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Contact probing of stretched membranes and adhesive interactions: graphene and other two-dimensional materials

Borodich, Feodor M. ORCID: and Galanov, Boris A. 2016. Contact probing of stretched membranes and adhesive interactions: graphene and other two-dimensional materials. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472 (2195) , 20160550. 10.1098/rspa.2016.0550

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Contact probing is the preferable method for studying mechanical properties of thin two-dimensional (2D) materials. These studies are based on analysis of experimental force–displacement curves obtained by loading of a stretched membrane by a probe of an atomic force microscope or a nanoindenter. Both non-adhesive and adhesive contact interactions between such a probe and a 2D membrane are studied. As an example of the 2D materials, we consider a graphene crystal monolayer whose discrete structure is modelled as a 2D isotropic elastic membrane. Initially, for contact between a punch and the stretched circular membrane, we formulate and solve problems that are analogies to the Hertz-type and Boussinesq frictionless contact problems. A general statement for the slope of the force–displacement curve is formulated and proved. Then analogies to the JKR (Johnson, Kendall and Roberts) and the Boussinesq–Kendall contact problems in the presence of adhesive interactions are formulated. General nonlinear relations among the actual force, displacements and contact radius between a sticky membrane and an arbitrary axisymmetric indenter are derived. The dimensionless form of the equations for power-law shaped indenters has been analysed, and the explicit expressions are derived for the values of the pull-off force and corresponding critical contact radius.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Uncontrolled Keywords: two-dimensional materials, graphene, membrane, Johnson, Kendall and Roberts theory, adhesion, nanoindentation
Additional Information: Published by the Royal Society under the terms of the Creative Commons Attribution License, which permits unrestricted use, provided the original author and source are credited.
Publisher: Royal Society, The
ISSN: 1364-5021
Funders: Leverhulme Trust
Date of First Compliant Deposit: 21 November 2016
Date of Acceptance: 17 October 2016
Last Modified: 04 May 2023 14:38

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