Robust eulerian-on-lagrangian rods

Fig. 1. Simulation of three yarn-level tablecloths stacked on top of each other. We handle both intra-fabric and inter-fabric contacts implicitly with our novel Eulerian-on-Lagrangian (EoL) simulation. Frictional contact is correctly handled, even under extreme sliding and crossing of yarns. We introduce novel EIL nodes to handle robustly pervasive degeneracies in the discretization. The rightmost image shows the soup of nodes around the edge of the table. White dots represent contacts between standard EoL nodes, red dots contacts between our novel EIL nodes, and pink dots contacts between EoL and EIL nodes.

This paper introduces a method to simulate complex rod assemblies and stacked layers with implicit contact handling, through Eulerian-on-Lagrangian (EoL) discretizations. Previous EoL methods fail to handle such complex situations, due to ubiquitous and intrinsic degeneracies in the contact geometry, which prevent the use of remeshing and make simulations unstable. We propose a novel mixed Eulerian-Lagrangian discretization that supports accurate and efficient contact as in EoL methods, but is transparent to internal rod forces, and hence insensitive to degeneracies. By combining the standard and novel EoL discretizations as appropriate, we derive mixed statics-dynamics equations of motion that can be solved in a unified manner with standard solvers. Our solution is simple and elegant in practice, and produces robust simulations on large-scale scenarios with complex rod arrangements and pervasive degeneracies. We demonstrate our method on multi-layer yarn-level cloth simulations, with implicit handling of both intraand inter-layer contacts.