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Multibody dynamics system with energy dissipation by hardening and softening plasticity

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Abstract

In this work we present a multibody dynamics system composed of geometrically exact nonlinear beams with inelastic behavior, representing flexible system components. The main focus of the work is to introduce advanced energy dissipation models using hardening and softening plasticity into such beam models and to show how they can also recover a vibration amplitude decay typical of viscous damping. The damping model is represented by the constitutive behavior of the flexible beam element chosen as an elasto-viscoplastic response with linear isotropic hardening and subsequent softening plasticity. The formulation is cast within the mixed variational framework, where the strong embedded discontinuity is introduced into displacement/rotation fields in the softening phase leading to localized plastic deformation. We also aim to ensure model capabilities to deliver results for long-term loading simulations, which is of interest for quantifying the risk of fatigue failure for such flexible system component. The corresponding numerical implementation combines the space discretization based on the finite element method with the time discretization based upon energy-conserving or energy-decaying integration schemes. The results of several numerical simulations are presented in the dynamics of flexible-rigid multi-body systems to illustrate a very satisfying performance of the proposed model.

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Acknowledgements

This work is financially supported by the French Ministry of Foreign Affairs (program ES-BALK, project CESPA) and the Ministry of Education, Science and Youth of Sarajevo Canton, Bosnia and Herzegovina. Moreover, the work was supported by the French Ministry of Foreign Affairs through a scholarship given by French Embassy in Sarajevo (SL) and Institut Universitaire de France (AI). These sources of funding are gratefully acknowledged.

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Authors and Affiliations

  1. Laboratoire Roberval de Mécanique, Centre de Recherche Royallieu, Université de Technologie de Compiègne/Alliance Sorbonne Université, 60200, Compiègne, France

    Suljo Ljukovac, Adnan Ibrahimbegovic & Rosa-Adela Mejia-Nava

  2. Faculty of Civil Engineering, University of Sarajevo, Patriotske lige 30, 71000, Sarajevo, Bosnia and Herzegovina

    Suljo Ljukovac & Ismar Imamovic

  3. Institut Universitaire de France, Paris, France

    Adnan Ibrahimbegovic

Authors
  1. Suljo Ljukovac
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  2. Adnan Ibrahimbegovic
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  3. Ismar Imamovic
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  4. Rosa-Adela Mejia-Nava
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Contributions

Authors AI and SL conceptualized the research idea and wrote the theoretical formulation. Author SL, with guidance and expertise from authors II and RAMN, developed the FEAP code and conducted the simulations. Author SL drafted the manuscript, and all authors contributed to its revision. All authors have given their final approval for publication.

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Correspondence to Suljo Ljukovac.

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Ljukovac, S., Ibrahimbegovic, A., Imamovic, I. et al. Multibody dynamics system with energy dissipation by hardening and softening plasticity. Multibody Syst Dyn (2024). https://doi.org/10.1007/s11044-024-09972-6

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