Effects of the Fibers' Shape and Volume Fraction on the Strength of Ideally Plastic Fiber Reinforced Composites

We consider fiber reinforced composites where both the matrix and the fibers are ideally plastic materials. We restrict our attention to microstructures and applied stresses that lead to both microscopic and macroscopic antiplane shear deformations. We describe a bound we have recently obtained on the yield set of the composite in terms of the shape of the fibers, their volume fraction, and the yield set of the matrix. We construct examples of composites showing that our bound is essentially optimal.