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The maximum dissipation principle in rigid-body dynamics with inelastic impacts

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Abstract

Formulating a consistent theory for rigid-body dynamics with impacts is an intricate problem. Twenty years ago Stewart published the first consistent theory with purely inelastic impacts and an impulsive friction model analogous to Coulomb friction. In this paper we demonstrate that the consistent impact model can exhibit multiple solutions with a varying degree of dissipation even in the single-contact case. Replacing the impulsive friction model based on Coulomb friction by a model based on the maximum dissipation principle resolves the non-uniqueness in the single-contact impact problem. The paper constructs the alternative impact model and presents integral equations describing rigid-body dynamics with a non-impulsive and non-compliant contact model and an associated purely inelastic impact model maximizing dissipation. An analytic solution is derived for the single-contact impact problem. The models are then embedded into a time-stepping scheme. The macroscopic behaviour is compared to Coulomb friction in a large-scale granular flow problem.

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Acknowledgements

The authors would like to acknowledge the support through the Cluster of Excellence Engineering of Advanced Materials (EAM).

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Authors and Affiliations

  1. Lehrstuhl für Informatik 10 (Systemsimulation), Friedrich-Alexander Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Tobias Preclik, Sebastian Eibl & Ulrich Rüde

  2. CERFACS, 42 Avenue Gaspard Coriolis, 31057, Toulouse Cedex 01, France

    Ulrich Rüde

Authors
  1. Tobias Preclik
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  2. Sebastian Eibl
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  3. Ulrich Rüde
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Correspondence to Tobias Preclik.

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Preclik, T., Eibl, S. & Rüde, U. The maximum dissipation principle in rigid-body dynamics with inelastic impacts. Comput Mech 62, 81–96 (2018). https://doi.org/10.1007/s00466-017-1486-0

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