Modelling of the low stress properties of plain knitted fabric

In the attempts of understanding the dimensional behavior of knitted fabrics, the key element is on the geometry of the knitted loop. Starting from Pierce, Shinn, Leaf, Doyle, Munden, Postle and recently Demiroz et al, they all have significant contributions to the geometrical analysis of plain knitted fabric. In particular, Leaf's geometric model has aroused the interests of the composite engineers. The success of the model is due to its simplicity and a good description of the actual fabric. The recent innovative work on loop geometry is the application of spline curves to represent the loop. It is especially useful in the visual display of knitted fabric in a CAD system. Jamming of yarn in a knitted fabric has long been identified as a major factor determining the dimensional and mechanical properties of the fabric. Knapton et al concluded that stability of a cotton loop is reached when yarn bulking is restricted by yarn jamming. A new knitted fabric mechanical model proposed is described in this paper which is an energy model with sufficient degrees of freedom for loop deformation, including changes in loop height and width. The yarn forming the loops is perfectly elastic and incompressible with zero friction. It is naturally curved and its paths in the deformed states are the elements of a prescribed family of space curves. This model can be applied to determine the biaxial tensile behavior of plain knitted fabric. The yarns can be axially compressed or extended at the low load region. Conditions of loop jamming are taken as the geometric constraints of loop deformation.