Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction

  • Valentin Popov Technische Universität Berlin, Berlin, Germany
Keywords: Adhesion, Viscoelastic bodies, Energetic criterion, Energetic surfaces, Entropic surfaces.


We suggest a detachment criterion for a viscoelastic elastomer contact based on Griffith's idea about the energy balance at an infinitesimal advancement of the boundary of an adhesive crack. At the moment of detachment of a surface element at the boundary of an adhesive contact, there is some quick (instant) relaxation of stored elastic energy which can be expressed in terms of the creep function of the material. We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and thus it is only this part of energy relaxation that must be used in Griffith's energy balance. The described idea has several restrictions. Firstly, in this pure form, it is only valid for adhesive forces having an infinitely small range of action (which we call the JKR-limit). Secondly, it is only applicable to non-entropic (energetic) interfaces, which detach "at once" and do not possess their own kinetics of detachment.


Barquins, M. & Maugis, D. (1981). Tackiness of elastomers. The Journal of Adhesion, 13, 53-65.

Ciavarella, M., McMeeking, R. M. & Cricri, G. (2021). On the Afferante-Carbone theory of ultratough tape peeling, Universitatis, Series: Mechanical Engineering, https://doi.org/10.22190/FUME210101019C.

Derjaguin, B.V., Muller, V.M., & Toporov, Y.P. (1975). Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science, 53, 314–326.

Griffith, A.A. (1921). The Phenomena of Rupture and Flow in Solids. Philosophical Transactions of the Royal Society of London, Series A, 221, 163–198.

Heß, M. (2011). Über die exakte Abbildung ausgewählter dreidimensionaler Kontakte auf Systeme mit niedrigerer räumlicher Dimension. Göttingen: Cuvillier.

Johnson, K.L., Kendall, K, Roberts, A.D. (1971). Surface Energy and the Contact of Elastic Solids. Proceedings of the Royal Society of London, Series A, 324, 301–313.

Kusche, S. (2016). Simulation von Kontaktproblemen bei linearem viskoelastischem Materialverhalten, Dissertation, Technische Universität Berlin.

Pohrt, R. & Popov, V.L. (2015). Adhesive contact simulation of elastic solids using local mesh-dependent detachment criterion in boundary elements method. Facta Universitatis, Series: Mechanical Engineering, 13 (1), 3-10.

Popov, V.L. (2017). Contact mechanics and friction: physical principles and applications. (2nd ed.) Heidelberg: Springer.

Popov, V.L., Pohrt, R., Li, Q. (2017). Strength of adhesive contacts: Influence of contact geometry and material gradients. Friction, 5 (3), 308-325.

Popov, V.L., Willert, E. & Heß, M. (2018). Method of dimensionality reduction in contact mechanics and friction: A user’s handbook. iii. viscoelastic contacts. Facta Universitatis, Series: Mechanical Engineering, 16 (2), 99-113.

Popov, V.L., Heß, M. & Willert, E. (2019). Handbook of Contact Mechanics. Exact Solutions of Axisymmetric Contact Problems. Berlin Heidelberg: Springer-Verlag.

Popova, E., Popov, V.L. (2018). Note on the history of contact mechanics and friction: Interplay of electrostatics, theory of gravitation and elasticity from Coulomb to Johnson–Kendall–Roberts theory of adhesion. Physical Mesomechanics 21 (1), 1-5.

Popova, E., Popov, V.L. (2020). Ludwig Föppl and Gerhard Schubert: Unknown classics of contact mechanics, Z Angew Math Mech., 100, e202000203.

How to Cite
Popov, V. (2021). Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction. Reports in Mechanical Engineering, 2(1), 57-64. https://doi.org/10.31181/rme200102057p