Generalized plane strain finite element model for the analysis of elastoplastic composites

A numerical model is presented, based on the finite element method in its displacement formulation, aimed at the analysis of the representative volume element (RVE) of composites reinforced by a regular array of long, parallel fibers, subjected to any 3-D macroscopic stress or strain state. Special finite elements are formulated, which are capable of describing three-dimensional deformation modes associated with strain fields invariant along the fiber axis. Periodicity boundary conditions at the sides of the RVE complete the kinematic formulation. The model is applied to metal–matrix composites, assuming an elastic–perfectly plastic behaviour for both phases; the compatibility matrix of the finite elements is modified, according to proposals of other authors, to avoid locking phenomena near the fully plastic range. Some numerical applications are shown to illustrate the possibility of employing the model to predict the macroscopic response of metal–matrix composites in the non-linear field and up to failure. Comparisons with analytical and experimental results available in the literature testify the reliability of the model estimates.