Bending Rigidity of Fabrics

Abstract

This article presents a theoretical equation on the bending rigidity of fabrics by treating yarn as a wavy beam whose apparent Young's modulus, cross section area, cross section coefficient and axial curve are E, S, κ and V(x), respectively (see Fig. 2).When the distribution of the pressure of contact between warp and weft can be expressed by the functions (FAx(x), FAy(x)) and (FRx(x), FBy(x)), bending rigidity K of fabrics is K=N/∫2b-2b{1+1/κ(x)}{1+v'(x)2}-5/2 v''.x)2dx{4bES-ρe(CA+CB-DA-DB)} where N is yarn density per unit width; 4b is the wave length of yarn;ρe is the radius of curvature of a bent fabric; CA, CB, DA and DB are terms originating from the pressure of contact and are reduced to eq. (12-3).The above equation shows that the bending rigidity of a fabric is divisible into the bending rigidity of yarn and the terms originating from the interaction between warp and weft. Calculations of K have been made by this equation to determine several given axial curves and distributions of the pressure of contact.