2—PLANAR STRESS–STRAIN RELATIONSHIPS IN WOVEN FABRICS

Abstract

The planar stress-strain relationships of a simple trellis in which the elements are pivoted together where they cross over one another, but which do not pass under and over one another, are presented. It is shown that these relationships are identical with those tor an anisotropic elastic lamina which does not display a Poisson effect whea extended in either the warp or weft directions. Real fabrics do show the Poisson effect when stretched in these directions because of crimp interchange, and it is suggested that a fabric may be regarded as being equivalent to an anisotropic lamina which shows the Poisson effect and with two planes of symmetry at right-angles to one another. The discussion is restricted to plain woven fabrics. The relationship between the extensional modulus of the fabric in any direction and the shear modulus is discussed and its importance emphasized. The shortcomings of the theoretical model are mentioned. However, it is suggested that the study of the deviations in behaviour of a real fabric from that of the model should be of importance in studying yam interactions in a fabric.