Continuum Mechanics of the Fiber Bundle

Abstract

The extent to which the methods of continuum mechanics may be used to model the mechanical properties of an idealized unit cell of untwisted but aligned fibers has been explored. An important question is the extent to which the continuum assumptions are applicable to a unit cell of fibers and the restrictions that exist with regard to interpolation of continuum solutions. The symmetry properties of the fiber bundle are used to show that, for small strains and linear elastic behavior, the fiber bundle might best be characterized mechanically as a degenerate square- symmetric homogeneous continuum, which is fully defined by six independent elastic constants. None of the existing yarn models includes all six of the elastic constants needed for a rigorous small-strain linear analysis; however, nearly all deformations of textile interest involve both large strains and nonlinear material deformation, and some of the difficulties involved in representing the constitutive properties of the material are discussed, using a tangent compliance matrix. The novel test methods needed indicate that the fiber bundle has various fundamental properties that have little relation to those of single fibers. The development of better test procedures for the key continuum parameters and consequent improve ments in the modeling of both mechanical and geometrical nonlinearities are seen as important stepping stones to improved modeling of the mechanics of textile structures.