Modelling of an electroactive polymer actuator

摘要

The aim of this paper is to build a model of an electroactive polymer actuator when external electric field is applied. Materials whose Theological properties can be varied by electric excitation are called electroactive materials. The behavior of these rubberlike media is commonly investigated in two different ways. Brigadnov, Dorfmann, Bustamante, Ogden and others describe the coupled problem of finite deformation of the continua in electromagnetic field by taking into account all the electromagnetic phenomena. Pelrine, Kornbluh, Sommer-Larsen and others present a phenomenological description. Our aim is to form a bridge between these two points of view by neglecting those terms of the governing and transformation equations that are smaller than other contributions by several orders of magnitude. First, those equations are presented that govern the finite deformation and the electromagnetic phenomena inside the material. After that, those estimations will be taken that show the order of magnitude of the different contributions to the so-called effective fields. Finally, the model of the EAP actuator under periodically changing electric field will be presented. Because of the periodically changing finite deformation of the actuator, the electromagnetic phenomena must be investigated in the rest frames fixed to every single point of the material body. The electromagnetic field-variables can be converted into the laboratory frame by the slow speed approximation of the Lorentz transformation. For the special case of thin electroactive polymer actuators, one can find that the velocity dependent contributions are smaller by ten orders of magnitude in the electric field transformation, and by five orders of magnitude in the magnetic field transformation equations. On the other hand, none of the terms of the effective current can be neglected, because they can be of the same order of magnitude as the free current.