Prediction of composite properties from a representative volume element

A vigorous mechanics foundation is established for using a representative volume element (RVE) to predict the mechanical properties of unidirectional fiber composites. The effective elastic moduli of the composite are determined by finite element analysis of the RVE. It is paramount in such analyses that the correct boundary conditions be imposed such that they simulate the actual deformation within the composite; this has not always been done previously. In the present analysis, the appropriate boundary conditions on the RVE for various loading conditions are determined by judicious use of symmetry and periodicity conditions. The non-homogeneous stress and strain fields within the RVE are related to the average stresses and strains by using Gauss theorem and strain energy equivalence principles. The elastic constants predicted by the finite element analysis agree well with existing theoretical predictions and available experimental data.