Wrinkles and creases in the bending, unbending and eversion of soft sectors
| Autor: | Michel Destrade, Robert Mangan, Taisiya Sigaeva, Luigi Vergori, Les Sudak |
|---|---|
| Přispěvatelé: | Irish Research Council, Carnegie Trust, Ireland Canada University Foundation |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Bending
General Mathematics INSTABILITY Nonlinear elasticity FOS: Physical sciences General Physics and Astronomy 02 engineering and technology Condensed Matter - Soft Condensed Matter FINITE Strain energy Physics and Astronomy (all) Engineering (all) 0203 mechanical engineering Mathematics (all) Elasticity (economics) Buckle BIFURCATIONS Research Articles Physics Cylindrical sector Eversion Instability Unbending Isotropy General Engineering RUBBER BLOCKS Mechanics 021001 nanoscience & nanotechnology Finite element method 020303 mechanical engineering & transports Hyperelastic material Soft Condensed Matter (cond-mat.soft) Deformation (engineering) 0210 nano-technology |
| Popis: | We study what is clearly one of the most common modes of deformation found in nature, science and engineering, namely the large elastic bending of curved structures, as well as its inverse, unbending, which can be brought beyond complete straightening to turn into eversion. We find that the suggested mathematical solution to these problems always exists and is unique when the solid is modelled as a homogeneous, isotropic, incompressible hyperelastic material with a strain-energy satisfying the strong ellipticity condition. We also provide explicit asymptotic solutions for thin sectors. When the deformations are severe enough, the compressed side of the elastic material may buckle and wrinkles could then develop. We analyse, in detail, the onset of this instability for the Mooney-Rivlin strain energy, which covers the cases of the neo-Hookean model in exact nonlinear elasticity and of third-order elastic materials in weakly nonlinear elasticity. In particular, the associated theoretical and numerical treatment allows us to predict the number and wavelength of the wrinkles. Guided by experimental observations, we finally look at the development of creases, which we simulate through advanced finite-element computations. In some cases, the linearized analysis allows us to predict correctly the number and the wavelength of the creases, which turn out to occur only a few per cent of strain earlier than the wrinkles. MD and RM gratefully acknowledge the financial support of the Irish Research Council. LS and TS are grateful for the support received from the Schulich School of Engineering and Zymetrix Biomaterials & Tissue Engineering Technology Development Centre, University of Calgary. LV would like to thank the Carnegie Trust for the financial support (R&E Project Code: 67954/1). This publication has also been made possible by a James M Flaherty Research Scholarship from the Ireland Canada University Foundation, with the assistance of the Government of Canada/avec l’appui du gouvernement du Canada. The authors gratefully acknowledge the SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities and support. peer-reviewed |
| Databáze: | OpenAIRE |
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