Plane strain limit analysis of periodic fiber-reinforced composites

A numerical model was developed to predict the macroscopic strength of metal matrix composites reinforced by long parallel fibers. The model is based on the application of the kinematic approach of classical limit analysis to homogenization theory for periodic media. The collapse factor for any macroscopic stress acting in a plane transverse to the fibers is computed through an iterative process that reduces the relevant stationarity problem of a nonlinear functional to a sequence of linear problems. The functional is discretized by finite elements that accommodate incompatible (or ‘enhanced’) strain rates, thus avoiding ‘locking’ problems associated with the plastic incompressibility constraint in plane strain conditions. The advantages of the proposed model are illustrated by comparisons with the results of other authors and those of incremental analyses.