Stress Concentrations in Filamentary Structures

Theoretical analyses are made of the stress distributions in a sheet of parallel filaments which carry normal loads and are imbedded in a matrix which carries only shear. In all cases, uniform loading at infinity is assumed and small-deflection elasticity theory is used. Static and dynamic stress-concentration factors due to one or more filaments being broken are determined. Particular attention is paid the dynamic overshoot resulting when the filaments are suddenly broken. The dynamic-response factor increases from 1.15 to 1.27 as the number of broken filaments is increased from one to infinity. A somewhat lower dynamic-response factor is obtained when a hole is suddenly caused in the filament sheet.