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Dynamic Variational Principles with Application for Contact Problems with Friction

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Encyclopedia of Continuum Mechanics

Synonyms

Boundary variational functional; Friction; Nonsmooth optimization algorithm; Unilateral contact; Variational principles

Definitions

A mathematical model of an elastodynamic contact problem with unilateral restrictions in classical and weak forms. Generalization of the Hamilton-Ostrogradskii and Tupin variational principles as well as boundary variational principles on unilateral contact problems with friction. Nonsmooth optimization algorithms of Udzawa type for the solution of these unilateral contact problems with friction.

Introduction

Mechanical contact is one of the most common and important solid bodies interactions. Dynamic contact and friction are phenomena that are of importance in uncountable scientific and engineering applications (Brogliato 2016) and especially in fracture dynamics (Guz and Zozulya 2002). Contact problems are inherently nonlinear, since the actual surface on which these bodies meet is generally unknown a priori and must be determined as part of...

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References

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, York University, Toronto, ON, Canada

    Aleksander Czekanski

  2. Department of Materials, Centro de Investigacion Cientifica de Yucatan, Merida, Yucatan, Mexico

    V. V. Zozulya

Authors
  1. Aleksander Czekanski
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  2. V. V. Zozulya
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Corresponding author

Correspondence to Aleksander Czekanski .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, QLD, Australia

    Andreas Öchsner

Section Editor information

  1. DISG, University of Rome La Sapienza, Rome, Italy

    Francesco dell’Isola

  2. International Research Center M&MoCS, University of L’Aquila, L’Aquila, Italy

    Francesco dell’Isola

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Czekanski, A., Zozulya, V.V. (2018). Dynamic Variational Principles with Application for Contact Problems with Friction. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_274-1

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  • DOI: https://doi.org/10.1007/978-3-662-53605-6_274-1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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