Electromechanical coupling in dielectric elastomer actuators

Abstract

In this paper the electromechanical coupling in dielectric elastomer actuators is investigated. An equation proposed by Pelrine et al. [R.E. Pelrine, R.D. Kornbluh, J.P. Joseph, Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation, Sens. Actuators A 64 (1998) 77–85] is commonly used for the calculation of the electrostatic forces in dielectric elastomer systems. This equation is analyzed here with (i) energy consideration and (ii) numerical calculations of charge and force distribution. A new physical interpretation of the electrostatic forces acting on the dielectric elastomer film is proposed, with contributions from in-plane and out-of-plane stresses. Representation of this force distribution using Pelrine's equation is valid for an incompressible material, such as the acrylic elastomer VHB 4910. Experiments are performed for the measurement of the dielectric constant ɛ r of the acrylic elastomer VHB 4910 for different film deformations. The values of ɛ r are shown to decrease with increasing pre-stretch ratio λ p, from 4.7 for the un-stretched film, down to 2.6 for equi-biaxial deformation with λ p = 5. This result is important in that it corrects the constant value of 4.7 largely applied in literature for pre-stretched dielectric elastomer actuator modeling. With the results of this work the predictive capabilities of a model describing the three-dimensional passive and active actuator behavior are remarkably improved.