Publications

Publications of our institute – sorted by year

Automatically generated publication list through the University Library

2024

Breuling, J., Capobianco, G., Eugster, S. R., & Leine, R. I. (2024). A nonsmooth RATTLE algorithm for mechanical systems with frictional unilateral constraints. Nonlinear Analysis: Hybrid Systems, 52, 101469. https://doi.org/10.1016/j.nahs.2024.101469
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BibTeX
@article{Breuling_etal_2024, abstract = {In 1983, Andersen proposed the RATTLE algorithm as an extension of the SHAKE algorithm. The RATTLE algorithm is a well-established method for simulating mechanical systems with perfect bilateral constraints. This paper further extends RATTLE for simulating nonsmooth mechanical systems with frictional unilateral constraints (i.e. frictional contact). With that, it satisfies the need for higher-order integration methods within the framework of nonsmooth contact dynamics in phases where the contact status does not change (i.e. no collisions/constant sliding states). In particular, the proposed method can simulate impact-free motions, such as persistent frictional contact, with second-order accurate positions and velocities and prohibits penetration by unilateral constraints on position level.}, author = {Breuling, Jonas and Capobianco, Giuseppe and Eugster, Simon R. and Leine, Remco I.}, doi = {10.1016/j.nahs.2024.101469}, issn = {1751-570X}, journal = {Nonlinear Analysis: Hybrid Systems}, month = {05}, pages = 101469, publisher = {Elsevier BV}, title = {A nonsmooth RATTLE algorithm for mechanical systems with frictional unilateral constraints}, url = {http://dx.doi.org/10.1016/j.nahs.2024.101469}, volume = 52, year = 2024 }
Link
http://dx.doi.org/10.1016/j.nahs.2024.101469
Stilz, M., Breuling, J., Eugster, S., Pawlikowski, M., & Grygoruk, R. (2024). Chirality effects in panto-cylindrical structures. Mathematics and Mechanics of Solids, 0(0), Article 0. https://doi.org/10.1177/10812865231212145
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BibTeX
@article{Stilz2024a, abstract = {In this paper, we apply a numerical integration strategy recently developed for determining the deformation shapes of structures constituted by Cosserat rods, to predict the behavior of panto-cylinders. Panto-cylinders have, as microstructure, a set of two families of helicoidal beams interconnected by perfect or elastic joints. The pivot’s free rotation axis is, in the reference configuration, orthogonal to the cylindrical surfaces spanned by the beams. We perform a series of numerical simulations looking for the mechanical parameters which exalt the chirality effects in the structure. For the performed compression, extensions, shear, and torsion tests, we find chiral deformation patterns with a dependence on the type of joint and its length.}, author = {Stilz, Maximilian and Breuling, Jonas and Eugster, Simon and Pawlikowski, Marek and Grygoruk, Roman}, doi = {10.1177/10812865231212145}, eprint = {https://doi.org/10.1177/10812865231212145}, journal = {Mathematics and Mechanics of Solids}, number = 0, pages = 10812865231212145, title = {Chirality effects in panto-cylindrical structures}, url = {https://doi.org/10.1177/10812865231212145}, volume = 0, year = 2024 }
Link
https://doi.org/10.1177/10812865231212145

2023

Youssef, B., & Leine, R. I. (2023, June). Vibro-impact NES: Nonlinear mode approximation using the multiple scales method. Proceedings of the Third International Nonlinear Dynamics Conference (NODYCON 2023). https://nodycon.org/2023/
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BibTeX
@inproceedings{Youssef&Leine2023NODYCON, address = {Rome, Italy}, author = {Youssef, B. and Leine, R. I.}, booktitle = {Proceedings of the Third International Nonlinear Dynamics Conference (NODYCON 2023)}, month = {06}, note = {P71}, title = {Vibro-impact {NES}: Nonlinear mode approximation using the multiple scales method}, url = {https://nodycon.org/2023/}, year = 2023 }
Documents
- 2023 Youssef & Leine -Vibro-impact NES nonlinear mode... MSM NODYCON.pdf
Bayer, F., & Leine, R. I. (2023, June). Optimal projection in a Koopman-based sorting-free Hill method. Proceedings of the Third International Nonlinear Dynamics Conference (NODYCON 2023). https://nodycon.org/2023/
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- Documents
BibTeX
@inproceedings{Bayer&Leine2023NODYCON, address = {Rome, Italy}, author = {Bayer, F. and Leine, R. I.}, booktitle = {Proceedings of the Third International Nonlinear Dynamics Conference (NODYCON 2023)}, month = {06}, privnote = {P66}, title = {Optimal projection in a Koopman-based sorting-free Hill method}, url = {https://nodycon.org/2023/}, year = 2023 }
Documents
- 2023 Bayer & Leine - Optimal projection in a ... Hill method NODYCON.pdf
Karoui, A. Y., & Leine, R. I. (2023). Model reduction of a periodically forced slow–fast continuous piecewise linear system. Nonlinear Dynamics. https://doi.org/10.1007/s11071-023-08858-0
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BibTeX
@article{karoui2023model, author = {Karoui, A. Y. and Leine, R. I.}, doi = {https://doi.org/10.1007/s11071-023-08858-0}, journal = {Nonlinear Dynamics}, title = {Model reduction of a periodically forced slow–fast continuous piecewise linear system}, year = 2023 }
Documents
- Karoui&Leine - Model reduction of a periodically forced slow-fast continuous piecewise linear system.pdf
Harsch, J., Sailer, S., & Eugster, S. R. (2023). A total Lagrangian, objective and intrinsically locking-free Petrov--Galerkin SE(3) Cosserat rod finite element formulation. International Journal for Numerical Methods in Engineering, n/a(n/a), Article n/a. https://doi.org/10.1002/nme.7236
Abstract
Based on more than three decades of rod finite element theory, this publication combines the successful contributions found in the literature and eradicates the arising drawbacks like loss of objectivity, locking, path-dependence and redundant coordinates. Specifically, the idea of interpolating the nodal orientations using relative rotation vectors, proposed by Crisfield and Jelenic in 1999, is extended to the interpolation of nodal Euclidean transformation matrices with the aid of relative twists; a strategy that arises from the SE(3)-structure of the Cosserat rod kinematics. Applying a Petrov--Galerkin projection method, we propose a rod finite element formulation where the virtual displacements and rotations as well as the translational and angular velocities are interpolated instead of using the consistent variations and time-derivatives of the introduced interpolation formula. Properties such as the intrinsic absence of locking, preservation of objectivity after discretization and parameterization in terms of a minimal number of nodal unknowns are demonstrated by representative numerical examples in both statics and dynamics.
BibTeX
@article{Harsch2023, abstract = {Based on more than three decades of rod finite element theory, this publication combines the successful contributions found in the literature and eradicates the arising drawbacks like loss of objectivity, locking, path-dependence and redundant coordinates. Specifically, the idea of interpolating the nodal orientations using relative rotation vectors, proposed by Crisfield and Jelenic in 1999, is extended to the interpolation of nodal Euclidean transformation matrices with the aid of relative twists; a strategy that arises from the SE(3)-structure of the Cosserat rod kinematics. Applying a Petrov--Galerkin projection method, we propose a rod finite element formulation where the virtual displacements and rotations as well as the translational and angular velocities are interpolated instead of using the consistent variations and time-derivatives of the introduced interpolation formula. Properties such as the intrinsic absence of locking, preservation of objectivity after discretization and parameterization in terms of a minimal number of nodal unknowns are demonstrated by representative numerical examples in both statics and dynamics.}, author = {Harsch, Jonas and Sailer, Simon and Eugster, Simon R.}, doi = {https://doi.org/10.1002/nme.7236}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.7236}, file = {:Harsch2023.pdf:PDF}, journal = {International Journal for Numerical Methods in Engineering}, number = {n/a}, title = {A total Lagrangian, objective and intrinsically locking-free Petrov--Galerkin SE(3) Cosserat rod finite element formulation}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7236}, volume = {n/a}, year = 2023 }
Documents
- Harsch2023.pdf
Harsch, J., & Eugster, S. R. (2023). Nonunit quaternion parametrization of a Petrov--Galerkin Cosserat rod finite element. PAMM, e202300172. https://doi.org/10.1002/pamm.202300172
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Abstract
Abstract The application of the Petrov--Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight-forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross-section orientations. In this concise communication, we present a total Lagrangian finite element formulation for Cosserat rods that attempts to minimize the number of required theoretical concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with nonunit quaternions results in a singularity-free formulation.
BibTeX
@article{Harsch2023b, abstract = {Abstract The application of the Petrov--Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight-forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross-section orientations. In this concise communication, we present a total Lagrangian finite element formulation for Cosserat rods that attempts to minimize the number of required theoretical concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with nonunit quaternions results in a singularity-free formulation.}, author = {Harsch, Jonas and Eugster, Simon R.}, doi = {https://doi.org/10.1002/pamm.202300172}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.202300172}, journal = {PAMM}, pages = {e202300172}, title = {Nonunit quaternion parametrization of a Petrov--Galerkin Cosserat rod finite element}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.202300172}, year = 2023 }
Eugster, S. R., & Harsch, J. (2023). A family of total Lagrangian Petrov–Galerkin Cosserat rod finite element formulations. GAMM-Mitteilungen, 46(2), Article 2. https://doi.org/10.1002/gamm.202300008
Abstract
The standard in rod finite element formulations is the Bubnov–Galerkin projection method, where the test functions arise from a consistent variation of the ansatz functions. This approach becomes increasingly complex when highly nonlinear ansatz functions are chosen to approximate the rod's centerline and cross-section orientations. Using a Petrov–Galerkin projection method, we propose a whole family of rod finite element formulations where the nodal generalized virtual displacements and generalized velocities are interpolated instead of using the consistent variations and time derivatives of the ansatz functions. This approach leads to a significant simplification of the expressions in the discrete virtual work functionals. In addition, independent strategies can be chosen for interpolating the nodal centerline points and cross-section orientations. We discuss three objective interpolation strategies and give an in-depth analysis concerning locking and convergence behavior for the whole family of rod finite element formulations.
BibTeX
@article{Eugster2023a, abstract = {The standard in rod finite element formulations is the Bubnov–Galerkin projection method, where the test functions arise from a consistent variation of the ansatz functions. This approach becomes increasingly complex when highly nonlinear ansatz functions are chosen to approximate the rod's centerline and cross-section orientations. Using a Petrov–Galerkin projection method, we propose a whole family of rod finite element formulations where the nodal generalized virtual displacements and generalized velocities are interpolated instead of using the consistent variations and time derivatives of the ansatz functions. This approach leads to a significant simplification of the expressions in the discrete virtual work functionals. In addition, independent strategies can be chosen for interpolating the nodal centerline points and cross-section orientations. We discuss three objective interpolation strategies and give an in-depth analysis concerning locking and convergence behavior for the whole family of rod finite element formulations.}, author = {Eugster, Simon R. and Harsch, Jonas}, doi = {https://doi.org/10.1002/gamm.202300008}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/gamm.202300008}, journal = {GAMM-Mitteilungen}, number = 2, pages = {e202300008}, title = {A family of total Lagrangian Petrov–Galerkin Cosserat rod finite element formulations}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/gamm.202300008}, volume = 46, year = 2023 }
Documents
- Eugster2023a.pdf
Capobianco, G., Harsch, J., & Leyendecker, S. (2023). Lobatto-type variational integrators for mechanical systems with frictional contact. Computer Methods in Applied Mechanics and Engineering, 418, 116496. https://doi.org/10.1016/j.cma.2023.116496
Abstract
This paper introduces a family of Lobatto IIIA-IIIB methods for simulating mechanical systems with frictional contact. These methods extend the existing schemes by addressing both bilateral and unilateral constraints, as well as set-valued Coulomb friction. The Lobatto IIIA-IIIB methods presented in this paper make a substantial contribution to the ongoing endeavor of developing event-capturing versions of high-order schemes. By stating a generalized version of the principle of virtual action for nonsmooth mechanical systems, the integrators are derived from an appropriate discretization of it. The discrete contact laws are found by discretizing the impenetrabilty condition as well as the Newton-type frictional impact laws in an event-capturing way. The presented discrete contact laws exhibit no contact penetration and satisfy the involved unilateral constraints both on position and on velocity level. This behavior is showcased using benchmark examples.
BibTeX
@article{capobianco2024lobattotype, abstract = {This paper introduces a family of Lobatto IIIA-IIIB methods for simulating mechanical systems with frictional contact. These methods extend the existing schemes by addressing both bilateral and unilateral constraints, as well as set-valued Coulomb friction. The Lobatto IIIA-IIIB methods presented in this paper make a substantial contribution to the ongoing endeavor of developing event-capturing versions of high-order schemes. By stating a generalized version of the principle of virtual action for nonsmooth mechanical systems, the integrators are derived from an appropriate discretization of it. The discrete contact laws are found by discretizing the impenetrabilty condition as well as the Newton-type frictional impact laws in an event-capturing way. The presented discrete contact laws exhibit no contact penetration and satisfy the involved unilateral constraints both on position and on velocity level. This behavior is showcased using benchmark examples.}, author = {Capobianco, Giuseppe and Harsch, Jonas and Leyendecker, Sigrid}, doi = {https://doi.org/10.1016/j.cma.2023.116496}, issn = {0045-7825}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = 116496, title = {Lobatto-type variational integrators for mechanical systems with frictional contact}, url = {https://www.sciencedirect.com/science/article/pii/S0045782523006205}, volume = 418, year = 2023 }
Documents
- Capobianco2023a.pdf
Bayer, F., & Leine, R. I. (2023). Sorting-free Hill-based stability analysis of periodic solutions through Koopman analysis. Nonlinear Dynamics, 111, 8439–8466. https://doi.org/10.1007/s11071-023-08247-7
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BibTeX
@article{Bayer&Leine2023, author = {Bayer, F. and Leine, R. I.}, doi = {https://doi.org/10.1007/s11071-023-08247-7}, journal = {Nonlinear Dynamics}, note = {J54}, pages = {8439–8466}, title = {Sorting-free Hill-based stability analysis of periodic solutions through Koopman analysis}, volume = 111, year = 2023 }
Documents
- 2023 Bayer & Leine - Sorting-free Hill-based stability analysis - NODY.pdf

2022

2022
1. Sailer, S., & Leine, R. I. (2022, July). Why does the Tippedisk invert? Theory and experiments. Proceedings of the 10th European Nonlinear Dynamics Conference (ENOC2020+2).
  - BibTeX
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  BibTeX
  @inproceedings{Sailer&Leine2022ENOC, address = {Lyon, France}, author = {Sailer, S. and Leine, R. I.}, booktitle = {Proceedings of the 10th European Nonlinear Dynamics Conference (ENOC2020+2)}, month = {07}, title = {Why does the Tippedisk invert? Theory and experiments}, year = 2022 }
  Documents
  - 2022 Sailer & Leine - Why does the tippedisk invert theory and experiments.pdf
2. Leine, R. I., Capobianco, G., Bartelt, P., & Lu, G. (2022, July). A rockfall simulation scheme which preserves the stability properties of rotating rocks. Proceedings of the 10th European Nonlinear Dynamics Conference (ENOC2020+2). https://enoc2020.sciencesconf.org/301850
  BibTeX
  @inproceedings{Leine&Capobianco&Bartelt&Lu2022ENOC, address = {Lyon, France}, author = {Leine, R. I. and Capobianco, G. and Bartelt, P. and Lu, G.}, booktitle = {Proceedings of the 10th European Nonlinear Dynamics Conference (ENOC2020+2)}, month = {07}, title = {A rockfall simulation scheme which preserves the stability properties of rotating rocks}, url = {https://enoc2020.sciencesconf.org/301850}, year = 2022 }
  Link
  https://enoc2020.sciencesconf.org/301850
  Documents
  - Leine et al - A rockfall simulation scheme which ... ENOC2020 301850.pdf
3. Karoui, A. Y., & Leine, R. I. (2022, July). Analysis of a singularly perturbed continuous piecewise linear system. Proceedings of the 10th European Nonlinear Dynamics Conference (ENOC2020+2).
  - BibTeX
  BibTeX
  @inproceedings{Karoui&Leine2022ENOC, address = {Lyon, France}, author = {Karoui, A. Y. and Leine, R. I.}, booktitle = {Proceedings of the 10th European Nonlinear Dynamics Conference (ENOC2020+2)}, month = {07}, title = {Analysis of a singularly perturbed continuous piecewise linear system}, year = 2022 }
4. Bayer, F., & Leine, R. I. (2022, July). A Koopman view on the harmonic balance and Hill method. Proceedings of the 10th European Nonlinear Dynamics Conference (ENOC2020+2). https://enoc2020.sciencesconf.org/394116/
  BibTeX
  @inproceedings{Bayer&Leine2022ENOC, address = {Lyon, France}, author = {Bayer, F. and Leine, R. I.}, booktitle = {Proceedings of the 10th European Nonlinear Dynamics Conference (ENOC2020+2)}, month = {07}, note = {P66}, title = {A Koopman view on the harmonic balance and Hill method}, url = {https://enoc2020.sciencesconf.org/394116/}, year = 2022 }
  Link
  https://enoc2020.sciencesconf.org/394116/
  Documents
  - 2022 Bayer & Leine - A Koopman view on the harmonic balance and Hill method ENOC.pdf
5. Preiswerk, P. V., & Leine, R. I. (2022). State observers for the time discretization of a class of impulsive mechanical systems. International Journal of Robust and Nonlinear Control. https://doi.org/10.1002/rnc.6168
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  - Documents
  BibTeX
  @article{Preiswerk&Leine2022, author = {Preiswerk, P. V. and Leine, R. I.}, doi = {10.1002/rnc.6168}, journal = {International Journal of Robust and Nonlinear Control}, title = {State observers for the time discretization of a class of impulsive mechanical systems}, year = 2022 }
  Documents
  - Intl J Robust Nonlinear - 2022 - Preiswerk - State observers for the time discretization of a class of impulsive.pdf
6. Harsch, J., Ganzosch, G., Barchiesi, E., Ciallella, A., & Eugster, S. R. (2022). Experimental analysis, discrete modeling and parameter optimization of SLS-printed bi-pantographic structures. Mathematics and Mechanics of Solids, 27(10), Article 10. https://doi.org/10.1177/10812865221107623
  Abstract
  Making use of experimental data for bias extension, shearing, and point-load tests in large deformation regime for rectangular and square bi-pantographic specimens, we perform a numerical identification to fit the a priori parameters of a planar discrete spring model. The main objective of the work is to develop an automatized optimization process based on the Nelder�Mead simplex algorithm for identifying the constitutive parameters of discrete modeling of bi-pantographic structures, as well as assessing its descriptiveness and predictive capacity. The analysis allows to conclude that there exists a single set of parameters for the adopted discrete modeling such that it is descriptive and predictive for several different tests and for a wide range of deformations.
  BibTeX
  @article{Harsch2022a, abstract = {Making use of experimental data for bias extension, shearing, and point-load tests in large deformation regime for rectangular and square bi-pantographic specimens, we perform a numerical identification to fit the a priori parameters of a planar discrete spring model. The main objective of the work is to develop an automatized optimization process based on the Nelder�Mead simplex algorithm for identifying the constitutive parameters of discrete modeling of bi-pantographic structures, as well as assessing its descriptiveness and predictive capacity. The analysis allows to conclude that there exists a single set of parameters for the adopted discrete modeling such that it is descriptive and predictive for several different tests and for a wide range of deformations.}, author = {Harsch, Jonas and Ganzosch, Gregor and Barchiesi, Emilio and Ciallella, Alessandro and Eugster, Simon R}, doi = {10.1177/10812865221107623}, eprint = {https://doi.org/10.1177/10812865221107623}, file = {:Harsch2022a.pdf:PDF}, journal = {Mathematics and Mechanics of Solids}, number = 10, pages = {2201-2217}, title = {Experimental analysis, discrete modeling and parameter optimization of SLS-printed bi-pantographic structures}, url = {https://doi.org/10.1177/10812865221107623}, volume = 27, year = 2022 }
  Link
  https://doi.org/10.1177/10812865221107623
  Documents
  - Harsch2022a.pdf
7. Eugster, S. R., dell’Isola, F., Fedele, R., & Seppecher, P. (2022). Piola transformations in second gradient continua. Mechanics Research Communications, 1–8. https://doi.org/10.1016/j.mechrescom.2022.103836
  - BibTeX
  BibTeX
  @article{Eugster2022b, author = {Eugster, S.R. and dell'Isola, F. and Fedele, R. and Seppecher, P.}, doi = {https://doi.org/10.1016/j.mechrescom.2022.103836}, journal = {Mechanics Research Communications}, pages = {1-8}, title = {Piola transformations in second gradient continua}, year = 2022 }
8. Eugster, S. R., Harsch, J., Herrmann, M., Capobianco, G., Bartholdt, M., & Wiese, M. (2022). Soft pneumatic actuator model based on a pressure-dependent spatial nonlinear rod theory. IEEE Robotics and Automation Letters, 7(2), Article 2. https://ieeexplore.ieee.org/document/9691781
  BibTeX
  @article{Eugster2022c, author = {Eugster, S. R. and Harsch, J. and Herrmann, M. and Capobianco, G. and Bartholdt, M. and Wiese, M.}, file = {:Eugster2022c.pdf:PDF}, journal = {IEEE Robotics and Automation Letters}, number = 2, pages = {1-8}, title = {Soft pneumatic actuator model based on a pressure-dependent spatial nonlinear rod theory}, url = {https://ieeexplore.ieee.org/document/9691781}, volume = 7, year = 2022 }
  Link
  https://ieeexplore.ieee.org/document/9691781
  Documents
  - Eugster2022c.pdf

2021

Sailer, S., Eugster, S. R., & Leine, R. I. (2021, December). The Tippedisk: A minimal model for friction-induced inversion. Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2021.
- BibTeX
- Documents
BibTeX
@inproceedings{Sailer&Eugster&Leine2021, address = {Budapest, Hungary}, author = {Sailer, S. and Eugster, S. R. and Leine, R. I.}, booktitle = {Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2021}, month = {12}, title = {The {Tippedisk}: {A} minimal model for friction-induced inversion}, year = 2021 }
Documents
- Sailer_x_Eugster_x_Leine-The_Tippedisk-A_Minimal_Model_for_Friction-Induced_Inversion.pdf
Youssef, B., & Leine, R. I. (2021). A complete set of design rules for a vibro-impact NES based on a multiple scales approximation of a nonlinear mode. Journal of Sound and Vibration, 501(116043), Article 116043. https://doi.org/10.1016/j.jsv.2021.116043
Abstract
The aim of the paper is to formulate a complete set of design rules for a vibro-impact nonlinear energy sink (VI NES). Hereto, analytical and numerical methods to extract the backbone curve of vibro-impact systems are presented. The adopted approach exploits the multiple scales method and is applied to a linear oscillator coupled with a VI NES. The dynamics of the system are explored and the system’s response under harmonic forcing in the vicinity of resonance is analyzed and approximated. The presented method allows for the derivation of a closed-form approximation of a nonlinear mode. The relation between the steady state response and the input parameters is established. The resonance frequency of the examined nonlinear system for different excitation levels is estimated and the corresponding backbone curve is identified. The theoretical predictions are confirmed through a comparison with the standard resonant decay method combined with a phase-locked loop. Finally, the closed-form approximations are used to derive a complete set of design rules for a vibro-impact nonlinear energy sink.
BibTeX
@article{Youssef&Leine2021, abstract = {The aim of the paper is to formulate a complete set of design rules for a vibro-impact nonlinear energy sink (VI NES). Hereto, analytical and numerical methods to extract the backbone curve of vibro-impact systems are presented. The adopted approach exploits the multiple scales method and is applied to a linear oscillator coupled with a VI NES. The dynamics of the system are explored and the system’s response under harmonic forcing in the vicinity of resonance is analyzed and approximated. The presented method allows for the derivation of a closed-form approximation of a nonlinear mode. The relation between the steady state response and the input parameters is established. The resonance frequency of the examined nonlinear system for different excitation levels is estimated and the corresponding backbone curve is identified. The theoretical predictions are confirmed through a comparison with the standard resonant decay method combined with a phase-locked loop. Finally, the closed-form approximations are used to derive a complete set of design rules for a vibro-impact nonlinear energy sink.}, author = {Youssef, B. and Leine, R. I.}, doi = {https://doi.org/10.1016/j.jsv.2021.116043}, journal = {Journal of Sound and Vibration}, number = 116043, title = {A complete set of design rules for a vibro-impact {NES} based on a multiple scales approximation of a nonlinear mode}, volume = 501, year = 2021 }
Documents
- Youssef-Leine-2021-A-complete-set-of-design-rules-for-a-vibro-impact-NES-based-on-a-multiple-scales-approximation-of-a-nonlinear-mode.pdf
Schindler, K., & Leine, R. I. (2021). Paradoxical simulation results of chaos-like chattering in the bouncing ball system. Physica D: Nonlinear Phenomena, 419. https://doi.org/10.1016/j.physd.2021.132854
Abstract
This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behavior) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.
BibTeX
@article{Schindler&Leine2021, abstract = {This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behavior) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.}, author = {Schindler, K. and Leine, R. I.}, doi = {https://doi.org/10.1016/j.physd.2021.132854}, journal = {Physica D: Nonlinear Phenomena}, title = {Paradoxical simulation results of chaos-like chattering in the bouncing ball system}, volume = 419, year = 2021 }
Documents
- Schindler_x_Leine_-_Paradoxical+simulation+results+of+chaos-like+chattering+in+the+bouncing+ball+system+PREPRINT.pdf
Sailer, S., & Leine, R. I. (2021). Singularly perturbed dynamics of the tippedisk. Proceedings of the Royal Society A, 477(2256), Article 2256. https://doi.org/10.1098/rspa.2021.0536
Abstract
The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disc, being reminiscent of (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global analysis of the reduced system is pursued using the framework of singular perturbation theory. It is shown how the presence of friction leads to slow fast dynamics and the creation of a two-dimensional slow manifold. Furthermore, it is revealed that a bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation leads to an explanation of the inversion phenomenon. In particular, a closed-form condition for the critical spinning speed for the inversion phenomenon is derived. Hence, the tippedisk forms an excellent mathematical-mechanical problem for the analysis of global bifurcations in singularly perturbed dynamics.
BibTeX
@article{Sailer&Leine2021ProcRSocA, abstract = {The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disc, being reminiscent of (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global analysis of the reduced system is pursued using the framework of singular perturbation theory. It is shown how the presence of friction leads to slow fast dynamics and the creation of a two-dimensional slow manifold. Furthermore, it is revealed that a bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation leads to an explanation of the inversion phenomenon. In particular, a closed-form condition for the critical spinning speed for the inversion phenomenon is derived. Hence, the tippedisk forms an excellent mathematical-mechanical problem for the analysis of global bifurcations in singularly perturbed dynamics.}, author = {Sailer, S. and Leine, R. I.}, doi = {https://doi.org/10.1098/rspa.2021.0536}, journal = {Proceedings of the Royal Society A}, number = 2256, title = {Singularly perturbed dynamics of the tippedisk}, volume = 477, year = 2021 }
Documents
- rspa.2021.0536.pdf
Sailer, S., & Leine, R. I. (2021). Model reduction of the tippedisk: a path to the full analysis. Nonlinear Dynamics, 105, 1955--1975. https://doi.org/10.1007/s11071-021-06649-z
Abstract
The tippedisk is a mechanical-mathematical archetype for friction-induced instability phenomena that exhibits an interesting inversion phenomenon when spun rapidly. The inversion phenomenon of the tippedisk can be modeled by a rigid eccentric disk in permanent contact with a flat support, and the dynamics of the system can therefore be formulated as a set of ordinary differential equations. The qualitative behavior of the nonlinear system can be analyzed, leading to slow fast dynamics. Since even a freely rotating rigid body with six degrees of freedom already leads to highly nonlinear system equations, a general analysis for the full system equations is not feasible. In a first step the full system equations are linearized around the inverted spinning solution with the aim to obtain a local stability analysis. However, it turns out that the linear dynamics of the full system cannot properly describe the qualitative behavior of the tippedisk. Therefore, we simplify the equations of motion of the tippedisk in such a way that the qualitative dynamics are preserved in order to obtain a reduced model that will serve as the basis for a following nonlinear stability analysis. The reduced equations are presented here in full detail and are compared numerically with the full model. Furthermore, using the reduced equations we give approximate closed form results for the critical spinning speed of the tippedisk.
BibTeX
@article{Sailer&Leine2021NODY, abstract = {The tippedisk is a mechanical-mathematical archetype for friction-induced instability phenomena that exhibits an interesting inversion phenomenon when spun rapidly. The inversion phenomenon of the tippedisk can be modeled by a rigid eccentric disk in permanent contact with a flat support, and the dynamics of the system can therefore be formulated as a set of ordinary differential equations. The qualitative behavior of the nonlinear system can be analyzed, leading to slow fast dynamics. Since even a freely rotating rigid body with six degrees of freedom already leads to highly nonlinear system equations, a general analysis for the full system equations is not feasible. In a first step the full system equations are linearized around the inverted spinning solution with the aim to obtain a local stability analysis. However, it turns out that the linear dynamics of the full system cannot properly describe the qualitative behavior of the tippedisk. Therefore, we simplify the equations of motion of the tippedisk in such a way that the qualitative dynamics are preserved in order to obtain a reduced model that will serve as the basis for a following nonlinear stability analysis. The reduced equations are presented here in full detail and are compared numerically with the full model. Furthermore, using the reduced equations we give approximate closed form results for the critical spinning speed of the tippedisk.}, author = {Sailer, S. and Leine, R. I.}, doi = {https://doi.org/10.1007/s11071-021-06649-z}, journal = {Nonlinear Dynamics}, pages = {1955--1975}, title = {Model reduction of the tippedisk: a path to the full analysis}, volume = 105, year = 2021 }
Documents
- Sailer2021a.pdf
Leine, R. I., Capobianco, G., Bartelt, P., Christen, M., & Caviezel, A. (2021). Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation. Multibody System Dynamics, 52(4), Article 4. https://doi.org/10.1007/s11044-021-09792-y?
Abstract
The stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov's direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks
BibTeX
@article{Leine&Capobianco&Bartelt&Caviezel2021, abstract = {The stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov's direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks}, author = {Leine, R. I. and Capobianco, G. and Bartelt, P. and Christen, M. and Caviezel, A.}, journal = {Multibody System Dynamics}, number = 4, pages = {431--455}, title = {Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation}, url = {https://doi.org/10.1007/s11044-021-09792-y?}, volume = 52, year = 2021 }
Documents
- Leine2021_Article_StabilityOfRigidBodyMotionThro.pdf
Leine, R. I., & Capobianco, G. (2021). An extended version of the Intermediate Axis Theorem for a freely rotating rigid body. Proceedings in Applied Mathematics and Mechanics (PAMM), 21, e202100103.
- BibTeX
- Documents
BibTeX
@inproceedings{Leine&Capobianco2021PAMM, author = {Leine, R. I. and Capobianco, G.}, booktitle = {Proceedings in Applied Mathematics and Mechanics (PAMM)}, pages = {e202100103}, title = {An extended version of the {Intermediate Axis Theorem} for a freely rotating rigid body}, volume = 21, year = 2021 }
Documents
- Leine_x_Capobianco-An_extended_version_of_the_Intermediate_Axis_Theorem_for_a_freely_rotating_rigid_body.pdf
Hinze, M., Schmidt, A., & Leine, R. I. (2021). Finite element formulation of fractional constitutive laws using the reformulated infinite state representation. Fractal Fractional, 5(132), Article 132. https://doi.org/10.3390/fractalfract5030132
Abstract
In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.
BibTeX
@article{Hinze&Schmidt&Leine2021, abstract = {In this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.}, author = {Hinze, M. and Schmidt, A. and Leine, R. I.}, journal = {Fractal Fractional}, number = 132, pages = {1--22}, title = {Finite element formulation of fractional constitutive laws using the reformulated infinite state representation}, url = {https://doi.org/10.3390/fractalfract5030132}, volume = 5, year = 2021 }
Documents
- fractalfract-05-00132-v2.pdf
Harsch, J., Capobianco, G., & Eugster, S. R. (2021). Dynamic simulation of the Wilberforce pendulum using constrained spatial nonlinear beam finite elements. PAMM, 21(1), Article 1. https://doi.org/10.1002/pamm.202100110
Abstract
More than 100 years ago, Lionel Robert Wilberforce did investigations On the Vibrations of a Loaded Spiral Spring 1. The spring was clamped at its upper side and on the other side, perpendicular to the spring axis, a steel cylinder was attached. Four screws with adjustable nuts were symmetrically attached around the cylinder in order to change its moment of inertia (Fig. 1). In this paper the Wilberforce pendulum is modeled by a rigid body attached to a constrained spatial nonlinear Timoshenko beam, discretized with B-spline shape functions. As shown by a numerical experiment, the presented model is capable of reproducing the characteristic pendulum motion.
BibTeX
@article{Harsch2021, abstract = {More than 100 years ago, Lionel Robert Wilberforce did investigations On the Vibrations of a Loaded Spiral Spring [1]. The spring was clamped at its upper side and on the other side, perpendicular to the spring axis, a steel cylinder was attached. Four screws with adjustable nuts were symmetrically attached around the cylinder in order to change its moment of inertia (Fig. 1). In this paper the Wilberforce pendulum is modeled by a rigid body attached to a constrained spatial nonlinear Timoshenko beam, discretized with B-spline shape functions. As shown by a numerical experiment, the presented model is capable of reproducing the characteristic pendulum motion.}, author = {Harsch, Jonas and Capobianco, Giuseppe and Eugster, Simon R.}, doi = {https://doi.org/10.1002/pamm.202100110}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.202100110}, file = {:Harsch2021.pdf:PDF}, journal = {PAMM}, number = 1, pages = {e202100110}, title = {Dynamic simulation of the Wilberforce pendulum using constrained spatial nonlinear beam finite elements}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.202100110}, volume = 21, year = 2021 }
Documents
- Harsch2021.pdf
Harsch, J., Capobianco, G., & Eugster, S. R. (2021). Finite element formulations for constrained spatial nonlinear beam theories. Mathematics and Mechanics of Solids, 26(12), Article 12. https://doi.org/10.1177/10812865211000790
Abstract
A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.
BibTeX
@article{Harsch2021a, abstract = {A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.}, author = {Harsch, Jonas and Capobianco, Giuseppe and Eugster, Simon R}, doi = {10.1177/10812865211000790}, eprint = {https://doi.org/10.1177/10812865211000790}, file = {:Harsch2021a.pdf:PDF}, journal = {Mathematics and Mechanics of Solids}, number = 12, pages = {1838-1863}, title = {Finite element formulations for constrained spatial nonlinear beam theories}, url = {https://doi.org/10.1177/10812865211000790}, volume = 26, year = 2021 }
Documents
- Harsch2021a.pdf
Capobianco, G., Harsch, J., Eugster, S. R., & Leine, R. I. (2021). Simulating mechanical systems with frictional contacts using a nonsmooth generalized-alpha method. Proceedings in Applied Mathematics and Mechanics (PAMM), 21, e202100141:1--3. https://doi.org/10.1002/pamm.202100141
Abstract
In this paper, we introduce a nonsmooth generalized-alpha method for the simulation of mechanical systems with frictional contact. In many engineering applications, such systems are composed of rigid and flexible bodies, which are interconnected by joints and can come into contact with each other or their surroundings. Prominent examples are automotive, wind turbine, and robotic systems. It is known from structural mechanics applications, that generalized-alpha schemes perform well for flexible multibody systems without contacts. This motivated the development of nonsmooth generalized-alpha methods for the simulation of mechanical systems with frictional contacts 2, 3, 5. Typically, the Gear-Gupta-Leimkuhler approach is used to stabilize the unilateral constraint, such that numerical penetration of the contact bodies can be avoided - a big issue of the most popular time-stepping schemes such as Moreau's scheme. The nonsmooth generalized-alpha method presented in this paper is derived in 2 and in contrast to 3,5 accounts for set-valued Coulomb-type friction on both velocity and acceleration level. Finally, we validate the method using a guided flexible hopper as a benchmark mechanical system.
BibTeX
@inproceedings{Capobianco&Harsch&Eugster&Leine2021PAMM, abstract = {In this paper, we introduce a nonsmooth generalized-alpha method for the simulation of mechanical systems with frictional contact. In many engineering applications, such systems are composed of rigid and flexible bodies, which are interconnected by joints and can come into contact with each other or their surroundings. Prominent examples are automotive, wind turbine, and robotic systems. It is known from structural mechanics applications, that generalized-alpha schemes perform well for flexible multibody systems without contacts. This motivated the development of nonsmooth generalized-alpha methods for the simulation of mechanical systems with frictional contacts [2, 3, 5]. Typically, the Gear-Gupta-Leimkuhler approach is used to stabilize the unilateral constraint, such that numerical penetration of the contact bodies can be avoided - a big issue of the most popular time-stepping schemes such as Moreau's scheme. The nonsmooth generalized-alpha method presented in this paper is derived in [2] and in contrast to [3,5] accounts for set-valued Coulomb-type friction on both velocity and acceleration level. Finally, we validate the method using a guided flexible hopper as a benchmark mechanical system.}, author = {Capobianco, G. and Harsch, J. and Eugster, S. R. and Leine, R. I.}, booktitle = {Proceedings in Applied Mathematics and Mechanics (PAMM)}, doi = {https://doi.org/10.1002/pamm.202100141}, pages = {e202100141:1--3}, title = {Simulating mechanical systems with frictional contacts using a nonsmooth generalized-alpha method}, volume = 21, year = 2021 }
Documents
- Capobianco_x_Harsch_x_Eugster_x_Leine-Simulating_mechanical_systems_with_frictional_contact_using_a_nonsmooth_generalized-alpha_method.pdf
Capobianco, G., Harsch, J., Eugster, S. R., & Leine, R. I. (2021). A nonsmooth generalized-alpha method for mechanical systems with frictional contact. International Journal for Numerical Methods in Engineering, 122(22), Article 22. https://doi.org/10.1002/nme.6801
- BibTeX
BibTeX
@article{Capobianco&Harsch&Eugster&Leine2021, author = {Capobianco, G. and Harsch, J. and Eugster, S. R. and Leine, R. I.}, doi = {https://doi.org/10.1002/nme.6801}, journal = {International Journal for Numerical Methods in Engineering}, number = 22, pages = {6497--6526}, title = {A nonsmooth generalized-alpha method for mechanical systems with frictional contact}, volume = 122, year = 2021 }

List of publications before 2023 (manually maintained)

Raff, M., Rosa, M. and Remy, C. D. "Generating Families of Optimally Actuated Gaits from a Legged System's Energetically Conservative Dynamics", 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 8866-8872, 2022. PDF IROS

Harsch, J., Ganzosch, G., Barchiesi, E., Ciallella, A., and Eugster, S.R.: "Experimental analysis, discrete modeling and parameter optimization of SLS-printed bi-pantographic structures", Mathematics and Mechanics of Solids, accepted, pp. 1-17, 2022, PDF MMS

Raff, M., Rosa, N. and Remy, C. D. "Connecting Gaits in Energetically Conservative Legged Systems", IEEE Robotics and Automation Letters, Vol. 7(3), pp. 8407-8414, 2022. PDF, RAL

Ciallella, A., Giorgio, I., Eugster, S. R., Rizzi, N. L., and dell'Isola, F.: "Generalized beam model for the analysis of wave propagation with a symmetric pattern of deformation in planar pantographic sheets", Wave Motion, pp. 102986, 2022. PDF Link

Preiswerk, P. V. and Leine, R. I. "State observers for the time discretization of a class of impulsive mechanical systems", International Journal of Robust and Nonlinear Control, 2022. PDF Link

Capobianco, G. and Eugster, S.R. "On the divergence theorem for submanifolds of Euclidean vector spaces within the theory of second gradient continua", Zeitschrift für angewandte Mathematik und Physik, Vol. 73(86), pp. 1-22, 2022. PDF Link

dell'Isola, F., Eugster, S. R., Fedele, R., and Seppecher, P. "Second-gradient continua: From Lagrangian to Eulerian and back", Mathematics and Mechanics of Solids, pp. 1-48, 2022. PDF Link

Lai, M., Eugster, S. R., Reccia, E., Spagnuolo, M., and Cazzani, A.: "Corrugated shells: An algorithm for generating double-curvature surfaces for structural analysis", Thin-Walled Structures, Vol. 173, pp. 109019:1-11, 2022. PDF Link

Eugster, S. R., Harsch, J., Herrmann, M., Capobianco, G., Bartholdt, M., and Wiese, M. "Soft pneumatic actuator model based on a pressure-dependent spatial nonlinear rod theory", IEEE Robotics and Automation Letters, Vol. 7(2), pp. 2471-2478, 2022. PDF Link.

Eugster, S.R., dell'Isola, F., Fedele, R. and Seppecher, P. "Piola transformations in second gradient continua", Mechanics Research Communications, Vol. 120, pp. 103836:1-8, 2022. PDF Link

2021

Preiswerk, P. V. and Leine, R. I. "A nonsmooth dynamics perspective on state observer design for mechanical systems with unilateral constraints.", In ECCOMAS Thematic Conference on Multibody Dynamics, pp. 48-54, Budapest University of Technology and Economics, 2021. PDF Link

Sailer, S., Eugster, S.R., and Leine, R.I., "The Tippedisk: A minimal model for friction-induced inversion", Proceedings in ECCOMAS Thematic Conference on Multibody Dynamics, pp. 37-47, 2021. PDF Link

Eugster, S. R., and Barchiesi, E. "A second gradient continuum formulation for bi-pantographic fabrics", Proceedings in Applied Mathematics and Mechanics, Vol. 21, pp. e202100192:1-3, 2021. PDF Link

Capobianco, G., Harsch, J., Eugster, S. R., and Leine, R. I. "Simulating mechanical systems with frictional contacts using a nonsmooth generalized-alpha method", In Proceedings in Applied Mathematics and Mechanics, Vol. 21, pp. e202100141:1-3, 2021. PDF Link

Harsch, J., Capobianco, G., and Eugster, S. R. „Dynamic simulation of the Wilberforce pendulum using constrained spatial nonlinear beam finite elements“, Proceedings in Applied Mathematics and Mechanics, Vol. 21, pp. e202100110:1-2, 2021. PDF Link

Leine, R., & Capobianco, G. "An extended version of the Intermediate Axis Theorem for a freely rotating rigid body", PAMM, Vol. 21(1), pp. e202100103, 2021. PDF Link

Leine, R. I., Capobianco, G., Bartelt, P., Christen, M., & Caviezel, A. "Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation", Multibody System Dynamics, pp. 1-25, 2021. PDF Link

Sailer, S., Leine, R.I. "Singularly perturbed dynamics of the tippedisk", Proc. R. Soc. A., Vol. 477(2256), 2021. PDF, Link

Capobianco, G., Harsch, J., Eugster S.R. and Leine, R.I. “A nonsmooth generalized-alpha method for mechanical systems with frictional contact”, International Journal for Numerical Methods in Engineering, Vol. 122(22), pp. 6497-6526, 2021. PDF Link

Sailer, S., Leine, R.I. "Model reduction of the tippedisk: a path to the full analysis", Nonlinear Dynamics, Vol. 105(3), pp. 1955-1975, 2021. PDF, Link

Leine, R. I., Capobianco, G., Bartelt, P., Christen, M., Caviezel, A. "Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation", Multibody System Dynamics, 52(4), pp. 431-455, 2021. PDF, Link

Harsch, J., Capobianco, G. and Eugster, S. R. "Finite element formulations for constrained spatial nonlinear beam theories", Mathematics and Mechanics of Solids, Vol. 26(12), pp. 1-26, 2021. PDF MMS

Balkis Youssef, Remco I. Leine "A complete set of design rules for a vibro-impact NES based on a multiple scales approximation of a nonlinear mode", Journal of Sound and Vibration, Vol. 501, 2021. PDF, Link

Kilian Schindler and Remco I. Leine. "Paradoxical simulation results of chaos-like chattering in the bouncing ball system", Physica D: Nonlinear Phenomena, Vol. 419, 2021. Link

2020

Sailer, S., Eugster, S.R. and Leine R.I. ”The Tippedisk: a Tippetop Without Rotational Symmetry“, Regular and Chaotic Dynamics, Vol. 25(6), pp. 553-580, 2020. PDF, Link

Hinze, M., Schmidt, A., Leine, R.I. "The direct method of Lyapunov for nonlinear dynamical systems with fractional damping", Nonlinear Dynamics, Vol. 102(4), pp. 2017-2037, 2020. PDF, Link

Schmidt, A., Beyer, H.R., Hinze, M., Vandoros, E.N. "Finite element approach for the solution of first-order differential equations", Journal of Applied Mathematics and Physics, Vol. 8(10), pp. 2072-2090, 2020. PDF, Link

Hinze, M., Schmidt, A. and Leine, R.I. "Lyapunov stability of a fractionally damped oscillator with linear (anti-)damping", International Journal of Nonlinear Science and Numerical Simulation, Vol. 21(5), pp. 425-442, 2020. PDF, Link

Barchiesi, E., Harsch, J., Ganzosch, G. and Eugster, S.R.:"Discrete versus homogenized continuum modeling in finite deformation bias extension test of bi-pantographic fabrics", Continuum Mechanics and Thermodynamics, pp. 1-14, 2020. PDF CMAT

Eugster S.R., Harsch J.: "A Variational Formulation of Classical Nonlinear Beam Theories" In: Abali B., Giorgio I. (eds) Developments and Novel Approaches in Nonlinear Solid Body Mechanics. Advanced Structured Materials, Vol. 130, Springer, 2020. ASM PDF

Harsch J., Eugster S.R. "Finite Element Analysis of Planar Nonlinear Classical Beam Theories". In: Abali B., Giorgio I. (eds) Developments and Novel Approaches in Nonlinear Solid Body Mechanics. Advanced Structured Materials, Vol. 130. Springer, 2020. ASM PDF

Eugster, S. R., Capobianco, G. and Winandy, T. "Geometric description of time-dependent finite-dimensional mechanical systems", Mathematics and Mechanics of Solids, Vol. 25(11) pp. 2050-2075, 2020. PDF MMS

Schulte, J., Dittmann, M., Eugster, S.R., Hesch, S., Reinicke, T., dell'Isola, F. and Hesch, C. "Isogeometric shell elements for fiber reinforced composites", Computer Methods in Applied Mechanics and Engineering, Vol. 362, pp. 112845:1-34, 2020. PDF CMAME

Barchiesi, E., Eugster, S.R., dell'Isola, F. and Hild, F. "Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenisation and experimental validation", Mathematics and Mechanics of Solids, Vol. 25(3), pp. 739-767, 2020. PDF MMS

2019

Hinze, M., Schmidt, A. and Leine, R.I.: "Numerical solution of fractional-order ordinary differential equations using the reformulated infinite state representation", in Fractional Calculus and Applied Analysis, Vol. 22(5), pp. 1321-1350, 2019. PDF, Link

Barchiesi, E., Eugster, S.R., Placidi, L. and dell'Isola, F.: "Pantographic beam: a complete second gradient 1D-continuum in plane", Zeitschrift für angewandte Mathematik und Physik, Vol. 70(5): pp. 135:1-24, 2019. PDF ZAMP

Capobianco, G., Winandy, T. and Eugster, S.R.: "Dynamics of finite-dimensional mechanical systems on Galilean manifolds", In Proceedings in Applied Mathematics and Mechanics, Vol. 19, pp. e201900328:1-2, 2019. PDF

dell'Isola, F., Volkov, I.A., Igumnov, L.A., Eugster, S.R., et al.: "Estimating fatigue related damage in alloys under block-typ non-symmetrical low-cycle loading", In Abali, B.E., Altenbach, H., dell'Isola, F., Eremeyev, V.A., Öchsner, A. (Eds.) New Achievements in Continuum Mechanics and Thermodynamics, Springer, pp. 81-92, 2019. ASM

dell'Isola et al.: "Advances in pantographic structures: design, manufacturing, models, experiments and image analyses", Continuum Mechanics and Thermodynamics, Vol. 31(4), pp. 1231-1282, 2019. CMAT

Gaul, L. and Schmidt A.: "Finite element simulation and experiments on rotor damping assembled by disc shrink fits", Mechanical Systems and Signal Processing, pp. 412-422, 2019. Link

Hinze, M., Schmidt, A. and Leine, R.I.: "Numerical Simulation of Fractionally Damped Mechanical Systems Using Infinite State Representation", Proceedings of the 2019 International Conference on Fractional Calculus Theory and Applications, Bourges, France, 2019. PDF

Eugster, S.R., Capobianco, G. and Winandy, T.: "On different geometric approaches to the dynamics of finite-dimensional mechanical systems", In Proceedings in Applied Mathematics and Mechanics, Vol. 19, pp. e201900327:1-2, 2019. PDF

Eugster, S.R., dell’Isola, F. and Steigmann, D.J.: "Continuum theory for mechanical metamaterials with a cubic lattice substructure", Mathematics and Mechanics of Complex Systems, Vol. 7(1), pp. 75-98, 2019. PDF M&MoCS

Preiswerk, P.V. and Leine, R.I. : "A nonsmooth state observer for vibro-impact systems: experimental validation", proceedings of NODYCON 2019, Rome, 2019. 2 pages PDF

Walker, S.V. and Leine, R.I.: "Set-valued anisotropic dry friction laws: formulation, experimental verification and instability phenomenon", in Nonlinear Dynamics, Vol. 96, pp. 885–920, 2019. PDF, Link

Winandy, T., Capobianco, G. and Eugster, S.R.: "Kinematics of finite-dimensional mechanical systems on Galilean manifolds", In Proceedings in Applied Mathematics and Mechanics, Vol. 19, pp. e201900329:1-2, 2019. PDF

Peter, S., Schreyer, F. and Leine, R.I.: "A method for numerical and experimental nonlinear modal analysis of nonsmooth systems", in Mechanical Systems and Signal Processing, Vol. 120, pp. 793-807, 2019. PDF

2018

Eugster, S.R., Deutschmann, B.: "A nonlinear Timoshenko beam formulation for modeling a tendon-driven compliant neck mechanism”, In Proceedings in Applied Mathematics and Mechanics, Vol. 18, e201800208, 2018. PDF

Winandy, T., Baumann, M. and Leine, R.I.: "Variational Analysis of Inequality Impact Laws for Perfect Unilateral Constraints", in Advanced Topics in Nonsmooth Dynamics, Eds. R. Leine; V. Acary; O. Brüls, Springer-Verlag, pp. 47-92, 2018.

Winandy, T., Capobianco, G., Eugster, S.R.: "A geometric view on the kinematics of finite dimensional mechanical systems”, In Proceedings in Applied Mathematics and Mechanics, Vol. 18, e201800221, 2018. PDF

Capobianco, G., Eugster, S.R., Winandy, T.: "Modeling planar pantographic sheets using a nonlinear Euler-Bernoulli beam element based on B-spline functions”, In Proceedings in Applied Mathematics and Mechanics, Vol. 18, e201800220, 2018. PDF

Deutschman, B., Eugster, S.R., Ott, Ch.: "Reduced models for the static simulation of an elastic continuum mechanicsm”, IFAC-PapersOnLine 51(2), pp. 403-408, 2018. PDF

Andreaus, U., Spagnuolo, M., Lekszycki, T. and Eugster, S.R.: "A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler-Bernoulli beams”, Continuum Mechanics and Thermodynamics, Vol. 30(5), pp. 1103-1123, 2018. PDF CMAT

Preiswerk, P.V. and Leine, R.I.: "Experimental performance verification of a synchronization based state observer using only collision time information", Proc. IDETC, Quebec, Canada, 2018. PDF

Hinze, M., Schmidt, A. and Leine, R.I.: "Mechanical Representation and Stability of Dynamical Systems Containing Fractional Springpot Elements", Proc. IDETC, Quebec, Canada, 2018. PDF

Scheel, M., Peter, S., Leine, R.I. and Krack, M.: "A phase resonance approach for modal testing of structures with nonlinear dissipation", in Journal of Sound and Vibration, Vol. 435, pp. 56-73, 2018. PDF

Schindler, K. and Leine, R.I. : "Paradoxical chaos-like chattering in the bouncing ball system", Proceedings of the ASME 2018 International Design Engineering Technical Conferences, Quebec, Canada, August 2018. PDF

Schreyer, F. and Leine R.I. : "Combined frequency-time reduction methods for calculating periodic solutions of unilaterally constrained systems", IUTAM Symposium on Model Order Reduction of Coupled Systems (MORCOS 2018), Stuttgart, Germany, 2018. 2 pages. PDF

R. Leine; V. Acary; O. Brüls: "Advanced Topics in Nonsmooth Dynamics", 2018. VIII, 457 p. 179 illus., 82 illus. in color, Springer Verlag. Link

Luo, J., Schmidt, A. and Gaul, L: "On the Eigensolutions of Circular Plate with Viscoelastic Filling Media Using Fractional Derivatives", proceedings of MATHMOD 2018: International Conference on Mathematical Modelling, Vienna, Austria, February 21-23, 2018, pdf

Schreyer, F., Peter, S. and Leine, R. I.: "Experimental and Numerical Nonlinear Modal Analysis of a Beam with Impact: Part I – Numerical Investigation", in Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, Orlando, USA, 2018. PDF

Peter, S., Schreyer, F. and Leine, R. I.: "Experimental and Numerical Nonlinear Modal Analysis of a Beam with Impact: Part II – Experimental Investigation", in Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, Orlando, USA, 2018. PDF

Scheel, M., Kleyman, G., Tatar, A., Brake, M. R. W., Peter, S., Noël, J.-P., Allen, M. S. and Krack, M.: "System Identification of Jointed Structures: Nonlinear Modal Testing vs. State-Space Model Identification", in Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, Orlando, USA, 2018. PDF

Capobianco, G., Eugster, S.R.: "Time finite element based Moreau-type integrators”, International Journal for Numerical Methods in Engineering, Vol. 114(3), pp. 1-21, 2018. PDF INTJNUMERMETHENG

Eugster, S.R., Steigmann, D.J.: "Variational methods in the theory of beams and lattices", in Encyclopedia of Continuum Mechanics, H. Altenbach, A. Öchsner (Eds.), pp. 1-9, 2018. PDF ECM

Eugster, S. R. and dell'Isola, F.: "Exegesis of sect. III.B from "Fundamental of the mechanics of continua" by E. Hellinger", Zeitschrift für Angewandte Mathematik und Mechanik, Vol 98(1), pp. 69-105, 2018. PDF ZAMM

Eugster, S. R. and dell'Isola, F.: "Exegesis of sect. II and III.A from "Fundamental of the Mechanics of Continua" by E. Hellinger", Zeitschrift für Angewandte Mathematik und Mechanik, Vol 98(1), pp. 31-68, 2018. PDF ZAMM

Baumann, M., Biemond, J.J.B., Leine, R.I. and van de Wouw, N.: "Synchronization of impacting mechanical systems with a single constraint", in Physica D: Nonlinear Phenomena, Vol. 362, pp. 9-23, 2018. PDF

Peter, S., Scheel, M., Krack, M. and Leine, R.I.: "Synthesis of nonlinear frequency responses with experimentally extracted nonlinear modes", in Mechanical Systems and Signal Processing, Vol. 101, pp. 498-515, 2018. https://doi.org/10.1016/j.ymssp.2017.09.014

2017

Eugster, S.R., dell'Isola, F.: "An ignored source in the foundations of continuum physics "Die Allgemeinen Ansätze der Mechanik der Kontinua" by E. Hellinger", In Proceedings in Applied Mathematics and Mechanics, Vol. 17, pp. 413-414, 2017. PDF

Winandy, T., Eugster, S.R., Bergold, M.: "A robot inspired by a non-smooth point mass model of a worm", In Proceedings in Applied Mathematics and Mechanics, Vol. 17, pp. 143-144, 2017. PDF

Capobianco, G., Eugster, S.R., Leine, R.I.: "Moreau-type integrators based on the time finite element discretization of the virtual action", In Proceedings in Applied Mathematics and Mechanics, Vol. 17, pp. 177-178, 2017. PDF

Baumann, M. and Leine, R.I.: "Synchronization-based estimation of the maximal Lyapunov exponent of nonsmooth systems", Procedia IUTAM 20, (2017), 26-33. PDF

Eugster, S.R., Glocker, Ch.: "On the notion of stress in classical continuum mechanics", Mathematics and Mechanics of Complex Systems, Vol. 5 (3-4), pp. 299-338, 2017. PDF MEMOCS

Eugster, S. R. and dell'Isola, F.: "Exegesis of the introduction and sect. I from "Fundamental of the Mechanics of Continua" by E. Hellinger", Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 97(4), pp. 477-506, 2017. PDF ZAMM

Hesch, C., Schuss, S., Dittmann, M., Eugster, S.R., Favion, M. and Krause, R.: "Variational space-time elements for large-scale systems", Computer Methods in Applied Mechanics and Engineering, Vol. 326, pp. 541-572, 2017. PDF COMPUTMETHODAPPLM

Capobianco, G., Winandy, T., Eugster, S.R., Leine, R.I.: "Comparison of Moreau-type integrators based on the time finite element discretization of the virtual action", In Proceedings of the 9th European Nonlinear Dynamics Conference, pp. 1-2, 2017. PDF

Walker, S. and Leine, R.I.: "Anisotropic dry friction with non-convex force reservoirs: modeling and experiments", Proc. ENOC, Budapest, Hungary, 2017. PDF

Peter, S. and Leine. R.I.: "Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation", in Mechanical Systems and Signal Processing, Vol. 96, pp. 139-158, 2017. PDF Link

Pagitz, M. and Leine, R.I.: "Shape optimization of compliant pressure actuated cellular structures", in International Journal of Non-Linear Mechanics, 2017. PDF

2016

Baumann, M. and Leine, R.I.: "Synchronization-based Estimation of the Maximal Lyapunov Exponent of Nonsmooth Systems", Proc. ICTAM, Montréal, Canada, 2016. PDF

Schreyer, F. and Leine, R.I.: "A Mixed Shooting–Harmonic balance method for unilaterally constrained mechanical �systems", in Archive of Mechanical Engineering, Vol. LXIII, No. 2, pp. 297-313, 2016. PDF

Winandy, T. and Leine, R.I.: "A maximal monotone impact law for the 3-ball Newton’s cradle", in Multibody System Dynamics, 39:79–94, 2017. PDF

Baumann, M., Biemond, B.J.J., Leine, R.I. and van de Wouw, N.: "Controlled Synchronization of Mechanical Systems with a Unilateral Constraint", Proc. 10th IFAC Symposium on Nonlinear Control Systems, Monterey, California, USA, pp. 345-350, 2016. PDF

Baumann, M. and Leine, R.I.: "Estimation of the maximal Lyapunov exponent of nonsmooth systems using chaos synchronization", Proc. IMSD, Montréal, Canada, 2016. PDF

Schreyer, F. and Leine, R.I.: "Mixed Shooting-HBM: a periodic solution solver for unilaterally constrained systems", Proc. IMSD, Montréal, Canada, 2016. PDF

Walker, S.V. and Leine, R.I.: "Modeling and numerical simulation of anisotropic dry friction with non-convex friction force reservoir", Proc. IMSD, Montréal, Canada, 2016. PDF

Capobianco, G. and Eugster, S.R.: "A Moreau-type variational integrator", In Proceedings in Applied Mathematics and Mechanics. 4 pages, submitted 2016. PDF

Eugster, S.R. and Glocker, Ch.: "An alternative perspective on the concept of stress in classical continuum mechanics", in Proceedings in Applied Mathematics and Mechanics. 2 pages, submitted 2016. PDF

Peter, S., Riethmüller, R. and Leine, R.I.: "Tracking of Backbone Curves of Nonlinear Systems using Phase-Locked-Loops", in Nonlinear Dynamics, Volume 1, Proceedings of the 34th IMAC, A Conference and Exposition on Structural Dynamics, 2016, Eds. Kerschen, G., Conference Proceedings of the Society for Experimental Mechanics Series, Springer. PDF

Ehrlich, C., Schmidt, A. and Gaul, L.: "Reduced thin-layer elements for modeling the nonlinear transfer behavior of bolted joints of automotive engine structures", Archive of Applied Mechanics 86:59–64, 2016, online-journal

2015

Baumann, M. and Leine, R.I.: "Synchronization-based state observer including position jumps for impacting multibody systems", in Proceedings of the 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, Japan, 2015. PDF

Ehrlich, C., Schmidt, A. and Gaul, L.: "Reduced Thin-Layer Element Model for Joint Damping", Proceedings of ICoEV 2015: International Conference on Engineering Vibration, Ljubljana, Slovenia, September 7-10, 2015. PDF

Baumann, M. and Leine, R.I.: "A synchronization-based state observer for impact oscillators using only collision time information", in International Journal of Robust and Nonlinear Control, 2016, 26:2542–2563. PDF

Schreyer, F. and Leine, R.I.: "Finding Periodic Solutions of Forced Systems with Local Nonlinearities: A Mixed Shooting Harmonic Balance Method", Proc. IDETC/CIE, 2015. PDF

Leine, R.I. and Schreyer, F.: "A Mixed Shooting and Harmonic Balance Method for Mechanical Systems with Dry Friction or other Local Nonlinearities", in Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics, Barcelona, Spain, 2015. PDF

Baumann, M. and Leine, R.I.: "Synchronization-based state observer for impacting multibody systems using switched geometric unilateral constraints", in Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics, Barcelona, Spain, 2015. PDF

Winandy, T. and Leine, R.I.: "Towards a Maximal Monotone Impact Law for Newton’s Cradle", in Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics, Barcelona, Spain, 2015. PDF

Peter, S., Grundler, A., Reuss, P., Gaul, L. and Leine, R. I. : "Towards Finite Element Model Updating Based on Nonlinear Normal Modes" in Nonlinear Dynamics, Volume 1, Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015, Eds. Kerschen, G., Conference Proceedings of the Society for Experimental Mechanics Series, Springer, Cham, pp. 209-217, 2016. PDF

Eugster, S.R.: "An Intrinsic Geometric Formulation of the Equilibrium Equations in Continuum Mechanics", In Proceedings in Applied Mathematics and Mechanics, 2 pages, to appear. PDF

Leine, R.I. and Winandy, T.: "Nonexpansivity of the Newton’s Cradle Impact Law", In Proceedings in Applied Mathematics and Mechanics, Vol. 15, pp. 59-60, 2015. PDF

Schmidt, A., Shivaswamy, A. and Gaul, L.: "Experimental investigation and finite element modelling of a new high damping metallic material", Materials Science & Engineering Technology 46(4-5), 2015, pp. 515-523.

Eugster, S.R.: Geometric Continuum Mechanics and Induced Beam Theories, Lecture Notes in Applied and Computational Mechanics Vol. 75, Springer-Verlag, 2015.

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