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A two-scale numerical approach to predict the effective in-plane properties of helical filament-wound thin-walled cylindrical tubes is provided. A meso-scale repeated unit cell (RUC) model for a filament-wound tube is established according to the manufacturing process, in which cross-overs, undulations and overlaps of fibre bundles are described using a bottom-up solid modelling technique. An approach to implement the general periodic boundary conditions in a finite element analysis scheme is also presented. As an application example, the effective in-plane elastic constants of glass fibre/epoxy filament-wound tubes are predicted and the influences of the number of the winding circuits and the shape of the fibre bundles are analyzed and discussed. In addition, the stress/strain distribution in the RUC is obtained which provides the essential information on the stress/strain concentration due to fibre cross-over/undulation/overlap. This then indicates the location where damage will initiate.

A micromechanical model of unidirectional fibre-reinforced polymer laminates under off-axis loading is analyzed using finite element method. A three-dimensional periodic unit cell is established with the matrix described by a nonlinear viscoelastic model and the fibre by an elastic one. Matrix cracking is modeled by smeared crack method which permits a crack description in terms of stress–strain relations and stiffness reduction in particular orientations. The micromechanical analysis features material nonlinearity, damage initiation and growth, and multiaxial loading. Numerical results reveal the local and global response of the laminate including the damage mechanism. The predictions are in good agreement with the test results performed on a similar composite system.

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 over-constrained 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 [± θ ] n angle-ply laminates. To facilitate the analysis, a meso/micro rhombohedral RVE model has been developed for the [± θ ] n angle-ply laminates. The results obtained are in good agreement with the available theoretical and experimental results.