New Method of Numerical Homogenization of Functionally Graded Materials

In the paper the method of numerical homogenization for FGM was proposed It was based on the method shown in Vemaganti and Deshmukh (2006), in which the gradient heterogeneous microstructure is divided into homogenous slices. In the presented study the model was built with the use of 2D elements, with two linear material models of Young modulus E=45 MPa and 748 MPa distributed in sample volume in accordance to linear and normal distributions. Firstly the RVE was calculated. Then the numerical homogenization was carried out with the division of the heterogeneous sample into 4, 5 and 8 slices. The substitute material characteristics were calculated and implemented into sliced model. The numerical compression tests of the sliced and heterogeneous models and were compared. The conclusion was that the more slices we apply the more exact results we will get. This selection should be based on the accuracy we want to get and on the computational capacity we have. Also in this kind of modeling we cannot asses the stress distribution in microstructure.