RAS Energy, Mechanics & ControlПрикладная математика и механика Journal of Applied Mathematics and Mechanics

  • ISSN (Print) 0032-8235
  • ISSN (Online) 3034-5758

Models of discrete contact of elastic bodies taking into account adhesion forces

PII
S3034575825030115-1
DOI
10.7868/S3034575825030115
Publication type
Article
Status
Published
Authors
Volume/ Edition
Volume 89 / Issue number 3
Pages
512-528
Abstract
The paper presents formulations and solutions of periodic contact problems for an elastic half-plane and an elastic half-space taking into account the adhesive interaction of contacting bodies’ surfaces. To describe the adhesive forces in the gap between the surfaces, an approximation of the adhesive potential in the form of a piecewise constant function (the Maugis–Dugdale approximation) is used. The dependences of the real contact area, as well as the approach of bodies on the nominal pressure, the parameters of adhesive potential, and the surface relief parameters of the indenting body are investigated. The obtained solutions are compared with the results following from the Johnson, Kendall, Roberts (JKR) model based on the use of a simplified form of the adhesive potential. An analysis of energy dissipation in the surfaces approach–retraction cycle is carried out, and the influence of the parameters of surface microrelief on this contact interaction characteristic is estimated.
Keywords
адгезионное взаимодействие дискретный контакт поверхностный рельеф
Date of publication
02.06.2025
Year of publication
2025
Number of purchasers
0
Views
45

References

  1. 1. Johnson K.L., Kendall K., Roberts A.D. Surface energy and the contact of elastic solids // Proc. Roy. Soc. London A. 1971. V. 324. P. 301–313.
  2. 2. Johnson K.L., Greenwood J.A. An adhesion map for the contact of elastic spheres // J. Coll.&Interface. Sci. 1997. V. 192. P. 326–333.
  3. 3. Tabor D. Surface forces and surface interactions // J. Coll.&Interface. Sci. 1977. V. 58. № 2.P. 13.
  4. 4. Derjaguin B.V., Muller V.M., Toporov Yu.P. Effect of contact deformation on the adhesion of particles // J. Colloid&Interface Sci. 1975. V. 53. № 2. P. 314–326.
  5. 5. Горячева И.Г. Механика фрикционного взаимодействия. М.: Наука, 2001. 478 с.
  6. 6. Johnson K.L. The adhesion of two elastic bodies with slightly wavy surfaces. // Int. J. Solids& Struct. 1995. V. 32. № 3/4. P. 423–430.
  7. 7. Westergaard H.M. Bearing pressures and cracks // J. Appl. Mech. T. ASME. 1939. V. 6. P. 49–52.
  8. 8. Koiter W. An infinite row of collinear cracks in an infinite elastic sheet // Ingng Arch. 1959. V. 28. P. 168–172.
  9. 9. Hui C.Y., Lin Y.Y., Baney J.M., Kramer E.J. The mechanics of contact and adhesion of periodically rough surfaces // J. Polym. Sci. Pt. B: Polym. Phys. 2001. V. 39. № 11. P. 1195–1214.
  10. 10. Maugis D. Adhesion of spheres: The JKR-DMT transition using a Dugdale model // J. Colloid&Interface Sci.1991. V. 150. P. 243–269.
  11. 11. Джонсон К. Механика контактного взаимодействия. М.: Мир, 1989. 510 с.
  12. 12. Маховская Ю.Ю. Скольжение вязкоупругих тел при наличии адгезии // ПММ. 2005. Т. 69. Вып. 2. С. 334–344.
  13. 13. Цуканов И.Ю. Термоупругая неустойчивость при скольжении неоднородных материалов с разными теплофизическими свойствами // Вестн. машиностр. 2021. № 10. С. 61–65.
  14. 14. Kuznetsov Ye.A. Effect of fluid lubricant on the contact characteristics of rough elastic bodies in compression // Wear. 1985. V. 102. P. 177–194.
  15. 15. Greenwood J.A. On the almost-complete contact of elastic rough surfaces: The removal of tensile patches // Int. J. Solids&Struct. 2015. V. 56–57. P. 258–264.
  16. 16. Maugis D. Contact, Adhesion and Rupture of Elastic Solids. 2000. 414 p.
  17. 17. Горячева И.Г., Маховская Ю.Ю. Адгезионное взаимодействие упругих тел // ПММ. 2001. Т. 65. № 2. С. 279–279.
  18. 18. Goryacheva I., Makhovskaya Y. Discrete Contact Mechanics with Applications in Tribology. Elsevier Inc., 2022. 220 p.
  19. 19. Маховская Ю.Ю. Дискретный контакт упругих тел при наличии адгезии // Изв. РАН. МТТ. 2003. № 2. С. 49–60.
  20. 20. Goryacheva I., Makhovskaya Yu. A model of the adhesive component of the sliding friction force // Wear. 2011. V. 270. P. 628–633.
  21. 21. Солдатенков И.А. Применение метода последовательных приближений к расчету упругого контакта при наличии молекулярной адгезии // ПММ. 2012. Т. 76. Вып. 5. С. 734–743.
  22. 22. Солдатенков И.А. Контактная задача при объемном приложении сил межмолекулярного взаимодействия: упрощенный метод решения (двухуровневая модель) // ПММ. 2019. Т. 83. Вып. 2. С. 314–322.
  23. 23. Muller V.M., Yushchenko V.S., Derjaguin B.V. On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane // J. Colloid&Interface Sci. 1980. V. 77. № 1. P. 91–101.
  24. 24. Goryacheva I., Makhovskaya Yu. A model of the adhesive component of the sliding friction force // Wear. 2011. V. 270. P. 628–633.
  25. 25. Горячева И.Г., Маховская Ю.Ю. Адгезионное сопротивление при качении упругих тел // ПММ. 2007. Т. 71. Вып. 4. С. 534–543
QR
Translate

Индексирование

Scopus

Scopus

Scopus

Crossref

Scopus

Higher Attestation Commission

At the Ministry of Education and Science of the Russian Federation

Scopus

Scientific Electronic Library