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.

Indentation of hairy surfaces: Role of friction and entanglement

“…When a fibre assembly is compressed, the number of contacts of a fibre with others increases and the length of segment between contacts decreases; since a short segment is stiffer than a long one, the compression force is a nonlinear function of φ [27]. The interactions at contact points also have an influence on the curve (slippage, jamming, adhesion) [25,30]. Durville found better agreement with van Wyk's model for nine randomly generated samples of entangled materials as the crimp of fibres was higher [29].…”

“…Since the late seventies, hysteresis has been primarily related to the fibre-to-fibre friction and slippage which generates the reorganisation of the fibres in the arrangement which may well have a viscous behaviour, even if a fibre has an elastic behaviour [30,38,39]. In 1979, Dunlop demonstrated the importance of slippages between fibres using acoustic measurements; in 1983, he scanned the assumption of viscosity as the hysteresis was independent of the rate of compression.…”

“…Curiskis performed compression tests with and without a chamber to hold the fibres for which the difference is obvious; for the same transverse strain, it was necessary to apply a greater transverse stress with a chamber than without [30]. Rees showed that friction between the fibres and the cylinder wall introduce errors into the determination of resilience (ability of the fibres mass to recover from compression), even if the cylinder wall is polished [44].…”

The Tangent Compliance of Staple-fibre Bundles in Tension

“…In a previous paper [1], the present authors described the task of defining the mechanical properties of an oriented "fibre bundle" so that its behaviour might be analysed by using the methods of continuum mechanics. By "bundle", the authors mean an untwisted assembly of fibres, such as a sliver, in which the fibres have a preferential orientation parallel to the axis of the bundle.…”

“…The incremental form of the constitutive law for the bundle may be written as: Ae = [C,J(CQ, EQ)] ACT (1) where Ae and Aa represent current increments of strain and stress, respectively, and is the tangent-compliance matrix whose terms are dependent on the stress (c^) and strain (EQ) states prior to the application of the increment. The non-zero entries in [C^ (c^, EQ)] can be related to various uniaxial tests such as compression normal to ttie direction of preferential fibre orientation or extension in the fibre (i.e., bundle) direction.…”