A New Aspect of Geometrical and Physical Principles Applicable to the Estimation of Textile Structures: An Ideal Model for the Plain-knitted Loop

Models of relaxed plain-knit structures proposed by previous researchers suffer from the disadvantage of being based on the arbitrary assumption of some geometrical shape for the knitted loop or subjected to the forces and couples applied to one loop by its neighbors. The work in this series of theoretical studies differs from previous studies. The classical curves that are similar to the knitted-fabric loop shape are considered as a function of an ideal model for a plain-knitted structure. The assumed function is then improved by adopting a buckled-elastic-rod theory, leading to a new equation as the ideal loop configuration. This analysis is presented for two- and three-dimensional models. These models obtain fabric dimensions. The resultant loop configuration is discussed in relation to experimental work previously done on relaxed plain-knit fabrics.