On the Flexure of Elastic Two-Filament Yarns

Abstract

Problems in the flexural deformation of yarns are studied for better understanding of the mechanical behavior of woven fabrics. Our investigation will focus on an elastic two-filament yarn. Two cases are considered, namely: (1) the pure bending of a yarn, and (2) the lateral deflection of a cantilever yarn introduced by a transverse force applied at its end. The filaments in the yarn are treated as slender curved rods. The linear theory of elastic slender curved rods is employed in our analysis. The deformation of the yarn is determined by the energy method. It is found that the contact force between the filaments is zero. Hence, the flexure of the yarn can be studied from the analysis of a single filament.