Finite Biaxial Extension of Completely Set Plain Woven Fabrics

Abstract

This paper is concerned with the analysis of the finite biaxial extension of completely set plain woven fabrics with the yarns treated as curved rods. The undeformed configuration of the yarn is assumed to consist of segments of elastica resulting from deformed cantilevers under transverse end loads. In the undeformed state, there is no residual stress in the yarn. During deformation of the fabric, yarns are subjected to extension and bending. The mechanical behavior of the yarn is regarded as linearly elastic in extension. However, for the flexural deformation, due to loss in friction between fibers, the moment-curvature relation is bilinear. A nonlinear boundary-value problem can be formulated for the finite biaxial extension phenomenon of the fabric. Numerical solutions are sought by a trial and error procedure.