Averaging and finite-element discretization approaches in the numerical analysis of functionally graded materials

Thermomechanical properties and responses of dual-phase functionally graded materials have been estimated by conventional averaging approaches, such as rules of mixtures, mean-field micromechanics and so on. However, the appropriateness of such models has been recently reported to be questionable. In this paper, we numerically investigated three representative averaging estimation methods, the linear and modified rules of mixtures and the Wakashima–Tsukamoto estimate, by comparing with the finite-element discretization approach utilizing rectangular cells. Through numerical experiments for the elastic and thermoelastic response of Ni–Al2O3 functionally graded materials (FGMs), we presented comparative results together with introduction of a suggestive approach.