Prediction of the elastic tensor of 3D composites by an analytical model

The aim of this study is the determination of the overall elastic tensor of two 3D composites. These materials have a multiscale architecture. The representative volume element of the composite architecture (symbolised by a unit-cell) is composed of three bundles in three orthogonal directions and two matrix pockets. Each bundle is a unidirectional composite formed by a juxtaposition of long fibres surrounded by the matrix. Due to their symmetry, the bundles are considered transversally isotropic according to the fibres axis, whereas the pockets are macroscopically isotropic. The analytical computation is produced in two steps. The first step consists of determining the elastic tensor of the bundles. The second step is the calculation of the elastic tensor of the whole composite. The most part of the used equations comes from bibliography, excepted the determination of shear coefficients of the composite. The last part of this study devoted to the influence of material parameters presents the relative role of the fibres, the matrix and their volume fraction.