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Archive for Rational Mechanics and Analysis

, Volume 208, Issue 1, pp 25–57 | Cite as

Normal Compliance Contact Models with Finite Interpenetration

  • Christof Eck
  • Jiří Jarušek
  • Jana StaráEmail author
Article

Abstract

We study contact problems with contact models of normal compliance type, where the compliance function tends to infinity for a given finite interpenetration. Such models are physically more realistic than standard normal compliance models, where the interpenetration is not restricted, because the interpenetration is typically justified by deformations of microscopic asperities of the surface; therefore it should not exceed a certain value that corresponds to a complete flattening of the asperities. The model can be interpreted as intermediate between the usual normal compliance models and the unilateral contact condition of Signorini type. For the static problem without friction, we prove the existence and uniqueness of solutions and establish the equivalence to an optimization problem. For the static problem with Coulomb friction, we show the existence of a solution. The analysis is based on an approximation of the problems by standard normal compliance models, the derivation of regularity results for these auxiliary problems in Sobolev spaces of fractional order by a special translation technique, and suitable limit procedures.

Keywords

Variational Inequality Contact Problem Coulomb Friction Normal Compliance Friction Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute for Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany
  2. 2.Mathematical InstituteAcademy of Sciences of the Czech RepublicPraha 1Czech Republic
  3. 3.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic

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