Towards a Gauß-Seidel solver for problems involving line-to-line beam contact

In recent years interest in the simulation of systems with flexible slender structures ex-
periencing contact has grown significantly. At the heart of many implementations lie
beam models with rigid cross-sections which introduce nonsmoothness into the contact
model. Interactions between beams may occur along distributed regions of finite length
(line-to-line) or be viewed as pointwise interactions (point-to-point). In both cases the
distribution of contact forces can be discontinuous. The authors proposed a quasi static
frictionless mortar formulation for modeling the former [1]. The constraints are enforced
using an augmented Lagrangian approach. The dynamic case involves the handling of
discontinuous velocities and impacts. We therefore select the NSGA [2] time integration
scheme. It is based on a smooth prediction that excludes impact contributions and two
subsequent projection steps that correct for the non-penetration constraint at position
level and the velocity jump. In this contribution, we explore the idea of using a Gauß-
Seidel method [3] for solving the discrete beam-to-beam contact problem at each time
step. This type of iterative approach has proven robust in the context of rigid body
contact. All developments are made within the SE(3) local frame formalism for flexible
multibody systems.