A two-stage inverse method for the evaluation of volume fraction distributions in 2D and 3D functionally graded materials

In this article, an inverse method is proposed to determine the volume fraction distributions in functionally graded materials (FGMs). By determining the space-dependent volume fractions of the FGM phases, the properties of the FGMs are characterized. The proposed method, which is based on a steady-state thermal test, is applied in two stages. In the first stage, the two- or three-dimensional material is considered piecewise homogenous and its properties are found by a simple inverse analysis. In the second stage, the unknown volume fraction distribution is considered as a continuous function with several unknown parameters. Estimated values of these unknown parameters are found using the results obtained in the first stage and by another inverse analysis. The obtained results show that the presented method is efficient in estimating the volume fraction distributions in FGMs.