Abstract: Knitted cloth is made of yarns that are stitched in regular patterns, and its macroscopic behavior is dictated by the contact interactions between such yarns. We propose an efficient representation of knitted cloth at the yarn level that treats yarn-yarn contacts as persistent, thereby avoiding expensive contact handling altogether. We introduce a compact representation of yarn geometry and kinematics, capturing the essential deformation modes of yarn loops and stitches with a minimum cost. Based on this representation, we design force models that reproduce the characteristic macroscopic behavior of knitted fabrics. We demonstrate the efficiency of our method on simulations with millions of degrees of freedom (hundreds of thousands of yarn loops), almost one order of magnitude faster than previous techniques.