An Optimized Yarn-Level Geometric Model for FEA Simulation of Weft-Knitted Fabrics Paras Wadekar, Eric Markowicz, Dani Liu, Genevieve Dion, Antonios Kontsos, David Breen 1 1 Drexel University, Philadelphia, PA USA Abstract Knitted fabrics are widely used in clothing and advanced tex- tile devices because of their unique and programmable mechan- ical properties. In order to better understand and control these properties it is necessary to investigate the influence of yarn level interactions and stitch structure on the macroscropic be- havior of the fabric via computational simulation, e.g. Finite Element Analysis (FEA). In this paper, we present a yarn-level model that produces geometric models suitable for FEA simu- lations of knitted fabrics. The geometric models of the yarns are produced via an optimization process. The centerlines of the yarns are defined as Catmull-Rom splines and their control points are modified during the optimization. The optimization is based on physical parameters such as interpenetration, con- tact, length of the yarn and bending energy. The results show that our approach produces valid yarn geometric models of knit- ted fabrics consisting of an arbitrary combination of knit and purl stitches, which can then be used for FEA simulations. 1 Introduction The modelling and simulation of textiles has gained increased interest in recent years. These simulation efforts include the modelling and analysis of both woven and knitted materials. Our research focuses on advancing knitted textiles as a sub- strate for next-generation smart fabrics. A major thrust of this research is the development of design tools that will au- tomate the specification of optimized knitted structures. A critical component of these tools are modelling and simulation technologies that are capable of accurately predicting the prop- erties of a knitted material, given the properties of its yarns and the stitch patterns/commands used to knit the yarns into a fab- ric. To attain these goals simulations of knitted materials are done at the yarn-level using Finite Element Analysis (FEA) [5, 6]. A critical component of these simulations are the geometric models that define the initial configuration of the fabrics. In order for the simulations to properly proceed these geometric models must meet stringent requirements. The most impor- tant feature of the models is how they define contact between crossing yarns. Crossing yarns must “touch” at two points, but must not inter-penetrate each other. These contact points are defined by yarns that are outside of each other, but are within an extremely short distance to each other. A secondary requirement is that the initial geometric models by “plausi- ble”, i.e. they should not have unnatural, sharp bends or self- intersections. A number of geometric models have been developed for knit- ted fabric simulation [2, 3, 4]. Other simulation models have been based on the topology of the fabric [1, 7]. None of these models though meet the strict contact requirements demanded by FEA in a general, parameterized approach. In order to produce valid initial geometric conditions for FEA simulation studies we have implemented an enhanced yarn-level model of knitted fabrics that incorporates mechanical prop- erties and spatial constraints with the underlying geometric representation of the yarns; thus producing initial parameter- ized geometric models that not only do not interpenetrate, but touch each other at point contacts, and additionally have a fea- sible, physically-accurate overall shapes. Our techniques pro- duce yarn-level geometric models of weft-knitted fabrics con- sisting of an arbitrary pattern of knit and purl stitches. The dimensions of these individual stitches may be set by the user. Together these features allow for the generation of a wide va- riety of yarn-level geometric models that support the inves- tigation of the relationship between yarn-level structures and macroscopic mechanical properties. Producing physically-accurate geometric models of yarns in a knitted material is framed as an optimization problem. In this computing context, a single “cost” function is defined that captures the various required features of the final geometric model. The function is specified in such a way that finding the variable values that minimize the function produces the desired geometric result [8]. The features incorporated into the model, and therefore the associated cost function, include maintaining yarn length, minimizing curvature and creating single contact points between crossing yarns. The variables that are modified to minimize the cost function are the spline control points that define the centerlines of the tubes used to represent the yarns. Once the optimization problem is formulated for a particular set of fabric parameters the cost function is minimized using a quasi-Newton method, which produces a spline that meets the requirements and constraints of the specified FEA initial conditions. This model has been utilized as the inputs to nu- merous FEA simulations of knitted materials. A number of output examples from the optimization process for a range of material size parameters are provided, which demonstrate the effectiveness of our approach to produce geometric models that are suitable initial conditions for FEA simulations. 2 Optimized Model Since a fabric consists of repeated stitches our approach focuses on defining and optimizing the geometry of individual stitches, rather than the more computationally costly strategy of laying out the whole fabric and doing a global optimization. Once optimized, specific stitches, which we call cells, are replicated to produce the entire fabric. In order to maintain continuity between replicated cells, precise boundary conditions, both po- sitional and tangential, must be defined and maintained for each cell. 1