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Research Papers

An Energy-Based Approach to Extract the Dynamic Instability Parameters of Dielectric Elastomer Actuators

[+] Author and Article Information
M. M. Joglekar

Department of Mechanical and
Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247667, India
e-mail: joglekarmm@yahoo.com

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 12, 2014; final manuscript received June 20, 2014; accepted manuscript posted June 30, 2014; published online July 10, 2014. Assoc. Editor: Chad M. Landis.

J. Appl. Mech 81(9), 091010 (Jul 10, 2014) (11 pages) Paper No: JAM-14-1206; doi: 10.1115/1.4027925 History: Received May 12, 2014; Revised June 20, 2014; Accepted June 30, 2014

An energy-based approach is presented to extract the thresholds on the transient dynamic response of step voltage driven dielectric elastomer actuators (DEAs). The proposed approach relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle followed by the application of an instability condition to extract the dynamic instability parameters. Explicit expressions are developed for the critical values of maximum stretch and the corresponding nominal electric field, thus circumventing the need to perform iterative time-integrations of the equation of motion. The underlying principles of the approach are enunciated for the neo-Hookean material model and further extended to analyze relatively complex multiparameter hyperelastic models (Mooney–Rivlin and Ogden) that are employed prevalently for investigating the behavior of DEAs. The dynamic instability parameters predicted using the energy method are validated by examining the time-history response of the actuator in the vicinity of the dynamic instability. The development of dynamic instability parameters is complemented by energy-based extraction of static instability parameters to facilitate a quick comparison between the two. It is inferred quantitatively that the nominal electric field sufficient to cause the dynamic instability and the corresponding thickness stretch is lower than those corresponding to the static instability. A set of representative case studies for multiparameter material models is presented at the end, which can be used as an input for further experimental corroboration. The results of the present investigation can find their potential use in the design of DEAs subjected to transient loading.

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Figures

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Fig. 1

Schematic of a step voltage driven DEA

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Fig. 2

Time-history response of step voltage driven DEA for different values of the applied dimensionless nominal electric field

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Fig. 3

Phase-plane plot of step voltage driven DEA for different values of the applied dimensionless nominal electric field

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Fig. 4

Comparison of static and dynamic instability parameters of a DEA made up of neo-Hookean material

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Fig. 5

Time-history response of a DEA subjected to different levels of the applied dimensionless nominal electric field. (a) Ogden model (Sr. No. 1 in Table 1) and (b) Mooney–Rivlin model (Sr. No. 1 in Table 1).

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Fig. 6

Voltage–stretch curves for a DEA made up of Mooney–Rivlin material for different values of ξ. (a) Static mode of actuation and (b) dynamic mode of actuation.

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Fig. 7

Variation of static and dynamic instability parameters with the material parameter ξ for the Mooney–Rivlin model

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Fig. 8

Voltage–stretch curves for a DEA made up of Ogden material for different values of ξ (0.001, 0.005, 0.01, 0.03, and 0.05). (a) Static mode of actuation and (b) dynamic mode of actuation.

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