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}
}

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References