Higher-Order Theory for Functionally Graded Materials

Functionally graded materials (FGM's) are a new generation of engineered materials wherein the microstructural details are spatially varied through nonuniform distribution of the reinforcement phase(s). Engineers accomplish this by using reinforcements with different properties, sizes, and shapes, as well as by interchanging the roles of the reinforcement and matrix phases in a continuous manner (ref. 1). The result is a microstructure that produces continuously or discretely changing thermal and mechanical properties at the macroscopic or continuum scale. This new concept of engineering the material's microstructure marks the beginning of a revolution both in the materials science and mechanics of materials areas since it allows one, for the first time, to fully integrate the material and structural considerations into the final design of structural components. Functionally graded materials are ideal candidates for applications involving severe thermal gradients, ranging from thermal structures in advanced aircraft and aerospace engines to computer circuit boards. Owing to the many variables that control the design of functionally graded microstructures, full exploitation of the FGM's potential requires the development of appropriate modeling strategies for their response to combined thermomechanical loads. Previously, most computational strategies for the response of FGM's did not explicitly couple the material's heterogeneous microstructure with the structural global analysis. Rather, local effective or macroscopic properties at a given point within the FGM were first obtained through homogenization based on a chosen micromechanics scheme and then subsequently used in a global thermomechanical analysis.