radially symmetric deformations whilst the matrix is comprised of a spherically uniform cubic material. Furthermore, when both the coating and the matrix become isotropic elastic, we obtain an exact expression for the effective bulk modulus of sphere assemblages completely replacing the original isotropic matrix. The exact expression for the effective bulk modulus of a polycrystal is simply given. The above analysis is further adapted to accomplish the neutrality of a radially inhomogeneous and spherically anisotropic spherical inhomogeneity with a radially homogeneous and spherically anisotropic coating.

Automated summary

We study the neutrality of a coated spherical inhomogeneity under a uniform remote hydrostatic stress distribution in the surrounding matrix. The inhomogeneity and the coating are made of the most general spherically uniform linear anisotropic elastic materials allowing radially symmetric deformations, while the matrix consists of a spherically uniform cubic material. Furthermore, we obtain an exact expression for the effective bulk modulus of sphere assemblages when both the coating and the matrix become isotropic elastic, replacing the original isotropic matrix completely. The analysis is also adapted to achieve the neutrality of a radially inhomogeneous and spherically anisotropic spherical inhomogeneity with a radially homogeneous and spherically anisotropic coating.