Contact-friction modeling within elastic beam assemblies: an application to knot tightening

In this paper we propose a finite element approach which simulates the mechanical behaviour of beam assemblies that are subject to large deformations and that develop contact-friction interactions. We focus on detecting and modeling contact-friction interactions within the assembly of beams. Contact between beams-or between parts of the same beam in the case of self-contact, is detected from intermediate geometries defined within proximity zones associating close parts of beam axes. The discretization of contact-friction interactions is performed on these intermediate geometries by means of contact elements, constituted of pairs of material particles which are predicted to enter into contact. A 3D finite strain beam model is used to represent the behaviour of each beam. This model describes the kinematics of each beam cross-section using nine degrees of freedom, and is therefore able to represent plane deformations of these cross-sections. Algorithms are proposed to solve the global nonlinear problem using an implicit scheme, under quasi-static assumptions. Simulation results of the tightening and releasing of knots made on monofilament and multifilament yarns are shown as an application. Straight fibers are first twisted together to make a yarn, before suitable conditions are applied to their ends to form and tighten the knot. Tightening forces are finally released to obtain an equilibrium configuration of the knot without external forces.