A two way particle mapping for calculation of the shear modulus of a spherical inclusion composite with inhomogeneous interphase

Based on the Mori--Tanaka method and a replacement scheme, a pair of coupled first order differential equations which model the shear modulus of a particulate composite with inhomogeneous interphase are derived. However, the results derived are not exact since the Mori--Tanaka method is not exact for the shear problem. An improved model is therefore proposed which utilises the generalised self consistent scheme for a spherical inclusion that is surrounded by a hypothetical homogeneous interphase layer. To find the properties of this hypothetical interphase layer a mapping of a homogeneous particle onto a two phase composite is utilised. The results are then presented for a simple power law profile and are shown to be consistent with the conclusions of Shen and Li [Int. J. Solids and Struct., 40, 2003, 1393--1409]