Improved Muller approximate solution of the pull-off of a sphere from a viscoelastic substrate

Abstract

The detachment of a sphere from a viscoelastic substrate is clearly a fundamental problem. In the case viscoelastic dissipation is concentrated at the contact edge, and the work of adhesion follows a quite popular simplified model, Muller has suggested an approximate solution, which however is based on an empirical observation. We revisit Muller’s solution and show it leads to very poor fitting of the actual full numerical results, particularly for the radius of contact at pull-off, and we suggest an improved fitting of the pull-off which works extremely well over a very wide range of withdrawing speeds, and correctly converges to the JKR value at very low speeds.

Keywords:

• Viscoelasticity
• adhesion
• JKR theory
• viscoelastic material

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The factor 2 which is missing in Muller [10] comes from the fact that strain energy exists only in one material, assuming the other is rigid. For two identical materials, $\frac{1}{E^{*}}=\frac{2}{E_1^{*}}$ and we return to the standard LEFM case with $G\left(a\right)=\frac{K{\left(a\right)}^2}{E_1^{*}}.$

2 Strictly speaking, during loading adhesion is reduced with respect to the adiabatic value at zero speed, but we neglect this effect, or else we consider that loading occurs near thermodynamic equilibrium.

Additional information

Funding

MC acknowledges support from the Italian Ministry of Education, University and Research (MIUR) under the program ‘Departments of Excellence’ [L.232/2016].