Theory of the Shear Deformation of Fibrous Assemblies

Abstract

The initial response of the unit fibrous cell to an externally applied shear stress is assumed to involve both the bending of fiber sections and slippage at contact points. The criterion used to determine whether a contacting fiber will bend the contacted fiber section or whether it will slip along it depends on the relative angles of the two fiber sections to the external stresses. The total proportion of slipping and nonslipping contact points is thus derived using the density function of fiber orientations within the unit fibrous cell. The derived modulus values for shear behavior are related to the moduli derived earlier for compression behavior. The symmetry rules for selected idealized orientation distributions (e.g., random) of the fibers in the unit cell provide a check on the validity of the derivations.