Micromechanical Modeling of Functionally Graded Composites

A micromechanics-based elastic model is developed for two-phase functionally graded materials with locally pair-wise interactions between particles. While the effective material properties change gradually along the gradation direction, there exist two microstructurally distinct zones: particle-matrix zone and transition zone. In the particle-matrix zone, pair-wise interactions between particles are employed using a modified Green’s function method. By integrating the interactions from all other particles over the representative volume element, the homogenized elastic fields are obtained. The effective stiffness distribution over the gradation direction is further derived. In the transition zone, a transition function is constructed to make the homogenized elastic fields continuous and differentiable in the gradation direction. The model prediction is compared with other models and experimental data to demonstrate the capability of the proposed method.