GEOMETRIC AND MECHANICAL MODELING OF WEFTKNITTED FABRICS USING HELICOID SCAFFOLDS

We present a bicontinuous, minimal surface (the helicoid) as a scaffold on which to define the topology and geometry of yarns in a weft-knitted fabric. Modeling with helicoids offers a geometric approach to simulating a physical manufacturing process, which should generate geometric models suitable for downstream analyses. The centerline of a yarn in a knitted fabric is specified as a geodesic path, with constrained boundary conditions, running along a helicoid at a fixed distance. The shape of the yarn’s centerline is produced via an optimization process over a polyline. The distances between the vertices of the polyline are shortened and a repulsive potential keeps the vertices at a specified distance from the helicoid. These actions and constraints are formulated into a single “cost” function, which is then minimized. The yarn geometry is generated as a tube around the centerline. The optimized configuration, defined for a half loop, is duplicated, reflected, and shifted to produce the centerlines for the multiple stitches that make up a fabric. The approach provides a promising framework for estimating the mechanical behavior/properties of weftknitted fabrics. Fabric-level deformation energy may be estimated by scaling the helicoid scaffold, computing new yarn paths, determining the amount of ensuing yarn stretch, and computing the total amount of yarn stretching energy. Computational results are calibrated and verified with measurements taken from actual yarns and fabrics.