Micromechanical approach to the thermomechanical analysis of FGMs

Abstract

Functionally graded materials (FGMs) distribute the material functions throughout the material body to achieve the maximum heat resistance and mechanical properties ideal for spacecraft where one side may be exposed to extremely high temperatures and the other side may be exposed to extremely low temperatures. Because FGMs characteristically have continuously varying material properties, many analytical methods developed for conventional composites with distinct phases may not be directly applicable to FGMs. In this chapter, a micromechanical approach is used to semi-analytically obtain the thermoelastic fields in an FGM by the eigenfunction expansion method. The thermoelastic fields in a functionally graded material (FGM) are derived semi-analytically by the use of the eigenfunction expansion method. The eigenfunctions are approximated by a linear combination of admissible functions each of which satisfies the homogeneous boundary condition. The eigenfunctions can also be used to construct the Green's function for the FGM which enables the handling of various boundary conditions and source terms. A numerical example is presented to show thermal stress distributions in a 2-D rectangular FGM under steady-state heat transfer subject to the first kind of displacement boundary condition.