A new mathematical model describing a plain knitted fabric is proposed in this paper.One major feature of this model is that the yarn in the fabric can be naturally curved with nonlinear mechanical properties. The new model is able to describe the dimensions and also the low stress mechanical properties of a plain knit. Based on an energy analysis, the inadequacy of the classic k -values is explained. Complex dimensional behavior and problems associated with relaxation of knitted fabric are discussed. A more precise prediction of fabric dimensions is possible by including the degree of set as one of the parameters. The paper also explains why most of the studies of knitted fabric dimensional properties in the past have been empirical.Fabrics knitted from cotton are a very popular, and thus very important to the textile industry. Cotton, being a nonthermoplastic fiber, is unable to be heat set. This category of knitted fabrics will relax naturally after knitting, resulting in changing fabric dimensions. Due to the nature of the knitting process, the fabric is knitted under high stress and extension. Therefore, grey cotton fabrics off the machine will exhibit large and varied amounts of shrinkage. Measurements of shrinkage in grey fabrics are therefore of little value to fabric finishers. What is of value is the reference state of the fabric. This reference state acts as a target of the norm for assessing fabric dimensional behavior.In attempts to understand the dimensional behavior of knitted fabrics, the key element is the geometry of the knitted loop. Pierce [21 ], Shinn 1271, Leaf [ 13, 14, 15], Doyle [4, 51, Munden 120], Postle 122, 23], and recently Demiroz et al. [3] have all significantly contributed to the geometric analysis of plain knitted fabrics. In particular, Leafs geometric model [15] has aroused the interest of composite engineers [24]. The success of that model is due to its simplicity and a good description of the actual fabric. Recent innovative work (3J on loop geometry has used spline curves to represent the loop, which is especially useful in the visual display of knitted fabrics on a CAD system. Yarn jamming in a knitted fabric has long been identified as a major factor determining its the dimensional and mechanical properties. Knapton et al. III) ] concluded . 1 1 -that the stability of a cotton loop is reached when yarn bulking is restricted by yarn jamming. Alternatively, the dimensional properties of knitted fabrics were studied by some researchers [8. 23, 25] using the force method. In the theoretical models of Postle et al. [23], Shanahan et al. [25], and Hepworth et al. [8], yarn was treated as an elastica [ 18] that is naturally straight. MacRory et al. [ 19) and Hepworth [91 attempted to tackle the biaxial load-extension problem of knitted fabrics. MacRory's model emphasized slippage between loops and the biaxial load case with the loop elements being straightened, while Hepworth's model concentrated on the effect of yarn jamming. &dquo;Extensive experimental works have been accom...
