An Impulse-Based Contact Framework for Dynamic Simulation of Slender Rods

  • Kusuma Chandrashekhara, Sudhanva (Fraunhofer ITWM)
  • Roller, Michael (Fraunhofer ITWM)
  • Schneider-Jung, Fabio (Fraunhofer ITWM)
  • Linn, Joachim (Fraunhofer ITWM)

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Fast and robust handling of contact interactions is a critical challenge in dynamic simulations of slender structures such as cables, hoses and wire bundles which undergo large geometric deformations and frequent interactions with surrounding geometries or themselves. Traditional approaches often require problem-dependent tuning of artificial stiffness / regularization parameters, and often impose severe restrictions on time step sizes, limiting their applicability to a large-scale dynamic scenario.In this work, we present an impulse-based collision framework for geometrically exact Cosserat rod dynamics that enables handling of rod–rod and rod–environment contact without regularization. This work is inspired by [1]. The underlying rod dynamics are modeled using the geometrically exact beam formulation proposed in [2], and Linear Implicit Euler time integration has been adopted, following [3], while contact interactions are incorporated as external forces that enforce non-penetration between colliding bodies. Contact constraints are formulated at the velocity level using unilateral complementarity conditions, ensuring that contact impulses are generated only when a relative normal motion indicates interpenetration. Rod segments are represented using a capsule-based geometric approximation, which allows the computation of gap, contact normals, and closest points between interacting bodies. The resulting set of contact constraints lead to a linear complementarity problem, which is solved iteratively using Projected Gauss–Seidel (PGS) method that solves for contact impulses while accounting for restitution effects. The contact impulses are then consistently mapped to nodal forces and segment moments enabling a unified treatment of segment interior and vertex contacts. The proposed framework supports multiple simultaneous contacts and evolving contact topologies. The effectiveness of the proposed methodology in robust and fast collision handling is demonstrated using several numerical examples. 1.Tschisgale S., Thiry L., Frölich J., A constraint-based collision model for Cosserat rods, Archives of Applied Mechanics, Vol. 89, pp. 167-193, 2019. 2.Lang H., Linn J., Arnold M., Multi-body dynamics of geometrically exact Cosserat rods, Multibody System Dynamics, Vol. 25, no.3 pp. 285-312, 2011. 3.Burgermeister B., Linear-implizite Zeitintegrationsverfahren für differentiell-algebraische Systeme in der Mehrkörperdynamik, PhD thesis, Martin Luther Universität, 2009.