Micromechanics-based elastic model for functionally graded materials with particle interactions

 H.M. Yin¹, L.Z. Sun¹ and G. H. Paulino²

¹Department of Civil and Environmental Engineering and Center for Computer-Aided Design,
The University of Iowa, Iowa City, IA 52242, USA

²Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign,
Newmark Laboratory, 205 North Mathews Avenue, IL 61801, U.S.A.

Abstract

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 particles' 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.

Keywords: Functionally graded materials; Composites; Micromechanical modeling; Elastic behavior; Pair-wise interaction

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