FEA in elasticity of random structure composites reinforced by heterogeneities of non canonical shape

One considers linearly elastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of aligned homogeneous heterogeneities of non canonical shape. Effective elastic moduli as well as the first statistical moments of stresses in the phases are estimated. The explicit new representations of the effective moduli and stress concentration factors are expressed through some building block described by numerical solution for one heterogeneity inside the infinite medium subjected to homogeneous remote loading. The method uses as a background a new general integral equation proposed in Buryachenko, 2010a and Buryachenko, 2010b, which incorporates influence of stress inhomogeneity inside the inclusion on the effective field and makes it possible to reconsider basic concepts of micromechanics such as effective field hypothesis, quasi-crystalline approximation, and the hypothesis of “ellipsoidal symmetry”. The results of this reconsideration are quantitatively estimated for some modeled composite reinforced by aligned homogeneous heterogeneities of non canonical shape. Some new effects are detected that are impossible in the framework of a classical background of micromechanics.