A unified periodical boundary conditions for representative volume elements of composites and applications

An explicit unified form of boundary conditions for a periodic representative volume element (RVE) is presented which satisfies the periodicity conditions, and is suitable for any combination of multiaxial loads. Starting from a simple 2-D example, we demonstrate that the "homogeneous boundary conditions" are not only overconstrained but they may also violate the boundary traction periodicity conditions. Subsequently, the proposed method is applied to: (a) the simultaneous prediction of nine elastic constants of a unidirectional laminate by applying multiaxial loads to a cubic unit cell model; (b) the prediction of in-plane elastic moduli for [+-(theta)]n angle-ply laminates. To facilitate the analysis, a meso/micro rhombohedral RVE model has been developed for the [+-(theta)]n angle-ply laminates. The results obtained are in good agreement with the available theoretical and experimental results.