Necessary Conditions at the Boundary for Minimizers in Incompressible Finite Elasticity

Sithigh, G. P. Mac

doi:10.1007/s10659-005-9013-5

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2007

2023

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Cited by 5 publications

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“…We note in passing that Gent & Cho's creases are, to a certain extent, very similar to those encountered on the curved surface of severely torsioned stocky rubber cylinders [17]. These phenomena are likely to be related to the failure at the boundary of the complementing condition (see [18] and the reference therein), and they fall outside the scope of our study.…”

Section: Introductionmentioning

confidence: 53%

Asymptotic results for bifurcations in pure bending of rubber blocks

Coman¹,

Destrade²

2008

The Quarterly Journal of Mechanics and Applied Mathematics

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The bifurcation of an incompressible neo-Hookean thick hyperelastic plate with a ratio of thickness to length η and subject to pure bending is considered within a plane-strain framework. The two incremental equilibrium equations corresponding to a nonlinear prebuckling state of strain are reduced to a fourth-order linear eigenproblem that displays a multiple turning point. It is found that for 0 < η < ∞ the plate experience an Euler-type buckling instability which in the limit η → ∞ degenerates into a surface instability. Singular perturbation methods enable us to capture this transition, while direct numerical simulations corroborate the analytical results.

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Section: Introductionmentioning

confidence: 53%