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Research Papers

Shape Bifurcation of a Spherical Dielectric Elastomer Balloon Under the Actions of Internal Pressure and Electric Voltage

[+] Author and Article Information
Xudong Liang

Department of Mechanical
and Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: x7liang@ucsd.edu

Shengqiang Cai

Department of Mechanical
and Aerospace Engineering,
University of California, San Diego,
La Jolla, CA 92093
e-mail: s3cai@ucsd.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 29, 2015; final manuscript received June 12, 2015; published online July 9, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(10), 101002 (Oct 01, 2015) (8 pages) Paper No: JAM-15-1273; doi: 10.1115/1.4030881 History: Received May 29, 2015; Revised June 12, 2015; Online July 09, 2015

Under the actions of internal pressure and electric voltage, a spherical dielectric elastomer balloon usually keeps a sphere during its deformation, which has also been assumed in many previous studies. In this article, using linear perturbation analysis, we demonstrate that a spherical dielectric elastomer balloon may bifurcate to a nonspherical shape under certain electromechanical loading conditions. We also show that with a nonspherical shape, the dielectric elastomer balloon may have highly inhomogeneous electric field and stress/stretch distributions, which can lead to the failure of the system. In addition, we conduct stability analysis of the dielectric elastomer balloon in different equilibrium configurations by evaluating its second variation of free energy under arbitrary perturbations. Our analyses indicate that under pressure-control and voltage-control modes, nonspherical deformation of the dielectric elastomer balloon is energetically unstable. However, under charge-control or ideal gas mass-control mode, nonspherical deformation of the balloon is energetically stable.

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Figures

Grahic Jump Location
Fig. 1

(a) Schematics of a dielectric elastomer balloon subjected to internal pressure and electric voltage. (b) The balloon with axisymmetric deformation. Dashed line represents the undeformed spherical balloon and solid line represents shape of the balloon after deformation.

Grahic Jump Location
Fig. 2

The pressure–volume (p–V) relation of a spherical dielectric elastomer balloon subjected to three different voltages. During the deformation, the balloon may keep a sphere, which is represented by the solid curves, or become nonspherical, which is represented by dashed curves. The circle and square dots stand for the bifurcation points predicted from the linear perturbation analysis for spherical and pear-shaped modes, respectively. Two adjacent deformation modes with pressure of pR/(μH)=0.9 and three different voltages are marked by triangles. The dashed-dotted lines represent ideal gas law for two different masses of ideal gas, where m0 is the mass of gas molecules when pressure and volume are unity.

Grahic Jump Location
Fig. 3

Spherical and pear-shaped bifurcation modes calculated from the linear perturbation analysis

Grahic Jump Location
Fig. 4

Calculated shapes and electric field in a spherical dielectric elastomer balloon in two adjacent deformation modes (spherical mode and pear-shaped modes) marked by triangles in Fig. 2. When the electric voltage is high, large electric field concentration can be observed in the pear-shaped mode (right column).

Grahic Jump Location
Fig. 5

Distribution of the electric field, stretch, and nominal stress in the dielectric elastomer balloon for homogeneous and inhomogeneous deformation modes for φ/(Hμ/ε)=0.16 as shown in Fig. 4

Grahic Jump Location
Fig. 6

Under pressure-control and voltage-control modes, second variation of free energy of the spherical deformation and nonspherical deformation in the descending path of p–V curve in Fig. 2 can be negative. The solid line represents a negative value for the spherical deformation mode, while the dashed line shows a negative value for the nonspherical deformation mode. The results indicate that under pressure-control and voltage-control modes, both spherical deformation in the descending path of p–V curve and nonspherical deformation of the dielectric elastomer balloon are energetically unstable.

Grahic Jump Location
Fig. 7

The ideal gas mass–volume (m–V) curves for a dielectric elastomeric balloon subjected to three different voltages. During the deformation, the gas molecules obey the ideal gas law. The spherical deformation is represented by the solid line and the nonspherical deformation is represented by dashed line.

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