Strong Influence of a Small Fiber on Shear Stress in Fiber-Reinforced Composites

In stiff fiber-reinforced material, the high shear stress concentration occurs in the narrow region between fibers. With the addition of a small geometric change in crosssection, such as a thin fiber or a overhanging part of fiber, the concentration is significantly increased. This paper presents mathematical analysis to explain the rapidly increased growth of the stress by a small particle in cross-section. To do so, we consider two crucial cases where a thin fiber exists between a pair of fibers, and where one of two fibers has a protruding small lump in cross-section. For each case, the optimal lower and upper bounds on the stress associated with the geometrical factors of fibers is established to explain the strongly increased growth of the stress by a small particle. MSC-class: 35J25, 73C40