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Research Papers

Effect of Dielectric Imperfections on the Electroactive Deformations of Polar Dielectric Elastomers

[+] Author and Article Information
Yanhui Jiang

Department of Mechanical and Industry Engineering,
Northeastern University,
Boston, MA 02115
e-mail: Jiang.ya@husky.neu.edu

Yang Liu

Department of Mechanical and Industry Engineering,
Northeastern University,
Boston, MA 02115
e-mail: yang1.liu@northeastern.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received February 14, 2019; final manuscript received May 5, 2019; published online May 23, 2019. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 86(8), 081007 (May 23, 2019) (7 pages) Paper No: JAM-19-1072; doi: 10.1115/1.4043720 History: Received February 14, 2019; Accepted May 06, 2019

We find that the ratio of dielectric permittivity to shear modulus is linearly related to the number of polar groups per polymer chain in polar dielectric elastomers (PDEs). Our discovery is verified via computational modeling and validated by experimental evidences. Based on the finding, we introduce the new concept of dielectric imperfection (DI) and provide some physical insights into understanding it through demonstrating the large nonlinear deformation of PDEs with DIs under electric fields. The results show remarkable DI-induced inhomogeneous deformation and indicate that the size and dielectric permittivity of DIs have a significant impact on the deformation stability of PDEs under electric fields. With this concept, we propose some potential applications of PDEs with DIs.

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Figures

Grahic Jump Location
Fig. 1

A schematic representation of the microstructure of a polymer network with polar groups

Grahic Jump Location
Fig. 2

A schematic showing for the actuation mechanism of a DE membrane: (a) the initial state and (b) the actuated state under the condition of biaxial prestresses and a voltage load

Grahic Jump Location
Fig. 3

(a) Stress–strain curves obtained by using the calibrated shear modulus and Kuhn numbers (listed in Table 1) of the five experimental samples, (b) the effective dielectric constant K is identified for the five experimental samples under the 10% strain level (gray dash line), and (c) the linear regression (solid line) of the normalized effective dielectric constant K/µn with respect to ξ

Grahic Jump Location
Fig. 4

A schematic representation showing the dielectrically hard imperfection ϕp1 and dielectrically soft imperfection ϕp2 in a polar dielectric elastomer with polar group ratio ϕp0, where ϕp1 < ϕp0 < ϕp2

Grahic Jump Location
Fig. 5

Showing the typical electromechanical instability types: snap through and pull in. (a) It shows the analysis result of a 3D unit cell under a ramping voltage load. For the unit cell, the Kuhn number N is set as 1. It is shown that there is no instability during the loading process. (b) It shows the analysis when N is set as 6. A bifurcation point occurs during the loading process and a snap through happens as a voltage load increases at the bifurcaion point. (c) It shows the analysis result when N is set as a very large number, i.e., 100, when the Arruda–Boyce model is turned to the neo-Hookean model. The well-known pull-in instability occurs as a limit point where larger loads cannot be sustained.

Grahic Jump Location
Fig. 6

(a) Initial state R/H = 0.4 with the boundary conditions and loading conditions in an axial-symmetric view, (b) limit point state (R/H = 0.4, ɛim is a very small number), (c) limit point state (R/H = 0.4, ɛim = 2), and (d) critical nominal electric field for the limit point state of samples with different relative radii R/H and relative permittivity ɛim

Grahic Jump Location
Fig. 7

(a) Initial state R/H = 0.4 with the boundary conditions and loading conditions for the plain-strain problem, (b) limit point state (R/H = 0.4, ɛim is a very small number), (c) limit point state (R/H = 0.4, ɛim = 2), and (d) critical nominal electric field for the limit point state of samples with different relative radii R/H and relative permittivity ɛim

Grahic Jump Location
Fig. 8

(a) The limit point states and the critical nominal electric field as a function of relatively permittivity for DIs with volume fraction fV = 2%, (b) DIs with volume fraction fV = 17%, and (c) DIs with volume fraction fV = 44%

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