Modeling Approaches for Electroactive Polymers Kaal W. a , Herold S. b and Melz T. c a,b,c Fraunhofer Institute for Structural Durability and System Reliability, Germany ABSTRACT The focus of this paper is on the modeling of dielectric elastomer actuators and generators. One of the eﬀects that is rarely considered in modeling of these systems is the inﬂuence of the materials’ speciﬁc resistance on the performance. The non-ideal electrical properties of both elastomer and electrode material will cause undesired parasitic eﬀects. Although for most laboratory scale prototypes these eﬀects are hardly recognizable, they may however play an important role for larger structures and especially for dynamic applications. Therefore, an analytical model is developed and presented in this paper which can give helpful instructions for the design and fabrication process of EAP-systems. It is proven to be valid by means of the ﬁnite element method and subsequently extended for more complex systems. Keywords: dielectric elastomers, electroactive polymers, actuators, modeling, simulation, smart systems, ﬁnite elements 1. INTRODUCTION EAP materials respond to external electrical stimulation with high deformations and can therefore outperform other smart materials in some applications. They can be used to design actuators which are capable of much higher displacements, e.g. compared to piezoelectric actuators. They can also be utilized to build generators for energy harvesting applications by exploiting the change in capacitance at large deformations. 1–3 In order to properly design and optimize robust and eﬃcient systems reliable models are required that take into account the various relevant physical eﬀects. Up to now there have been only a few publications on modeling of EAP material, 4–7 and hardly any work has been done to investigate the inﬂuence of the electrical material properties on the performance of EAP actuators. Especially the electric resistivity of both the elastomer and the electrode material can however have a signiﬁcant eﬀect on the actuator’s eﬃciency. The eﬀects investigated in this study are especially critical for large EAP systems and higher frequencies like in applications of structural dynamics. Since most EAP actuators have not exceeded laboratory scale or have primarily been used for static and quasi-static applications, this subject has not been paid much attention yet. As will be shown the eﬀects are minimized for electrodes with excellent conductivity properties like graphite powder 8 electrodes or thin-ﬁlm metallized electrodes. However, for large stroke actuators and also for EAP energy harvesting devices, where large strains are indispensable, non-metallic electrodes with naturally much worse conductivity properties will have to be used. In these cases the results presented in this work will contribute valuable instructions for the proper selection of a material in question and the right dimensioning of the electrode geometry. 2. PHYSICAL PHENOMENON A sketch of a single elastomer ﬁlm with electrodes on both sides and a voltage source attached at one end is shown in Figure 1, with an ideal potential distribution (left: without inﬂuences of resistances) and with a qualitative potential distribution due to inner resistances (right). The reason for the inhomogenous distribution is that the speciﬁc volume resistivity of the electrode material is not zero (ρ El > 0) and the insulating resistivity ρ Is is ﬁnite (ρ Is < ∞). Further author information: (Send correspondence to a) a.: E-mail: william.kaal@lbf.fraunhofer.de, Telephone: +49 6151 705440 b.: E-mail: sven.herold@lbf.fraunhofer.de, Telephone: +49 6151 705259 b.: E-mail: tobias.melz@lbf.fraunhofer.de, Telephone: +49 6151 705252 Electroactive Polymer Actuators and Devices (EAPAD) 2010, edited by Yoseph Bar-Cohen, Proc. of SPIE Vol. 7642, 764211 · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.848756 Proc. of SPIE Vol. 7642 764211-1