Dynamic analysis of dielectric elastomer actuators

Abstract

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...

Dynamic Electromechanical Response of a Viscoelastic Dielectric Elastomer under Cycle Electric Loads

“…To be specific, the following parameters are used in the dynamic examples: A = 110 KPa, B = 55 KPa, = 0.5, = 1, and̃= 1 [20,[34][35][36].…”

“…Poincaré map can be used to detect the stability transition of the system [20,23,28]. The Poincaré maps for the oscillation with the frequency Ω = 10, 1, 0.1, and 0.0213 are shown in Figure 8.…”

“…Li et al [19] analyzed the electromechanical and dynamic analyses of tunable pure-shear DE-based resonator and identified the safe operation range for failure prevention while actuating the resonator. Xu et al [20] obtained an analytical model for the DE by the Euler-Lagrange equation to study the dynamic analysis of a DE with stretching deformation. Jia et al [21] investigated the response time and dynamic range for a DE actuator.…”

Stacked dielectric elastomer actuator (SDEA): casting process, modeling and active vibration isolation

“…Viscoelasticity of DE material induces the damping force, dissipating energy and causing a reduction of energy conversion efficiency of DE actuators. The work done by the damping force along direction 3 can be calculated as is the damping force, c is denotes the viscous damping coefficient[21,26]. Thermodynamics indicates that the variation of Helmholtz free energy of the DE is equal to the work done jointly by the voltage, the inertial force, the damping force, and the tensile force from the mass in direction 3, expressed by[20,21,25] …”