Model for defective fibrous composites

We consider the problem of modeling fibrous composite materials which have defective regions in their microstructure. These defects take the form of either local fiber spreading or local fiber clumping. Due to the number of fibers, the problem requires an asymptotic analysis and so we develop a mathematical theory of homogenization for defective microstructures. In order to understand the effect of such defects on the overall behavior of the composite, we solve a global boundary value problem. We then combine the results from this global analysis with our homogenization to show that even when the defective region is very small, substantial increases in the constituent stresses occur.