Stress Analysis of FGM-Matrix Medium

Abstract

This study presents the derivation of the three-dimensional elastic stress field is derived for an elastic medium that contains a spherical inclusion composed of a functionally graded material (FGM). The material properties for the matrix phase are uniform, while those for the FGM inclusion are assumed to vary linearly. The FGM-matrix medium is subject to constant strain at the far fields. First, the elastic field subject to uniform hydrostatic strains at the far-field is analytically solved. Subsequently, the elastic field subject to uniform deviatoric strains at the far-field is sought and is solved semi-analytically by converting the Navier equation for the displacement into a set of two ordinary differential equations which can be solved using the method of weighted residuals. Numerical examples show that the stress distribution is continuous at the FGM-matrix interface.