The shape and orientation effects of inhomogeneity on the elastic modulus of continuous matrix including discontinuous inhomogeneities

A numerical method is presented in this paper for elastic modulus calculation of heterogeneous material having continuous matrix including discontinuous inhomogenity. The effect of shape and orientation of inhomogenity were estimated. For an existing heterogeneous material, microstructural geometry was taken into consideration with a simple geometrical parameter for microstructure of heterogeneous domain. Elastic moduli predictions of numerical method belonging to the cases of void, elastic and rigid inhomogenity were very good agreement with MTM results which give elastic moduli for the case of ellipsoidal shaped inhomogenity. Numerical method presented can consider the shape and orientation effects of inhomogenity via a simple parameter named geometrical factor (Gf). Gf value varies from 0 to 1 and indicates stress-strain distribution conditions in the components of heterogeneous domain. If stress-strain distributions in the components of heterogeneous domain close to parallel loading condition, Gf value becomes close to 0. If stress-strain distributions close to serial loading condition, Gf value becomes close to 1. There is important advantage of numerical method presented that allows systematic and parametric investigation of effects of microstructural geometry on the elastic modulus of heterogeneous material. In order to design a heterogeneous material having optimum microstructural architecture or tailoring the specific elastic modulus, numerical method presented in this study can provide quick information and easy implementation for respected calculations.