Yibin Fu y.fu@keele.ac.uk
Buckling of a coated elastic half-space when the coating and substrate have similar material properties
Fu, YB; Ciarletta, P
Authors
P Ciarletta
Abstract
This study investigates the buckling of a uni-axially compressed neo-Hookean thin film bonded to a neo-Hookean substrate. Previous studies have shown that the elastic bifurcation is supercritical if r=µf/µs>1.74 and subcritical if r<1.74, where µf and µs are the shear moduli of the film and substrate, respectively. Moreover, existing numerical simulations of the fully nonlinear post-buckling behaviour have all been focused on the regime r>1.74. In this paper, we consider instead a subset of the regime r<1.74, namely when r is close to unity. Four near-critical regimes are considered. In particular, it is shown that, when r>1 and the stretch is greater than the critical stretch (the subcritical regime), there exists a localized solution that arises as the limit of modulated periodic solutions with increasingly longer and longer decaying tails. The evolution of each modulated periodic solution is followed as r is decreased, and it is found that there exists a critical value of r at which the deformation gradient develops a discontinuity and the solution becomes a static shock. The semi-analytical results presented could help future numerical simulations of the fully nonlinear post-buckling behaviour.
Acceptance Date | Apr 1, 2015 |
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Publication Date | Jun 8, 2015 |
Journal | Proceedings Of The Royal Society A-mathematical Physical And Engineering Sciences |
Print ISSN | 1364-5021 |
Publisher | The Royal Society |
DOI | https://doi.org/10.1098/rspa.2014.0979 |
Keywords | soft materials, bifurcation, film-wrinkling, pattern formation |
Publisher URL | https://doi.org/10.1098/rspa.2014.0979 |
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fu-ciarletta-revised-2015.pdf
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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
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