Defect Green's function of multiple point-like inhomogeneities in a multilayered anisotropic elastic solid

Defect Green's function (GF) of multiple point-like inhomogeneities in a multilayered solid has been derived within the theory of linear anisotropic elasticity. It is related to the (reference) GF of the multilayered matrix excluding the inhomogeneities through the continuum Dyson's equation. While the reference GF is available, the defect GF can be solved. The expressions are first analytically reduced by realizing the point-likeness of the inhomogeneities. The subsequent procedure involves the solution of the response of each individual inhomogeneity to a far-field straining in the multilayered matrix and a matrix inversion on the order of the number of inhomogeneities. Furthermore, the defect GF is applied to derive the field induced by inhomogeneous substitutions in a multilayered solid. Numerical results are reported for arrays of cubic and semispherical Ge inclusions in a Si/Ge superlattice. The numerical results have demonstrated the validity and efficiency of the present formulation.