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First yield in the Maugis‐adhesive contact of elastic spheres

Leroy, Jean‐Emmanuel; Willert, Emanuel

We analyze the onset of plastic yield in the Maugis‐adhesive contact of elastic spheres. Written in proper dimensionless variables, the problem solution depends on Poisson's ratio, the Tabor parameter and a non‐dimensional adhesion strength. The influences of adhesion range and strength are studied in detail. First yield can either occur inside the bodies on the axis of symmetry (for long range adhesion) or at the contact boundary (for short range adhesion). Adhesion significantly reduces the external load necessary to initiate plastic yield. A simple analytic solution for the critical load in the DMT‐limit of adhesion is being derived. Our results are quantitatively similar to previously published findings based on the double Hertz model of adhesion and can for example be applied to study an adhesive spherical microcontact in the contact of rough surfaces.
Published in: ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 10.1002/zamm.201900313, Wiley