Modeling and simulation of electro-viscoelastic polymers

Abstract: The electroactive polymer materials considered in this work react to electric stimuli by producing deformations. In some cases, the electrically induced deformations are moderate, while in other cases they can be very large and the specimen is stretched to more than twice its original length. The latter response is seen in so called dielectric elastomer actuators (DEA). The possibility of very large deformation output together with other attractive qualities in the elastomers such as resilience and light weight have resulted in increasing interest in DEA for technical applications during the last few decades. As interest in practical applications grows, so does the interest in modeling and simulation of the DEA. This work deals with modeling of electroactive polymers from a continuum mechanics point of view. An electromechanical framework is adopted where the electromagnetic field equations are solved together with the mechanical balance equations. The equations are inherently coupled, as a dielectric body experiences body forces and couples of electromagnetic origin when it is placed in an electromagnetic field. For the case of quasi-electrostatics, which is a valid assumption for all problems considered in this work, the electric field can be derived from a scalar electric potential, allowing for treatment using standard finite element methods. This enables the numerical treatment of the electromechanically coupled problem to be done by simply extending the usual finite element formulation of mechanical boundary value problems to include the electric problem. Accurate constitutive models are always important when performing numerical analysis of material behavior. The complex material behavior affects important aspects of the DEA behavior, such as stability and response time, as well as the overall behavior. For the elastomers considered in this work, this includes rubber-like elastic behavior, viscosity and coupling between mechanical and electric quantities.