A finite element approach for modelling multilayer unimorph dielectric elastomer actuators with inhomogeneous layer geometry

In this paper we present a finite element (FE) approach for modelling the performance of multilayer unimorph dielectric elastomer actuators (MUDEAs) with inhomogeneous layer geometry. MUDEAs are made up of a dielectric elastomer actuator (DEA) stack bonded to a flexible substrate and are capable of large out-of-plane displacements and resonant operation. MUDEAs are useful for many applications such as steerable endoscopes for minimally invasive surgery procedures, where high manoeuvrability and mechanical flexibility are required. Models of MUDEAs are useful for feasibility assessment and actuator design optimisation. The current analytical models of unimorph DEAs are inadequate for more unconventional unimorph configurations with multiple layers. The FE approach presented is capable of efficiently modelling MUDEAs with non-uniform geometries and multiple layers. The Maxwell stress equation for MUDEAs was also derived and was found to be the same as for the unconstrained DEA case. The static deflection against input voltage for two, three and four layer MUDEAs was simulated using the developed FEA approach and validated against experiments. The experimental MUDEAs had an inhomogeneous Gaussian layer geometry resulting from the fabrication process used. The model showed good agreement with the experimental data. The validated finite element model was used to investigate the effects of layer number on unimorph tip deflection for several layer thicknesses. The results show that there is an optimum number of layers for which tip deflection is a maximum and that when large deflections are expected it is more efficient to use thinner layers, rather than thicker layers, for a given overall stack thickness.