Computation of Elastic Constants of Functionally Graded Materials Using Eigenfunction Virtual Fields Method

The Virtual Fields Method (VFM) is a technique for computing material properties from full-field data. Recently, a variant of this technique, called Eigenfunction Virtual Fields Method (EVFM) has been proposed and applied to homogeneous linear elastic property evaluation. In this work, we extend this technique to heterogeneous materials by applying it to linear elastic material with exponentially varying elastic modulus. For such materials, there are three constitutive parameters to be evaluated: an elastic modulus, the Poisson’s ratio and a material length scale parameter β that controls spatial variation of the elastic modulus. We consider a plate made of such a material, with a circular hole, subjected to uni-axial tension in this study. The elasticity solution to this problem is synthesized using FEM, and strain fields in the vicinity of the hole are obtained on a rectangular grid. These strain component fields are assembled into an augmented strain matrix, whose eigenfunctions are obtained through Principal Components Analysis (PCA). EVFM is then performed using these eigenfunctions as virtual fields and solution of the resulting system of nonlinear equations yields values for the material parameters that are in excellent agreement with the true values.