Indentation mapping of stretched adhesive membranes

Author:

Argatov Ivan I.12ORCID

Affiliation:

1. Biofilms—Research Center for Biointerfaces, Malmö University, Malmö SE-205 06, Sweden

2. Institut für Mechanik, Technische Universität Berlin, Berlin 10623, Germany

Abstract

Unilateral adhesive contact between a rigid indenter and a uniformly stretched membrane of arbitrary shape is considered. The generalized Johnson–Kendall–Roberts (JKR)-type and Derjaguin– Muller–Toporov (DMT)-type models of non-axisymmetric adhesive contact are presented for short- and long-range adhesion, respectively, and the JKR–DMT transition is established in the framework of the generalized Maugis–Dugdale model. A refined method of matched asymptotic expansions is applied to construct the leading-order asymptotic model for indentation mapping of freestanding two-dimensional materials with an axisymmetric probe, using the approximate analytical solution obtained in explicit form for an infinite membrane in the limit of short-range adhesive contact with an indenter in the form of an elliptic paraboloid. The cases of a spherical indenter and a rectangular membrane are studied in detail.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Indentation of a circular hyperelastic membrane by a rigid cylinder;International Journal of Non-Linear Mechanics;2022-01

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