Rubber models of yarns and cords: continuum theory

A theory of rubber-filament models of yarns is developed, using two alternative basic assumptions, namely 1, no lateral pressure between filaments, and 2, uniform lateral pressure between filaments. Treating the stress distribution as continuous, formulae are derived for the axial force and couple required to maintain a specified axial extension and torsion. It is shown that 2, though more complicated, is free from certain logical inconsistencies inherent in 1. Numerical examples show the increasing effect of lateral pressure with increasing axial extension. It is shown also that with increasing axial extension the behaviour of the model 2 approximates to the behaviour of a solid cylinder of rubber subjected to equivalent strains. The effects of torsion and bending of the filaments, neglected in the main treatment, are considered in an Appendix. It is shown that the couple arising directly from filament torsion is not necessarily negligible compared with the couple arising from tension along the filament axes, even when the ratio of filament radius to yarn radius is small.