An approach for predicting the elastic modulus of heterogeneous materials

This paper presents a numerical method for the calculation of the elastic modulus of heterogeneous materials with a continuous matrix, including discontinuous inhomogenity. The effects of the shape, orientation, and arrangement of the inhomogenity were estimated. For an existing heterogeneous material, microstructural geometry was taken into consideration using a simple geometrical parameter for the inhomogenity and the representative volume element (RVE) in which the inhomogenity was embedded. Elastic moduli, predicted using a numerical method, in the case of voids and rigid inhomogenity were in very good agreement with results obtained by the Mori–Tanaka method (MTM), which gives the elastic moduli for the case of an ellipsoidal-shaped inhomogenity. The numerically predicted elastic moduli presented here were also in very good agreement with the results of finite element analysis for different cases of inhomogenity, such as the simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), close packing hexagonal (CPH) type regular arrangements and random distributions. There is an important advantage to the numerical method presented here, as it allows systematic- and parametric investigation of effects of microstructural geometry on the elastic modulus of a heterogeneous material. In order to design a heterogeneous material with an optimal microstructural architecture or tailor a specific elastic modulus, the numerical method proposed in this study can quickly provide information and allows easy implementation of calculations.