Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Dynamic Variational Principles with Application for Contact Problems with Friction

  • Aleksander CzekanskiEmail author
  • V. V. Zozulya
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_274-1



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.


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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringYork UniversityTorontoCanada
  2. 2.Department of MaterialsCentro de Investigacion Cientifica de YucatanMeridaMexico

Section editors and affiliations

  • Francesco dell’Isola
    • 1
    • 2
  1. 1.DISGUniversity of Rome La SapienzaRomeItaly
  2. 2.International Research Center M&MoCSUniversity of L’AquilaL’AquilaItaly