Materials Science

, Volume 54, Issue 2, pp 194–201 | Cite as

Contact of Two Elastic Bodies with Wavy Topography in the Presence of Gases in Gaps

  • O. P. KozachokEmail author
  • B. S. Slobodian
  • R. M. Martynyak

The contact of two elastic semiinfinite bodies one of which has a wavy surface in the presence of real gases in interface gaps is investigated. The state of the gas is described by the van der Waals equation, which makes it possible to consider the gas-liquid phase transition. The posed contact problem is reduced to a singular integral equation (SIE) with Hilbert kernel for the derivative of the height of interface gaps. Then this SIE is transformed into a SIE with Cauchy kernel, which is solved analytically. The condition of existence of a solution of this SIE and the van der Waals equation yield a system of transcendental equations for the width of the gaps and gas pressure. This system is solved numerically. The dependences of the width of the gaps, the pressure and volume of the gas, the average normal displacement, and the contact compliance of the bodies on the applied load and temperature are analyzed.


contact interaction wavy topography interface gaps real gas phase transitions singular integral equations 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • O. P. Kozachok
    • 1
    Email author
  • B. S. Slobodian
    • 1
  • R. M. Martynyak
    • 1
  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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