Micromechanical Analysis of Functionally Gradient Materials

A micromechanical approach is adopted to derive physical fields semi-analytically in functionally gradient materials (FGMs). The numerical Green’s function is sought for FGMs by the eigenfunction expansion method. Computer algebra systems such as Mathematica are essential to derive admissible functions that satisfy the given homogeneous boundary conditions and to manipulate algebra involved. With the Green’s function, physical fields in FGMs can be expressed semi-analytically while retaining all the relevant parameters. In addition, any change in boundary conditions such as temperature drop/rise can be immediately updated without incurring the entire re-calculation. A limited example indicates that the current approach is effective and promising for the analysis of finite-sized and heterogeneous materials in general.