Robust eulerian-on-lagrangian rods

Abstract

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 intra-and inter-layer contacts.

Cosserat Rod with rh‐Adaptive Discretization

“…in yarn‐level cloth simulations. While such scenarios are not common in our experiments, integrating the techniques of [SBRBO20] into our method is definitely an elegant alternative to resolve the infinitely large stiffness.…”

“…However, these approaches are arguably limited in adaptivity brought by Eulerian coordinates, seemingly going in an opposite way as r ‐adaption intends. Targeting at numerical conditioning, a recent work [SBRBO20] introduced a special type of nodes to avoid infinitely large stiffness resulted from tiny segments, which can be also empirically solved by collapsing tiny segments in each step.…”

“…A similar situation could also happen to highly curved region due to node sliding. As system advances, these tiny segments are probably no longer critical to capture sharp features on a rod, but instead might make the system infinitely stiff [SBRBO20]. Therefore, considering both numerical conditioning and computational efficiency, we technically collapse all tiny line segments in practice as [SJLP11] did, as long as the segment length is smaller than a given tolerance relevant to the length scale used for collision detection.…”

“…For instance, the augmented Lagrangian method is probably worth trying. The inspiring idea of statics‐dynamics separation in [SBRBO20] is also an interesting direction to explore.…”

A Bending Model for Nodal Discretizations of Yarn‐Level Cloth

“…They modeled yarns as flexible rods, and added sliding degrees of freedom at yarn crossings, allowing complex plastic effects, such as snags. Recently, Sánchez-Banderas et al [SBRBO20] have improved the discretization of persistent contacts, extending the applicability of the model to more complex fabrics. Earlier, they also improved the damping behavior of yarn-level models, making it more controllable [SBO18].…”