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

Abstract

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 vali dated 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 compari son 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 multi parameter material models is presented at the end, which can be used as an input for fur ther experimental corroboration. The results of the present investigation can find their potential use in the design of DEAs subjected to transient loading.

Analysis and application of a rolled dielectric elastomer actuator with two degrees of freedom

“…In addition, once the function W s is given, the constitutive models (21) and (22) are able to analyze the mechanical response of the DEAs. In the literature, exclusive simulation and experimental results that can verify the effectiveness of these equations have been reported, for instance, in [50,55,68,69,[71][72][73].…”

“…In applications, the Ogden model usually gives a superior prediction of the response of DEAs compared to the neo-Hookean model and Gent model. Therefore, the Ogden model is also widely utilized to analyze the behaviors of DEAs [53,72,[85][86][87][88][89][90].…”

“…This analytical model was validated to be applicable for a certain range of ambient pressure and active frequency tuning of the resonator could be realized by increasing the applied electrical voltage within a certain range avoiding the mechanical instability. According to the Euler-Lagrange equations, Xu et al [98] provided an alternative method to analyze the dynamic analysis of a homogeneously deformed DEA and extensive works have then been reported in [72,99,100].…”

Constitutive models of artificial muscles: a review

“…It is known that there are multiple large-scale failure modes in dielectric elastomers, such as material strength failure, electric breakdown, loss of tension, electromechanical instability, etc. (Plante and Dubowsky, 2006;Liu et al, 2008;2009a;Leng et al, 2009;Zhou et al, 2013;Joglekar, 2014;Li et al, 2014;Liu et al, 2014a;Mao et al, 2014;Zhu, 2015). To prevent failure and to harness the large deformation of dielectric elastomers, it is necessary to construct a theoretical framework.…”

DC dynamic pull-in instability of a dielectric elastomer balloon: an energy-based approach

“…With reference to planar DEAs, Xu et al [42] also suggested the same approach for pull-in instability analysis in the dynamic mode of operation and inferred that the dynamic pull-in instability can be set at an electric field remarkably lower than that in the quasi-static mode of operation. This was followed by Joglekar [43,44], who proposed an energy-based method for excerpting the instability parameters of a planar DEA in the dynamic mode considering the effect of prestress. To the best of our knowledge, the effect of pre-inflation pressure on the dynamic pull-in instability parameters of a DE balloon has not been yet reported.…”