A study on the extent of the contact and stick zones in multiple contacts

  • P. GhanatiEmail author
  • S. Adibnazari


In this paper, we analyze a general quasi-static two-dimensional multiple contact problem between two elastically similar half-planes under the constant normal (including applied moments) and oscillatory tangential loading utilizing the classical singular integral equations approach. Boundary conditions at nonsingular edges of discrete contact zones are applied and new side conditions are extracted and named “the consistency conditions” for multiple contacts. These conditions are mandatory for determination of the positions of the nonsingular edges of the contact and stick zones, when the number of them exceeds the number of the discrete contact and stick zones, respectively. Consequently, a mathematical relation between the pressure and shear distribution functions and between the extent of the contact and stick zones is obtained for the mentioned problem that shows all of the contact zones reach the full slip state simultaneously. Moreover, we show that for the weak normal loading, the approximated extent of the contact zones in multiple contacts with nonsingular edges may be estimated conveniently by assuming that the extent of the contact zones is the same as the overlapped extent in the free interpenetration figure.


Analytical approach Multiple contacts Similar materials Boundary conditions Nonsingular edges Consistency conditions 



Authors are grateful for the constructive discussion they had with professor James Richard Barber.


This research received no specific Grant from any funding agency in the public, commercial, or not-for-profit sectors.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUrmia University of TechnologyUrmiaIran
  2. 2.Department of Aerospace EngineeringSharif University of TechnologyTehranIran

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