Numerical simulation of the edge stress singularity and the adhesion strength for compliant mushroom fibrils adhered to rigid substrates

R. G. Balijepalli, M. R. Begley, N. A. Fleck, R. M. McMeeking, E. Arzt*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

63 Citations (Scopus)
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Bio-inspired adhesion of micropatterned surfaces due to intermolecular interactions has attracted much research interest over the last decade. Experiments show that the best adhesion is achieved with compliant "mushroom"-shaped fibrils. This paper analyses numerically the effects of different mushroom shapes on adhesion to a rigid substrate. When a remote stress is applied on the free end of a fibril perfectly bonded to a rigid substrate, the resultant stress distribution along the fibril is found to change dramatically between the straight punch and mushroom fibrils. A singular stress field is present at the edge of the fibril where it contacts the substrate and, in this work, the amplitude of the singularity is evaluated for fibrils perfectly bonded to a flat substrate so that sliding cannot occur there. This exercise is carried out for fibril geometries involving combinations of different diameters and thicknesses of the mushroom cap. By assuming a pre-existing detachment length at the corner where the stress singularity lies, we predict the adhesive strength for various mushroom cap shapes. Our study shows that a smaller stalk diameter and a thinner mushroom cap lead to higher adhesive strengths. A limited number of results are also given for other shapes, including those having a fillet radius connecting the stalk to the cap. The results support the rational optimisation of synthetic micropatterned adhesives. (c) 2016 The Authors. Published by Elsevier Ltd.

Original languageEnglish
Pages (from-to)160-171
Number of pages12
JournalInternational Journal of Solids and Structures
Early online date20 Feb 2016
Publication statusPublished - 15 May 2016

Bibliographical note

Open Access funded by European Research Council

RB thanks GRADUS, Faculty 8.4. Natural Sciences, of Saarland University for partially funding his research visit to the University of California, Santa Barbara. RB would also thank to Dr. S. Khaderi for his help in setting up the model. He also thanks Dr. R. Hensel and Dr. N. Guimard for fruitful discussions and for their continuous support. EA acknowledges funding from the European Research Council under the European Union's Seventh Framework Program (FP/2007-2013)/ERC Advanced Grant no. 340929.


  • fibrils
  • adhesion
  • contact mechanics
  • gecko
  • finite element modelling


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