Analysis of Composites Reinforced with Functionally Graded Inclusions

Abstract

In this paper, the thermal stress field is derived for an elastic medium that contains a spherical inclusion made of a functionally graded material (FGM) where the material properties vary continuously. A uniform heat source in the inclusion generates a temperature distribution which causes thermal stresses due to the thermal expansion. The temperature field is derived analytically. It is shown that only a single ordinary differential equation is needed to express the thermal stress which is solved numerically using the least square method. Once the stress field for a single inclusion problem is obtained, it is possible to extend the result to a composite with distributed inclusions using a variety of methods available in micromechanics.