Multiscale modelling of a composite electroactive polymer structure

Abstract

Danfoss PolyPower has developed a tubular actuator comprising a dielectric elastomersheet with specially shaped compliant electrodes rolled into a tube. This paper is concernedwith the modelling of this kind of tubular actuator. This is a challenging task due to thesystem’s multiscale nature which is caused by the orders of magnitude difference betweenthe length and thickness of the sheets as well as the thickness of the electrodes and theelastomer in the sheets. A further complication is the presence of passive parts at both endsof the actuator, i.e. areas without electrodes which are needed in order to avoid shortcircuits between negative and positively charged electrodes on the two sides of the sheet.Due to the complexities in shape and size it is necessary to introduce some simplifyingassumptions. This paper presents a set of models where the three-dimensional problem hasbeen reduced to two-dimensional problems, ensuring that the resulting models can behandled numerically within the framework of the finite element method. Thesemodels have been derived by expressing Navier’s equation in elliptical cylindricalcoordinates in order to take full advantage of the special shape of these actuators.Emphasis is placed on studying the passive parts of the actuator, as these degrade theeffectiveness of the actuator. Two approaches are used here to model the passive parts: aspring-stiffness analogy model and a longitudinal section model of the actuator. Themodels have been compared with experimental results for the force–elongationcharacteristics of the commercially available PolyPower ‘InLastor push’ actuator. Thecomparison shows good agreement between model and experiments for the casewhere the passive parts were taken into account. One of the models developed issubsequently used to study geometric effects—specifically the effect of changing theellipticity of the tubular actuator on the actuator’s performance is investigated.