# The FEM Model of the Pump Made of Dielectric Electroactive Polymer Membrane
## 1 Introduction  
Smart materials are ones that can change their properties in a controlled manner in response to environmental stimuli. Such materials can be used both as sensors and actuators [1, 2]. Electroactive materials like DEAPs (dielectric electroactive polymers) are included in the group of smart materials and are increasingly used in many automation and robotics systems [3]. This work presents the concept of a device using an electroactive polymer that changes its mechanical properties under the influence of voltage excitation.  
Finite element model (FEM) modeling of the behavior of DEAPs is a useful tool to understand such systems better and help in the optimal design of prototypes. The modelling and simulating of DEAP actuators is a cost-effective way of providing a better understanding of the devices built with their usage. DEAPs offer excellent performance, are lightweight, flexible and inexpensive. Therefore, dielectric elastomers, provide many potential applications as micro-actuators. A technique to accurately model this material--taking into account its nonlinearities as well as its large deformations--is being developed in this study. This work presents a model of the innovative construction of the pump using DEAP membrane deformation.  
There are many works that describe different modeling methods and analytical models [4]. One of the works presents a technique for accurate modeling of electroactive polymer taking into account nonlinearities and large deformations [5]. The authors simulated an algorithm in the ANSYS environment that considers the electromechanical coupling of the EAP (electroactive polymers) model. Simulation of charge distribution and electrostatic force is the subject of another work which uses COMSOL software [6]. Another work focuses on studying the kinematics of forming and loading, along with thermodynamics [7]. While much theoretical and computational modeling effort has gone into describing the ideal, time-independent behavior of these materials, viscoelasticity is a crucial component of the observed mechanical response, and hence has a significant effect on electromechanicalactuation. In [8], the authors show that viscoelasticity provides stabilization that delays the onset of instability under monotonic loading and may fully suppress instabilities under sufficiently fast cyclic loading, which may be desirable for many applications. Although all of these models provide advantageous insights into the behavior of the elastomer material, they lack the ability to accurately predict the complete DEAP actuator structure. They focus on several aspects of modeling but are not able to reflect the full complexity.  
In this work, an FEM model was made that was verified faithfully with measurements. First, the relationship between static deformation and applied force was presented. Next, three series of displacement measurements were compared for a given force during alternating voltage applied to the membrane. The results prepared in this way allowed us to identify the values of the virtual Young's modulus corresponding to individual points of states by collecting a sufficient number of real object measurements. Using the work state mapping method, it was possible to model devices with sufficient precision having the knowledge how the membrane will deform; it was not necessary to calculate the full complexity of the model each time.