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

Synonyms

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...

This is a preview of subscription content, log in to check access.

References

  1. Antes H, Panagiotopoulos PD (1992) The boundary integral approach to static and dynamic contact problems. Birkhauser, Basel/Boston/BerlinCrossRefGoogle Scholar
  2. Brogliato B (2016) Nonsmooth mechanics. Models, dynamics and control, 3rd edn. Springer, New YorkzbMATHGoogle Scholar
  3. Cea J (1978) Optimization. Theory and algorithms. Springer, Berlin/Heidelberg/New YorkzbMATHGoogle Scholar
  4. Czekanski A, Meguid SA (2001) Solution of dynamic frictional contact problems using nondifferentiable optimization. Int J Mech Sci 43:1369–1386CrossRefGoogle Scholar
  5. Czekanski A, Meguid SA (2006) On the use of variational inequalities to model impact problems of elasto-plastic media. Int J Impact Eng 32:1485–1511CrossRefGoogle Scholar
  6. Eringen AC, Suhubi ES (1975) Elastodynamics. Vol. 2. Linear theory. Academic, New YorkzbMATHGoogle Scholar
  7. Gurtin ME (1964) Variational principles for linear elastodynamics. Arch Ration Mech Anal 16(1):34–50MathSciNetCrossRefGoogle Scholar
  8. Guz AN, Zozulya VV (2002) Elastodynamic unilateral contact problems with friction for bodies with cracks. Int Appl Mech 38(8):895–932MathSciNetCrossRefGoogle Scholar
  9. Oden JT, Reddy JN (1983) Variational methods in theoretical mechanics. Springer, New YorkCrossRefGoogle Scholar
  10. Panagiotopoulos PD (1985) Inequality problems in mechanics and applications. Convex and non convex energy functions. Birkhauser, StuttgartCrossRefGoogle Scholar
  11. Zozulya VV (2011) Variational formulation and nonsmooth optimization algorithms in elastodynamic contact problems for cracked body. Comput Methods Appl Mech Eng 200:525–539MathSciNetCrossRefGoogle Scholar

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