2D Finite element model for the analysis of elastic-plastic composites subjected to 3D stresses

This work deals with the prediction of the macroscopic response of ductile composites reinforced by a regular array of long, parallel fibers, subjected to any 3D stress, in the plastic range and up to failure. This task is accomplished through a micromechanical approach, based on homogenization theory for periodic media. Special finite elements are formulated to analyze any cross-section of the Representative Volume of the material (a prism of unlimited length, embedding a single fiber) under ‘generalized plane strain conditions’ (i.e., with strain fields invariant along the fiber axis). Particular kinematic conditions are enforced along the boundary of the model to accommodate the periodicity of the microscopic strain field. Such a model turns out to be definitely advantageous in terms of allocated memory and number of kinematic constraints to be enforced, in comparison with fully 3D finite element models. Its effectiveness is assessed in predicting the macroscopic response of MMCs beyond the elasticity limit, until a macroscopic yielding is detected. The numerical results match available theoretical and experimental results with a fair degree of accuracy.