Adhesive contact of elastic solids with stohastic roughness

  • I. K. Valeeva Frantsevich Institute for Problems in Materials Science NAS of Ukraine, Krzhizhanovsky str., 3, 03142, Kyiv


Model of normal adhesive contact between elastic bodies with stochastic surface roughness is under consideration. Roughness is simulated by Winkler-Fuss nonlinear layer, which can resist to compressive and tensile (in the case of adhesion) contact stresses. Mechanical properties of the layer are determined by statistical theories of adhesive contact between nominally flat rough surfaces. The contact of solids is described by nonlinear boundary integral equations with non-monotonic operators. Their solutions determine reduction of effective thickness of rough layer, contact stresses, contact region, adhesion force. Formulas for adhesion force calculation are presented for the most frequent nominal gap between solids in contact for DMT–theory of contact.

Key words: adhesive interaction, contact of rough solids, adhesion force.

Pages of the article in the issue: 53 - 56

Language of the article: Ukrainian


GERBERICH, W. W., CORDILL, M. J. (2006) Physics of adhesion. Rep. Prog. Phys., – 69. pp. 2157–2203.

BOURAGO N.G., KUKUDZHANO V.N. (2005) A review of contact algorithms / The Institute for problems in mechanics of RAS, Moscow, Izv. RAN, MTT, No. 1. pp. 45–87.

SAUER R.A. (2015) A Survey of Computational Models for Adhesion // The Journal of Adhesion. 92, Issue 2. pp. 1–43

SAUER R.A. (2012) Computational contact formulations for soft body adhesion Advanses in soft Matter Mechanics (Chapter 2), Li, S., Sun, B. (Eds.), Springer.

Friction and Wear: From Elementary Mechanisms to Macroscopic Behavior (2019) ed. by Popov V.L., Pohrt R. Front. Mech. Eng. doi:10.3389/fmech.2019.00047

MAUGIS D. (2000) Contact, Adhesion and Rupture of Elastic Solids. – Berlin: Springer-Verlag.

JOHNSON K.L. (1975) Non-Hertzian contact of elastic spheres. In: The mechanics of the contact between deformable bodies, ed. by de Pater, Kalker. - Delft:University Press. pp. 26–40.

FULLER K.N.G., TABOR D. (1975) The effect of surface roughness on the adhesion of elastic solids // Proc. R. Soc. Lond. A. – 345. pp. 327–342.

GALANOV B. A., VALEEVA I. K. (2016) Sliding adhesive contact of elastic solids with stochastic roughness. Int. J. Eng. Sci. 101. pp. 64–80.

GALANOV B.A. (2011) Models of adhesive contact between rough elastic bodies. Int. J. Mech. Sci. 53. pp. 968–977.

TABOR D. (1997) Surface forces and surface interactions // J. Colloids Interface Sci. V. 58. pp. 2–13.

How to Cite
Valeeva, I. K. (1). Adhesive contact of elastic solids with stohastic roughness. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, (1-2), 53-56.
Differential equations, mathematical physics and mechanics