Calculation of effective elastic moduli of composite materials with multiphase interactions taken into consideration

Abstract

The effective tensors of elastic moduli and pliability were calculated by renormalizing the equations of equilibrium and incompatibility. All multiphase interactions were taken into consideration, but the calculation was done approximately by using only the singular parts of derivatives of Green's functions, which is equivalent to the assumption of uniformity of the random components of stress and strain fields within grain boundaries. Solutions derived by two methods are reconciled, making it possible to determine the position of the elastic moduli of shear and of bulk K between the Hashin-Shtrikman bounds. Particular cases in which only the bulk modulus is not uniform, as well as those of composite materials with all of their constituents having the same ratio K=4μ/3 are considered.