Wrinkles and creases in the bending, unbending and eversion of soft sectors

Author:

Sigaeva Taisiya1ORCID,Mangan Robert2,Vergori Luigi3,Destrade Michel2ORCID,Sudak Les1

Affiliation:

1. Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Alberta, Canada

2. School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road Galway, , Ireland

3. Dipartimento di Ingegneria, Università degli studi di Perugia, 06125 Perugia, Italy

Abstract

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.

Funder

Ireland Canada University Foundation

Carnegie Trust for the Universities of Scotland

Zymetrix Biomaterials & Tissue Engineering Technology Development Centre

Irish Research Council

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

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