Solutions for Macroscopic Elastic Moduli and Microscopic Stress–Strain Fields of Spherically Symmetric Inclusion Composites with Surface Stress Imperfect Interface

Mechanical behavior of the spherically symmetric inclusion composites (two- and three-dimensional) with stress interface is studied. From the three-point correlation variational principle for elasticity of the doubly coated sphere assemblage, limiting procedures have been developed to derive the bounds for the macroscopic elastic moduli of the composite. These bounds depend on the elastic surface parameters ks and μs. The upper and lower bounds of an effective bulk modulus converge to an exact value which can be constructed by the Hill substitution scheme. The bounds for an effective shear modulus involve the three-point correlation parameters which are only estimated. Algebraic expression of the respective microscopic stress–strain fields and their visual illustration within and around the inhomogeneity are presented. Scaling laws governing the effective moduli of composite are also derived. The analytical model combining the available macroscopic experimental data is useful in the inverse problem for estimating the surface properties.