On electromechanical stability analysis of dielectric elastomer actuators

Xu, Bai‐Xiang; Mueller, Ralf; Klassen, Markus; Groß, Dietmar

doi:10.1063/1.3504702

Cited by 81 publications

(48 citation statements)

References 13 publications

(17 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar conditions have been used to study electromechanical instability in dielectric elastomers Diaz-Calleja et al 2008;Leng et al 2009;Dorfmann & Ogden 2010;Xu et al 2010;Bertoldi & Gei 2011 In the case of discontinuous phase transition, the stable equilibrium state changes abruptly at the transition point, which is typically beyond the reach of small perturbation analysis.…”

Section: Stability Of a Homogeneous State Against Small Perturbationmentioning

confidence: 99%

“…Electromechanical instability has been recognized as a mode of failure for dielectric elastomers subject to increasing voltage (Stark & Garton 1955;Plante & Dubowsky 2006), which limits the amount of energy conversion by dielectric elastomers in practical applications Diaz-Calleja et al 2008;Koh et al 2009Koh et al , 2011Leng et al 2009;Tommasi et al 2010;Xu et al 2010). In particular, an experimental manifestation of the electromechanical instability was reported by Plante & Dubowsky (2006): under a particular voltage, a prestretched dielectric elastomer membrane deformed into a complex pattern with a mixture of two states, one being flat and the other wrinkled.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Electromechanical phase transition in dielectric elastomers

Huang

Suo

2011

Proc. R. Soc. A.

View full text Add to dashboard Cite

Subject to forces and voltage, a dielectric elastomer may undergo electromechanical phase transition. A phase diagram is constructed for an ideal dielectric elastomer membrane under uniaxial force and voltage, reminiscent of the phase diagram for liquid-vapour transition of a pure substance. We identify a critical point for the electromechanical phase transition. Two states of deformation (thick and thin) may coexist during the phase transition, with the mismatch in lateral stretch accommodated by wrinkling of the membrane in the thin state. The processes of electromechanical phase transition under various conditions are discussed. A reversible cycle is suggested for electromechanical energy conversion using the dielectric elastomer membrane, analogous to the classical Carnot cycle for a heat engine. The amount of energy conversion, however, is limited by failure of the dielectric elastomer owing to electrical breakdown. With a particular combination of material properties, the electromechanical energy conversion can be significantly extended by taking advantage of the phase transition without electrical breakdown.

show abstract

Section: Stability Of a Homogeneous State Against Small Perturbationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electromechanical phase transition in dielectric elastomers

Huang

Suo

2011

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…As the applied voltage increases, the elastomer reduces its thickness and in return the voltage induces an even higher electric field. When the increase of the Maxwell stress overruns that of the mechanical stress, it may lead to the collapse of the devices, namely the electromechanical instability [4]. Using an analytic formulation for the dynamic response of the homogeneous DEAs, dynamic electromechanical stability analysis will be presented in the following work of the authors.…”

Section: Outlooksmentioning

confidence: 99%

Dynamic analysis of dielectric elastomer actuators

Müller

Klassen

et al. 2011

Proc Appl Math and Mech

Self Cite

View full text Add to dashboard Cite

Dielectric elastomer actuators (DEAs) with a typical sandwich structure of electrode-elastomer-electrode arrangement provide large deformation. DEAs outperform most large displacement actuators in terms of light weight, low cost, and high efficiency. The actuation mechanism of DEAs relies primarily on the electrostatic force or the Maxwell stress which is due to the reaction of material polarization in an electric field. By a dynamic nonlinear electromechanical continuum model implemented with the finite element method, the dynamic response of a homogeneous DEA is studied. Results show that the actuation magnitudes can be increased when the frequency of the applied electric field approaches to the eigenfrequency of the DEAs. The dynamic nonlinear electromechanical modelDielectric elastomers are widely used for artificial muscles and haptic displays, thanks to its practical features e.g. large deformation up to 300%, low cost and high fracture toughness. In an actuator setup the material is usually sandwiched between two compliant electrodes. Due to the electromechanical coupling effect, dielectric elastomers can be actuated under an electric loading. To achieve various applications, the material works usually under dynamic electric loadings, and hence the dynamic response of the material should be taken into account. In the following a dynamic nonlinear continuum model is presented, which takes the electromechanical coupling into account. The large deformation of the material is treated as a nonlinear mapping of the body from its reference configuration B 0 to the actual or current configuration B at time t, i.e. x = χ(X, t), see e.g. [1]. The fundamental quantity to describe the kinematics of the motion is the deformation gradient Fwhere the gradient Grad with a capital initial character is to be computed with respect to the coordinates of the reference configuration. The material involves both electric and mechanical fields. In terms of the electrostatics in the current configuration, the theory of dielectrics can be applied, namely the Gauß equation and the definition of the electric field,where D is the dielectric displacement, E is the true electric field, ϕ is the electric potential, and no free volume charge is considered. The relation between the electric displacement and the electric field is given through,where P is the material polarization, κ 0 is the vacuum permittivity, and κ r is the relative permittivity of the dielectric elastomer. Different from the dielectrics in the case of small deformations, the material polarization has a nonlinear dependence on the true electric field which involves the volume change J = detF . In the formulation the time dependent effect in electrostatics is neglected. In terms of the mechanics, one has the following equilibrium in the absence of mechanical volume forcein which σ M is the mechanical stress, f E the electrostatic volume force due to the material polarization, u the displacement vector, c and ρ are the damping coefficient and the mass density. The last tw...

show abstract

“…Theoretical analysis of electromechanical instability has been considered by many authors, exemplified in [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Based on the theory of small deformations superimposed on large deformations for a general electroelastic material following the development of Dorfmann & Ogden [43], an analysis of the stability of an electroelastic plate was performed by the same authors in [44].…”

Section: (A) Planar Geometriesmentioning

confidence: 99%

Nonlinear electroelasticity: material properties, continuum theory and applications

Dorfmann

Ogden

2017

Proc. R. Soc. A.

View full text Add to dashboard Cite

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

show abstract

On electromechanical stability analysis of dielectric elastomer actuators

Cited by 81 publications

References 13 publications

Electromechanical phase transition in dielectric elastomers

Electromechanical phase transition in dielectric elastomers

Dynamic analysis of dielectric elastomer actuators

Nonlinear electroelasticity: material properties, continuum theory and applications

Contact Info

Product

Resources

About