Generalized Maxwell viscoelasticity for geometrically exact strings: Nonlinear port-Hamiltonian formulation and structure-preserving discretization
Authors
P.L. Kinon, T. Thoma, P. Betsch, P. Kotyczka
Abstract
This contribution proposes a nonlinear and dissipative infinite-dimensional port-Hamiltonian (PH) model for the dynamics of geometrically exact strings. The mechanical model provides a description of large deformations including finite elastic and inelastic strains in a generalized Maxwell model. It is shown that the overall system results from a power-preserving interconnection of PH subsystems. By using a structure-preserving mixed finite element approach, a finite-dimensional PH model is derived. Eventually, midpoint discrete derivatives are employed to deduce an energy-consistent time-stepping method, which inherits discrete-time dissipativity for the irreversible system. An example simulation illustrates the numerical properties of the present approach.
Keywords
Nonlinear port-Hamiltonian systems; generalized Maxwell model; structure-preserving discretization; mixed finite elements; discrete gradients
Citation
- Journal: IFAC-PapersOnLine
- Year: 2024
- Volume: 58
- Issue: 6
- Pages: 101–106
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2024.08.264
- Note: 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2024- Besançon, France, June 10 – 12, 2024
BibTeX
@article{Kinon_2024,
title={{Generalized Maxwell viscoelasticity for geometrically exact strings: Nonlinear port-Hamiltonian formulation and structure-preserving discretization}},
volume={58},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2024.08.264},
number={6},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Kinon, P.L. and Thoma, T. and Betsch, P. and Kotyczka, P.},
year={2024},
pages={101--106}
}
References
- Bauchau, O. A. & Nemani, N. Modeling viscoelastic behavior in flexible multibody systems. Multibody System Dynamics vol. 51 159–194 (2020) – 10.1007/s11044-020-09767-5
- Brugnoli, A., Haine, G. & Matignon, D. Explicit structure-preserving discretization of port-Hamiltonian systems with mixed boundary control. IFAC-PapersOnLine vol. 55 418–423 (2022) – 10.1016/j.ifacol.2022.11.089
- Brugnoli, A., Rashad, R., Califano, F., Stramigioli, S. & Matignon, D. Mixed finite elements for port-Hamiltonian models of von Kármán beams. IFAC-PapersOnLine vol. 54 186–191 (2021) – 10.1016/j.ifacol.2021.11.076
- Cardoso-Ribeiro, F. L., Matignon, D. & Lefèvre, L. A partitioned finite element method for power-preserving discretization of open systems of conservation laws. IMA Journal of Mathematical Control and Information vol. 38 493–533 (2020) – 10.1093/imamci/dnaa038
- Duindam, (2009)
- Gonzalez, O. Time integration and discrete Hamiltonian systems. Journal of Nonlinear Science vol. 6 449–467 (1996) – 10.1007/bf02440162
- Kinon, (2023)
- Kinon, P. L., Thoma, T., Betsch, P. & Kotyczka, P. Discrete nonlinear elastodynamics in a port‐Hamiltonian framework. PAMM vol. 23 (2023) – 10.1002/pamm.202300144
- Linn, J., Lang, H. & Tuganov, A. Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping. Mechanical Sciences vol. 4 79–96 (2013) – 10.5194/ms-4-79-2013
- Mehrmann, (2019)
- Ponce, C., Wu, Y., Le Gorrec, Y. & Ramirez, H. A systematic methodology for port-Hamiltonian modeling of multidimensional flexible linear mechanical systems. Applied Mathematical Modelling vol. 134 434–451 (2024) – 10.1016/j.apm.2024.05.040
- Rashad, R., Califano, F., van der Schaft, A. J. & Stramigioli, S. Twenty years of distributed port-Hamiltonian systems: a literature review. IMA Journal of Mathematical Control and Information vol. 37 1400–1422 (2020) – 10.1093/imamci/dnaa018
- Simo, (2006)
- Ströhle, T. & Betsch, P. A simultaneous space‐time discretization approach to the inverse dynamics of geometrically exact strings. International Journal for Numerical Methods in Engineering vol. 123 2573–2609 (2022) – 10.1002/nme.6951
- Thoma, T. & Kotyczka, P. Port-Hamiltonian FE models for filaments. IFAC-PapersOnLine vol. 55 353–358 (2022) – 10.1016/j.ifacol.2022.11.078