A Multiscale Numerical Model for Structures with Internal Frictional Contacts

  • K. Truyaert
  • V. Aleshin
  • S. DelrueEmail author
  • K. Van Den Abeele
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Many engineering applications are related to or deal with materials and systems having internal frictional contacts in their structure. The effects induced by these contacts, such as friction-induced heat generation, wear, nonlinear vibrations, etc., can be significant and cannot be ignored in numerical models. However, friction models are computationally cumbersome because they often require implicit data exchange procedures to describe the contact evolution. Moreover, detailed meshing of the contact zone is needed to cover the microgeometry (roughness). Here, an alternative model is proposed, based on a semi-analytical method of contact mechanics, called the Method of Memory Diagrams (MMD), that allows for an automated explicit calculation of the hysteretic frictional contact response. The key strength of the method is that it uses a multiscale approach in which mesoscopic cells, containing a section of the frictional contact, are introduced to resolve the stress and displacement fields at the contact interface into a single load-displacement relationship. Hence, the essential constitutive information of the contact is supplied to the macroscale model by the mesoscopic cells, drastically simplifying the account for rough contacts and avoiding microscopic meshing of the contact geometry. The MMD contact model is directly integrated into a Finite Element Modeling (FEM) environment enabling the study of the dynamic behavior of structures with frictional interfaces. The potential of the proposed model for engineering applications will be demonstrated by simulating the contact behavior of a dynamically excited frictional contact and by linking this behavior to friction-induced effects such as nonlinear vibrations and heat production.


Computational modeling Contact mechanics Method of memory diagrams Acoustic wave propagation Thermosonics 



The research leading to these results has gratefully received funding from Internal Funds KU Leuven (C24/15/021).


  1. 1.
    Yastrebov, V.A.: Numerical Methods in Contact Mechanics. Wiley-ISTE, London (2013)CrossRefGoogle Scholar
  2. 2.
    Blanloeuil, P., Meziane, A., Bacon, C.: Numerical study of nonlinear interaction between a crack and elastic waves under an oblique incidence. Wave Motion 51(3), 425–437 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Mindlin, R., Deresiewicz, H.: Elastic spheres in contact under varying oblique forces. J. Appl. Mech. 20, 327–344 (1953)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Popov, V.L., Heß, M.: Method of dimensionality reduction in contact mechanics and friction: a users handbook. I. Axially-symmetric contacts. Facta Univ., Ser. Mech. Eng. 12, 1–14 (2014)Google Scholar
  5. 5.
    Jäger, J.: Axi-symmetric bodies of equal material in contact under torsion or shift. Arch. Appl. Mech. 65(7), 478–487 (1995)CrossRefGoogle Scholar
  6. 6.
    Ciavarella, M.: The generalized cattaneo partial slip plane contact problem. I-Theory. Int. J. Solids Struct. 35(18), 2349–2362 (1998)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Aleshin, V., Bou Matar, O., Van Den Abeele, K.: Method of memory diagrams for mechanical frictional contacts subject to arbitrary 2d loading. Int. J. Solids Struct. 60, 84–95 (2015)CrossRefGoogle Scholar
  8. 8.
    Aleshin, V., Delrue, S., Trifonov, A., Bou Matar, O., Van Den Abeele, K.: Two dimensional modeling of elastic wave propagation in solids containing cracks with rough surfaces and friction - Part I: theoretical background. Ultrasonics 82, 11–18 (2018)CrossRefGoogle Scholar
  9. 9.
    Delrue, S., Aleshin, V., Truyaert, K., Bou Matar, O., Van Den Abeele, K.: Two dimensional modeling of elastic wave propagation in solids containing cracks with rough surfaces and friction - Part II: numerical implementation. Ultrasonics 82, 19–30 (2018)CrossRefGoogle Scholar
  10. 10.
    Barber, J.R., Davies, M., Hills, D.A.: Frictional elastic contact with periodic loading. Int. J. Solids Struct. 48(13), 2041–2047 (2011)CrossRefGoogle Scholar
  11. 11.
    Putignano, C., Ciavarella, M., Barber, J.R.: Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads. J. Mech. Phys. Solids 59(12), 2442–2454 (2011)CrossRefGoogle Scholar
  12. 12.
    Truyaert, K., Aleshin, V., Van Den Abeele, K., Delrue, S.: Theoretical calculation of the instantaneous friction-induced energy losses in arbitrarily excited axisymmetric mechanical contact systems. Int. J. Solids Struct. (2018, accepted)Google Scholar
  13. 13.
    COMSOL AB, Stockholm, Sweden: Structural Mecanics Module User’s Guide, COMSOL Multiphysics\(^{\textregistered }\) v. 5.3 (2017)Google Scholar
  14. 14.
    COMSOL AB, Stockholm, Sweden: Heat Transfer Module User’s Guide, COMSOL Multiphysics\(^{\textregistered }\) v. 5.3 (2017)Google Scholar
  15. 15.
    COMSOL AB, Stockholm, Sweden: LiveLink\(^{\text{TM}}\) for MATLAB\(^{\textregistered }\), COMSOL Multiphysics\(^{\textregistered }\) v. 5.3 (2017)Google Scholar
  16. 16.
    Biwa, S., Nakajima, S., Ohno, N.: On the acoustic nonlinearity of solid-solid contact with pressure-dependent interface stiffness. Trans. Am. Soc. Mech. Eng. J. Appl. Mech. 71(4), 508–515 (2004)CrossRefGoogle Scholar
  17. 17.
    Yuan, M., Zhang, J., Song, S.-J., Kim, H.-J.: Numerical simulation of Rayleigh wave interaction with surface closed cracks under external pressure. Wave Motion 57, 143–153 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Scalerandi, M., Gliozzi, A.S., Bruno, C.L.E., Van Den Abeele, K.: Nonlinear acoustic time reversal imaging using the scaling subtraction method. J. Phys. D: Appl. Phys. 41(21), 215404 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Wave Propagation and Signal Processing Research GroupKU Leuven KulakKortrijkBelgium
  2. 2.Joint International Laboratory LICS/LEMAC, IEMNVilleneuve d’Ascq CedexFrance

Personalised recommendations