Probing into classical theory of yarn cross-section shape of plain woven fabric and its generization

The cross-section of yarn of plain woven fabric has always been viewed as a regular shape by academe.Based on classical convex model,with visualization technology,problems in the classical model are found,i.e.,when solving the problems with calculus,the rule of yarn cross-section deformation is found.The results show that the diversity of the yarn cross-section shape in both one-layer and multi-layer woven fabrics,instead of single one,especially for the warp binding multi-layer wefts,whose concave cross-section alternates with convex one periodically along lengthwise.The findings take exception to ″invariant cross-section assumption″ and have theoretical value and guidance for research on the real shape of yarns and the simulation of fabric appearance.