On buckling of a soft incompressible electroactive hollow cylinder

Su, Yipin; Zhou, Weijian; Chen, Weiqiu; Lü, Chaofeng

doi:10.1016/j.ijsolstr.2016.07.008

Cited by 28 publications

(16 citation statements)

References 36 publications

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“…Recently, the theory in [73] has been used by Su et al [4] to solve the boundary value problem of small-amplitude sinusoidal wrinkles appearing on the free faces of a dielectric thin plate. Su et al [77] and Melnikov & Ogden [5] specialized the theory of [73] so as to investigate prismatic and axisymmetric bifurcations of an electroelastic tube. The results in [5] highlighted differences from those for the purely elastic case.…”

Section: (D) the Incremental Methodsmentioning

confidence: 99%

Instabilities of soft dielectrics

Dorfmann

Ogden

2019

Phil. Trans. R. Soc. A.

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The basic modern theory of nonlinear electroelasticity and its use in the formulation of constitutive laws governing the behaviour of dielectric elastomer materials was summarized in a recent review article by Dorfmann & Ogden (Dorfmann & Ogden 2017 Proc. R. Soc. A 473 , 20170311 ( doi:10.1098/rspa.2017.0311 )). The theory is used, in particular, to analyse the behaviour of transducer devices such as actuators and sensors. Important considerations for the design and effective functioning of such devices are the issues of material and geometric instabilities. Following on from the above-cited work, the present paper provides a detailed account of the types of instabilities that arise for some of the geometries used in transducer devices and the theory that is adopted for the analysis of such instabilities. The theory is then used in two illustrative examples: (i) determination of instabilities of a thin electroelastic plate with flexible electrodes attached to its major surfaces, in particular comparison of the results for the so-called Hessian approach and a general incremental bifurcation analysis in respect of an equibiaxially stretched plate, with numerical results presented for a Gent electroelastic model; (ii) a general analysis of axi-symmetric bifurcation from a circular cylindrical configuration of a thin-walled tube of an electroelastic material with flexible electrodes on its curved surfaces, illustrated by numerical results for neo-Hookean and Gent electroelastic models. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

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Section: (D) the Incremental Methodsmentioning

confidence: 99%

Instabilities of soft dielectrics

Dorfmann

Ogden

2019

Phil. Trans. R. Soc. A.

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“…In the review [7] corresponding results were obtained for the same neo-Hookean model and also for a Gent electroelastic model. The theory of [5] was also used by Su et al [8] for the analysis of bifurcation (buckling) of a tube subject to an axial electric field instead of a radial one.…”

Section: Introductionmentioning

confidence: 99%

Waves and vibrations in a finitely deformed electroelastic circular cylindrical tube

Dorfmann

Ogden

2020

Proc. R. Soc. A.

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In two recent papers, conditions for which axisymmetric incremental bifurcation could arise for a circular cylindrical tube subject to axial extension and radial inflation in the presence of an axial load, internal pressure and a radial electric field were examined, the latter being effected by a potential difference between compliant electrodes on the inner and outer radial surfaces of the tube. The present paper takes this work further by considering the incremental deformations to be time-dependent. In particular, both the axisymmetric vibration of a tube of finite length with appropriate end conditions and the propagation of axisymmetric waves in a tube are investigated. General equations and boundary conditions governing the axisymmetric incremental motions are obtained and then, for purposes of numerical evaluation, specialized for a Gent electroelastic model. The resulting system of equations is solved numerically and the results highlight the dependence of the frequency of vibration and wave speed on the tube geometry, applied deformation and electrostatic potential. In particular, the bifurcation results obtained previously are recovered as a special case when the frequency vanishes. Specification of an incremental potential difference in the present work ensures that there is no incremental electric field exterior to the tube. Results are also illustrated for a neo-Hookean electroelastic model and compared with those previously obtained for the case in which no incremental potential difference (or charge) is specified and an external field is required.

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“…For E In Section 2 we recall the equations governing the large deformation of a dielectric plate subject to pre-stretch and voltage. We then rely on the theory of incremental deformations superposed on large actuation (Dorfmann and Ogden, 2010a,b;Bertoldi and Gei, 2011;Rudykh and deBotton, 2011;Gei et al, 2012;Rudykh et al, 2014;Su et al, 2016;Bortot and Shmuel, 2018) to solve the boundary value problem of small-amplitude sinusoidal wrinkles appearing on the mechanically-free faces of the plate (Section 3). This problem was treated earlier by Dorfmann and Ogden (2014a,c) and more recently, by Yang et al (2017) and Díaz-Calleja et al (2017), but not in a fully analytical manner as here.…”

Section: Introductionmentioning

confidence: 99%

Wrinkles in soft dielectric plates

Broderick

Chen

et al. 2018

Journal of the Mechanics and Physics of Solids

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We show that a smooth giant voltage actuation of soft dielectric plates is not easily obtained in practice. In principle one can exploit, through predeformation, the snap-through behavior of their loading curve to deliver a large stretch prior to electric breakdown. However, we demonstrate here that even in this favorable scenario, the soft dielectric is likely to first encounter the plate wrinkling phenomenon, as modeled by the onset of small-amplitude sinusoidal perturbations on its faces. We provide an explicit treatment of this incremental boundary value problem. We also derive closed-form expressions for the two limit cases of very thin membranes (with vanishing thickness) and of thick plates (with thickness comparable to or greater than the wavelength of the perturbation). We treat explicitly examples of ideal dielectric free energy functions (where the mechanical part is of the neo-Hookean, Mooney-Rivlin or Gent form) and of dielectrics exhibiting polarization saturation. Finally we make the link with the classical results of the Hessian electro-mechanical instability criterion and of Euler buckling for an elastic column.

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On buckling of a soft incompressible electroactive hollow cylinder

Cited by 28 publications

References 36 publications

Instabilities of soft dielectrics

Instabilities of soft dielectrics

Waves and vibrations in a finitely deformed electroelastic circular cylindrical tube

Wrinkles in soft dielectric plates

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