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A Hyperelastic Dynamic Frictional Contact Model with Energy-Consistent Properties

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Advances in Variational and Hemivariational Inequalities

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 33))

Abstract

In this chapter we present an energy-consistent numerical model for the dynamic frictional contact between a hyperlastic body and a foundation. Our contribution has two traits of novelty. The first one arises from the specific frictional contact model we consider, which provides intrinsic energy-consistent properties. The contact is modeled with a normal compliance condition of such a type that the penetration is limited with unilateral constraint and, the friction is described with a version of Coulomb’s law of dry friction. The second trait of novelty consists in the construction and the analysis of an energy-consistent scheme, based on recent energy-controlling time integration methods for nonlinear elastodynamics. Some numerical results for representative impact problems are provided. They illustrate both the specific properties of the contact model and the energy-consistent properties of the numerical scheme.

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Acknowledgements

This research was supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118 and the project Polonium “Mathematical and Numerical Analysis for Contact Problems with Friction” 2014/15.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Physique (LAMPS), Université de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860, Perpignan, France

    Mikael Barboteu, David Danan & Mircea Sofonea

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  1. Mikael Barboteu
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  2. David Danan
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  3. Mircea Sofonea
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Correspondence to Mikael Barboteu .

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Editors and Affiliations

  1. University of Iowa, Iowa City, IA, USA and Xi'an Jiaotong Universiry, Xi'an, China

    Weimin Han

  2. Faculty of Mathematics and Computer Scie Institute of Computer Science, Jagiellonian University, Kraków, Poland

    Stanisław Migórski

  3. Laboratoire de Mathématiques et Physique (LAMPS), Université de Perpignan Via Domitia, Perpignan, France

    Mircea Sofonea

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Barboteu, M., Danan, D., Sofonea, M. (2015). A Hyperelastic Dynamic Frictional Contact Model with Energy-Consistent Properties. In: Han, W., Migórski, S., Sofonea, M. (eds) Advances in Variational and Hemivariational Inequalities. Advances in Mechanics and Mathematics, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-14490-0_10

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