A numerical framework for modeling 3D electrostrictive dielectric elastomer actuators

In this paper, we have developed a numerical framework to investigate the effects of the electrostriction phenomenon on the deformations of three-dimensional dielectric elastomer actuators with complex geometries and inhomogeneous displacement fields at finite strains. The finite element method has been used to solve the governing equations. In this investigation, we adopt one of the most complete constitutive equations with regard to the electrostrictive behavior of dielectric elastomers which is capable of analyzing general three-dimensional states of deformation. The terms emerging in the tangent stiffness matrix as a result of the electrostrictive model are fully derived in this study. The implementation of the finite element modeling is conducted via an in-house computer code. Three three-dimensional actuators, namely a bending actuator, a buckling actuator, and a torsional actuator are selected to demonstrate the capabilities of the numerical framework. In conclusion, we have proved that the electrostriction phenomenon is effective in terms of improving the performance of dielectric elastomer actuators and in lowering their operating voltage. Moreover, the relationship of the diagonal entries of the permittivity tensor and the left Cauchy-Green tensor have been depicted on the deformed bodies of the actuators.