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Normal Compliance Contact Models with Finite Interpenetration

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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.

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Authors and Affiliations

  1. Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, Stuttgart, 70569, Germany

    Christof Eck

  2. Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Jiří Jarušek

  3. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18600, Praha 8, Czech Republic

    Jana Stará

Authors
  1. Christof Eck
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  2. Jiří Jarušek
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  3. Jana Stará
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Corresponding author

Correspondence to Jana Stará.

Additional information

Communicated by G. Dal Maso

We regret to record the death at the age of merely 43 years of Prof. Christof Eck. Our sense of loss will be shared by his family, his collegues, his former students and many friends.

The work presented here was partially supported by the Czech Academy of Sciences under grant IAA100750802 till the end of 2011, and by the Grant Agency of the Czech Republic under the grant P201/12/0671 later. Moreover it was supported by RVO 67985840. The third author was supported by the Grant Agency of the Czech Republic under the grant GACR 201/09/0917 and by the research project MSM0021620839.

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Eck, C., Jarušek, J. & Stará, J. Normal Compliance Contact Models with Finite Interpenetration. Arch Rational Mech Anal 208, 25–57 (2013). https://doi.org/10.1007/s00205-012-0602-8

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  • DOI: https://doi.org/10.1007/s00205-012-0602-8

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