Bifurcation of a dielectric elastomer balloon under pressurized inflation and electric actuation

Xie, Yuxin; Liu, J.-C.; Fu, Yibin

doi:10.1016/j.ijsolstr.2015.08.027

Cited by 50 publications

(34 citation statements)

References 27 publications

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“…The bifurcation of a spherical dielectric elastomer balloon under inflation and electrical actuation was investigated by Xie et al [68]. They showed that, on application of a potential difference and an inflating pressure, bifurcation into a pear shape was possible for all material models, which contrasts with the purely elastic case.…”

Section: (C) the Energy 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: (C) the Energy Methodsmentioning

confidence: 99%

Instabilities of soft dielectrics

Dorfmann

Ogden

2019

Phil. Trans. R. Soc. A.

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“…Lu et al (2015) investigated the electromechanical bifurcation and bulging propagation in a cylindrical DE tube and derived the bifurcation and phase coexistence conditions which were verified by experimentation. Xie et al (2016) studied the bifurcation of ideal and non-ideal DE balloons under pressurized inflation and electric actuation. DE structure is mostly expected to work under dynamic excitation in many applications, e.g., pump, loudspeaker, and vibrotactile displays for mobile application.…”

Section: Introductionmentioning

confidence: 99%

Typical dielectric elastomer structures: dynamics and application in structural vibration control

Huang

Jin

Ruan

et al. 2016

J. Zhejiang Univ. Sci. A

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Abstract:In recent years, dielectric elastomer (DE) structures have received great attention in various fields of engineering, such as artificial muscle, soft robot, resonator, and structural vibration control, due to its prominent advantages. In the present paper, the theoretical and experimental research into the dynamical behavior of DE structures and their application for vibration control is reviewed. In the theoretical research into dynamical behavior, from a mechanics viewpoint, DE structures are usually categorized into four types, i.e., spherical, rectangular, tubular, and circular. For each type of DE structure, the mathematical description is given and the dynamical behavior, such as the resonant property, jump, and bifurcation, is summarized. Moreover, the work on dynamical experiments is briefly outlined. In the application for vibration control, stack-type and tubular-type DE structures usually used as actuators are surveyed. The established control algorithms for the controlled systems using DE actuators are described. The challenges for the research into the dynamics of DE structure and its application for vibration control and some promising theories which may be applied for the research are pointed out.

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“…With respect to material models, the rubber-like balloon can bifurcate into pear shape when the inflation reaches the critical value for the Ogden material in general, but not for the neo-Hookean, Mooney-Rivlin or Gent models in the purely mechanical loading case. A thorough discussion on the dependence of bifurcation on the constitutive models was carried out by Xie et al [39]. For rubber balloons, assuming incompressibility, the three-term Ogden material [32,33]…”

Section: Modelmentioning

confidence: 99%

“…where and̃are material constants. In this paper, we take the following material parameters from [32], which are widely used for the analyses of inflation of hyperelastic balloons [16,22,27,39]: 1 = 1.3, 2 = 5.0, 3 = −2.0,̃1 = 1.4919,̃2 = 0.003 and̃3 = −0.024, in which̃are dimensionless, scaled by the ground state shear modulus . Practically, these values of the parameters refer to a vulcanized natural rubber which has highly reversible hyperelastic behavior but low crystallization upon extreme stretching [40].…”

Section: Modelmentioning

confidence: 99%

Snap-through instabilities of pressurized balloons: Pear-shaped bifurcation and localized bulging

Wang

Huo

et al. 2018

International Journal of Non-Linear Mechanics

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This paper investigates numerically the post-bifurcation evolution of ellipsoidal or spherical balloons subject to internal pressure, where the primary -shaped curves of pressure vs. principal stretch and the corresponding bifurcated branch, i.e. pear-shaped deformation, are captured quantitatively. We quantify and discuss the range of pear-shaped bifurcation intervals of ellipsoids and the associated critical points. For rugby-shaped ellipsoidal balloons, we find that there exists a threshold for the aspect ratio of the major and minor axes that leads to pear-shaped bifurcation, which is detected by the finite element method. When the rugby shape becomes sufficiently slender, the nonlinear response of the ellipsoidal balloons is well approximated by the deformation of a tube with localized bulging instead of pear-shaped configuration. We obtain the nonlinear evolution of the localized bulging of rugby-like ellipsoids numerically. Furthermore, we examine the influence of various aspect ratios for rugby-shaped balloons on the localized bulging response. We find that pumpkinshaped ellipsoids can always bifurcate into pear shape. Lastly, we provide a unified phase diagram on instability mode selection of various aspect ratios of ellipsoidal balloons, with diverse representative deformed configurations.

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Bifurcation of a dielectric elastomer balloon under pressurized inflation and electric actuation

Cited by 50 publications

References 27 publications

Instabilities of soft dielectrics

Instabilities of soft dielectrics

Typical dielectric elastomer structures: dynamics and application in structural vibration control

Snap-through instabilities of pressurized balloons: Pear-shaped bifurcation and localized bulging

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