Determination of effective elastic properties of functionally graded materials using Voronoi cell finite element method

A Voronoi cell finite element method (VCFEM) has been implemented into the commercial finite element package ABAQUS and used to determine the effective microstructure-dependent elastic properties (the Youngʹs modulus and the Poissonʹs ratio) of functionally graded materials (FGMs). Before applying VCFEM to FGM, the microstructure of FGM has been idealized as follows. At low volume fractions of either of the two materials in FGM, the microstructure is taken to consist of discrete particles embedded in a continuous matrix. In the region of FGM where the volume fractions of the two materials are comparable, the microstructure is taken to consist of intertwined clusters of the materials. In addition, for both types of microstructures, void inclusions are introduced to account for the porosity in FGM. Application of VCFEM to Ni/MgO and Ni3Al/TiC yielded the values of the effective elastic properties which are in significantly better agreement with the experimental values than the values predicted by the commonly used Eshelbyʹs equivalent inclusion method and the self consistent method.