Mathematical model and analysis of the strength of particle reinforced ideally plastic composites

Abstract

We consider fiber reinforced ideally plastic composites. We analyze a mathematical model valid for microstructures and applied stresses that lead to both microscopic and macroscopic anti-plane shear deformations. We obtain a bound on the yield set of the reinforced material in terms of the shapes of the cross section of the fibers, their volume fraction, and the yield stresses of the matrix. We construct examples showing that our bound is sharp.