Estimation of Effective Elastic Properties of Random Structure Composites for Arbitrary Inclusion Shape and Anisotropy of Components Using Finite Element Analysis

We consider a linearly thermoelastic composite medium of arbitrary anisotropic constituents, which consists of a homogeneous matrix containing a statistically homogeneous random set of inclusions of any shape, orientation, and inhomogeneous microstructure. We use the main hypothesis of many micromechanical methods, according to which each inclusion is located inside a homogeneous so-called "effective field," accompanied by the quasi-crystalline approximation describing the inclusion interactions. We estimate effective elastic properties of composites and statistical averages of stresses, which are in general inhomogeneous in the inclusions. The proposed analytical numerical method is efficient from a computational standpoint and is based on the use of the finite element analysis implemented for the one-particle problem in the infinite-homogeneous matrix with forthcoming incorporation of the stress concentrator tensors found in the known analytical homogenization scheme of micromechanics described above. The method is presented for both two- and three-dimensional problems, but the numerical examples are carried out just for plane strain and plane-stress problems.