Deformation and enclosed volume change of axisymmetric non-linear dielectric elastomer membrane pump: a theoretical study

Abstract This work investigates the change in the enclosed volume of an axisymmetric non-linear hyper-elastic membrane pump subjected to dielectric actuation. The equilibrium equations in cylindrical coordinates, coupled with non-linear constitutive relations, are solved numerically to obtain the deformed membrane geometry under pressure loading (using Variational Calculus). The effect of dielectric actuation is then incorporated by considering the change in material properties and deformation induced by the applied electric field. The deformed geometry under dielectric actuation is determined, and the change in enclosed volume is calculated by comparing the deformed states with and without the applied electric field. The proposed approach enables quantifying the volumetric change in non-linear hyper-elastic membrane pumps due to dielectric actuation for potential applications in soft robotics, adaptive optics, and microfluidics. By non-dimensionalizing variables, key dimensionless parameters governing the problem are identified for broader applicability. Furthermore, this methodology can estimate volume changes for different electric actuations when a specific material is chosen with experimentally derived parameter trends, facilitating material selection or synthesis to meet targeted volumetric requirements.