SOLID MODELING OF YARN AND FIBER ASSEMBLIES

Fibers are the basic structure in yarns, and yarns are basic structure for fabrics. Although the approach described can be applied easily and naturally to fibers, especially when dealing with composite-material fabrics, the applications presented are thought of primarily as yarn-based assemblies. Hence, when talking about the developed model, 'yarn' and 'fiber' can be thought of as interchangeable. In general, fabric models assume underlying yarns to be of zero thickness. Those who have looked at yarns as three-dimensional structures have limited themselves to simple geometric arrangements of the yarns or have used assumptions which are non-geometric in order to simplify the model. A basic model is proposed which treats a yarn as a true three-dimensional solid object. This approach is first applied to three yarns twisted to form a rope-like bundle. Next, the technique is used to model a woven fabric; the Peirce geometry is analyzed, and then the model is extended to look at fabric shear. An approach for a three-yarn braid is presented as the most recent work.