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Research Papers

The Buckling and Postbuckling of Fibrils Adhering to a Rigid Surface

[+] Author and Article Information
Sebastian Stark

Institute of Solid Mechanics,
Technische Universität Dresden,
01062 Dresden, Germany
e-mail: Sebastian.Stark1@tu-dresden.de

Matthew R. Begley

Department of Mechanical Engineering,
University of California,
Santa Barbara, CA 93106
e-mail: begley@engr.ucsb.edu

Robert M. McMeeking

Department of Mechanical Engineering,
University of California,
Santa Barbara, CA 93106;
Materials Department,
University of California,
Santa Barbara, CA 93106;
INM-Leibniz Institute for New Materials,
Campus D2 2,
66123 Saarbrücken, Germany;
School of Engineering,
University of Aberdeen,
King's College,
Aberdeen AB24 3UE, UK
e-mail: rmcm@engineering.ucsb.edu

1Corresponding author.

Manuscript received January 31, 2012; final manuscript received November 8, 2012; accepted manuscript posted November 28, 2012; published online May 23, 2013. Assoc. Editor: Lawrence A. Bergman.

J. Appl. Mech 80(4), 041022 (May 23, 2013) (11 pages) Paper No: JAM-12-1041; doi: 10.1115/1.4023107 History: Received January 31, 2012; Revised November 08, 2012; Accepted November 28, 2012

Recent experiments in which arrays of compliant fibrils are compressed axially against a rigid surface and then released have shown that there is load-displacement hysteresis during this process, accompanied by buckling and unbuckling of the fibrils. Furthermore, the adhesive performance of the system is decreased by such prior buckling. We present a model describing the buckling and postbuckling characteristics of a fibril with an aspect ratio of 10 or greater. The possibility during buckling of partial detachment of the end of the fibril is taken into account. The results are presented and discussed for both load and displacement control and the load-displacement hysteresis is identified. It is found that due to instabilities sudden spreading and shrinkage of the adhered area at the end of the fibril can accompany the hysteresis. Numerical results are provided to substantiate the findings and possible reasons for the observed influence of buckling on adhesive performance are reviewed.

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Figures

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Fig. 2

Load-displacement curves for an aspect ratio of 10

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Fig. 1

Model for buckling of the fibril: (a) undeformed configuration; (b) deformed configuration

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Fig. 3

Finite element result in comparison with the Euler–Bernoulli beam theory solution for aspect ratio 10, K¯ad=0.01, a¯init=0.2

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Fig. 4

(a) Undeformed configuration, (b) deformed configuration, (c) free body diagram

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Fig. 5

(a) Finite element model; (b) evaluation of detachment behavior

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