A Multiscale Framework for Elastic Deformation of Functionally Graded Composites
A micromechanics-based elastic model is developed for two-phase functionally graded composites with locally pair-wise particle interactions. In the gradation direction, there exist two microstructurally distinct zones: particle-matrix zone and transition zone. In the particle-matrix zone, the homogenized elastic fields are obtained by integrating the pair-wise interactions from all other particles over the representative volume element. In the transition zone, a transition function is constructed to make the homogenized elastic fields continuous and differentiable in the gradation direction. The averaged elastic fields are solved for transverse shear loading and uniaxial loading in the gradation direction.
Omer Van der Biest, Michael Gasik, Jozef Vleugels
H.M. Yin et al., "A Multiscale Framework for Elastic Deformation of Functionally Graded Composites ", Materials Science Forum, Vols. 492-493, pp. 391-396, 2005