Strong influence of a small fiber on shear stress in fiber-reinforced composites

In stiff fiber-reinforced composites, it has been known that the shear stress increases at the rate of as the distance between adjacent fibers approaches 0. This paper reveals a strong influence of a combination of a triple fiber, as well as the distance between a pair of fibers, on the blow-up so that the stress concentration can be significantly accelerated by adding a small fiber in-between fibers. Specifically, if a fiber with a small diameter δ is located in-between fibers and , and , then the stress blows up at the exact rates of and between and and between and , respectively. This estimate still holds even when a part of overlaps with . The magnification factor yields the enormous increase in the stress that greatly surpasses the expectancy by previous methods.