Computational Contact Mechanics

Geometrically Exact Theory for Arbitrary Shaped Bodies

  • Alexander Konyukhov
  • Karl Schweizerhof

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 67)

Table of contents

  1. Front Matter
    Pages 1-18
  2. Alexander Konyukhov, Karl Schweizerhof
    Pages 1-24
  3. Alexander Konyukhov, Karl Schweizerhof
    Pages 25-34
  4. Alexander Konyukhov, Karl Schweizerhof
    Pages 63-118
  5. Alexander Konyukhov, Karl Schweizerhof
    Pages 119-133
  6. Alexander Konyukhov, Karl Schweizerhof
    Pages 135-184
  7. Alexander Konyukhov, Karl Schweizerhof
    Pages 185-207
  8. Alexander Konyukhov, Karl Schweizerhof
    Pages 293-313
  9. Alexander Konyukhov, Karl Schweizerhof
    Pages 315-329
  10. Alexander Konyukhov, Karl Schweizerhof
    Pages 367-380
  11. Alexander Konyukhov, Karl Schweizerhof
    Pages 381-412
  12. Back Matter
    Pages 0--1

About this book


This book contains a systematical analysis of geometrical situations  leading to  contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface.  Each contact pair  is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system.  The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a  certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others  are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are  then ready-for-implementation numerical algorithms within the finite element method including any arbitrary discretization techniques such as high order and isogeometric finite elements, which are most convenient for the considered geometrical situation.

The book proposes a consistent study of geometry and kinematics, variational formulations, constitutive relations for surfaces and discretization techniques for all considered geometrical pairs and  contains the associated  numerical analysis as well as some new analytical results in contact mechanics.


Closest Point Projection Procedure Computational Contact Mechanics Contact Mechanics Covariant Existence Finite Elements Geometry of Surfaces and Curves Linearization Numerical Methods Solid-Beam Surface-To-Surface Uniqueness

Authors and affiliations

  • Alexander Konyukhov
    • 1
  • Karl Schweizerhof
    • 2
  1. 1.Institute of MechanicsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2., Institut für MechanikKarlsruher Institut für TechnologieKarlsruheGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-31530-5
  • Online ISBN 978-3-642-31531-2
  • Series Print ISSN 1613-7736
  • Series Online ISSN 1860-0816
  • Buy this book on publisher's site