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

M. Ciavarella (2021) Improved Muller approximate solution of the pull-off of a sphere from a viscoelastic substrate, Journal of Adhesion Science and Technology, DOI: 10.1080/01694243.2021.1882766

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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.The figure shows the load obtained at pull off depending on the single dimensionless parameter beta (proportional to speed), and for various exponents n of the Gent-Schulz law n.