Quasi-Static Cosserat Rods in Contact With Implicit Surfaces

We propose a method for the quasi-static solution of Cosserat rods in contact with implicit surfaces. By leveraging the strain parameterization reduction approach, the quasi-static evolution is computed by solving an ordinary differential equation (ODE). To address the inherent stiffness of the ODE, we employ implicit solvers and derive the Jacobian matrix analytically. The smoothness of the functions defining our contact surfaces enables the use of implicit solvers. Numerical results show the stability of the proposed method in challenging contact scenarios, as well as improvements in computational time by two orders of magnitude compared to the use of explicit solvers. Our implementation is open-source and can be found at gitlab.inria.fr/rjilani/ral2024.