Implicit Contact Model for Discrete Elastic Rods in Knot Tying

Implicit Contact Model for Discrete Elastic Rods in Knot Tying. Choi, A., Tong, D., Jawed, M. K., & Joo, J. Journal of Applied Mechanics, February, 2021.

Paper doi abstract bibtex

Rod-rod contact is critical in simulating knots and tangles. In order to simulate contact, typically a contact force is applied to enforce non-penetration condition. This force is often applied explicitly (Euler forward). At every time step in a dynamic simulation, the equations of motions are solved over and over again until the right amount of contact force successfully imposes the non-penetration condition. There are two drawbacks: (1) Explicit implementation brings numerical convergence issues. (2) Solving equations of motion iteratively to find this right contact force slows down the simulation. In this paper, we propose a simple, efficient, and fully-implicit contact model with high convergence properties. This model is shown to be capable of taking large time steps without forfeiting accuracy during knot tying simulations when compared to previous methods. We introduce “contact energy” and express it as a differentiable analytical expression with the four nodes of the two contacting edges as inputs. Since this expression is differentiable, we can incorporate its force (negative gradient of the energy) and Jacobian (negative Hessian of the energy) into the elastic rod simulation.

@article{choi_implicit_2021,
	title = {Implicit {Contact} {Model} for {Discrete} {Elastic} {Rods} in {Knot} {Tying}},
	issn = {0021-8936},
	url = {https://doi.org/10.1115/1.4050238},
	doi = {10.1115/1.4050238},
	abstract = {Rod-rod contact is critical in simulating knots and tangles. In order to simulate contact, typically a contact force is applied to enforce non-penetration condition. This force is often applied explicitly (Euler forward). At every time step in a dynamic simulation, the equations of motions are solved over and over again until the right amount of contact force successfully imposes the non-penetration condition. There are two drawbacks: (1) Explicit implementation brings numerical convergence issues. (2) Solving equations of motion iteratively to find this right contact force slows down the simulation. In this paper, we propose a simple, efficient, and fully-implicit contact model with high convergence properties. This model is shown to be capable of taking large time steps without forfeiting accuracy during knot tying simulations when compared to previous methods. We introduce “contact energy” and express it as a differentiable analytical expression with the four nodes of the two contacting edges as inputs. Since this expression is differentiable, we can incorporate its force (negative gradient of the energy) and Jacobian (negative Hessian of the energy) into the elastic rod simulation.},
	urldate = {2021-02-21},
	journal = {Journal of Applied Mechanics},
	author = {Choi, Andrew and Tong, Dezhong and Jawed, Mohammad Khalid and Joo, Jungseock},
	month = feb,
	year = {2021},
	keywords = {computational mechanics, elasticity, mentions sympy},
	pages = {1--13},
}

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