Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory

Abstract

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than characteristic dimension of the contact area, a direct derivation of asymptotic relations for displacements and stress is presented. The proposed approach is compared with other published approaches. The cases are established when the leading order approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler-Fuss elastic foundation. For this elastic foundation, the axisymmetric adhesive contact is studied in the framework of the JKR (Johnson, Kendall, and Roberts) theory. The JKR approach has been generalized to the case of the punch shape being described by an arbitrary blunt axisymmetric indenter. Connections of the results obtained to problems of nanoindentation in the case of the indenter shape near the tip has some deviation from its nominal shape are discussed. For indenters whose shape is described by power-law functions, the explicit expressions are derived for the values of the pull-o force and for the corresponding critical contact radius.

Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials

“…Overall, it is typical to represent the solutions of more complex contact problems in the form of parametric functions, in which both the external load and the indenter displacement depend on the contact radius as the parameter [34]. Among numerous examples of this kind, one can find asymptotic mathematical models of JKR-type contact for layered and coated medium [83][84][85][86], implementations of the Maugis theory [87,88], or the double-Hertz theory [89]. These models have complex mathematical form of parametric functions that cannot be exactly reduced to explicit or implicit ones.…”

“…The mathematical model of such a DSI experiment in the framework of the JKR theory of adhesive contact can be written in a dimensionless form [85]:…”

A Macro Model for Electroadhesive Contact of a Soft Finger With a Touchscreen

“…The Winkler-Fuss model allows analytical treatment of contact problems even for non-convex indenters [27]. The JKR-type adhesive contact problem for thin elastic layers have been considered in [28][29][30][31][32]. The Winkler-Fuss modeling framework has been used in a number of papers (see, e.g., [33]) for the purpose of modeling the finger contact deformation.…”

Adhesion of Soft Materials to Rough Surfaces: Experimental Studies, Statistical Analysis and Modelling

“…In the linear case, this layer is the Winkler-Fuss elastic foundation that may stick to the surface. It is well known that the leading terms of relations for the problem of contact between a compressible thin layer and a blunt punch may be treated as a problem for the Winkler-Fuss elastic foundation; it is also possible to solve the appropriate adhesive contact problem (see, e.g., [43]).…”