A computationally efficient locking free numerical framework for modeling visco-hyperelastic dielectric elastomers

Abstract

In this paper, we present a finite element formulation for simulating the electromechanical behavior of nonlinear visco-hyperelastic dielectric elastomers undergoing isochoric finite strain deformations. The incompressible nature of dielectric elastomer results in the problem of volumetric locking. In order to alleviate this problem various techniques, such as selective reduce integration method, F-bar method, and mixed formulation have been used. In the present numerical framework, we treat this problem by adapting the computationally efficient J-bar method. This method of alleviating locking is based on the assumption of the dependence of volumetric density function only on the smoothed volumetric part of the multiplicatively decomposed deformation gradient. A staggered solution algorithm is used for solving the coupled nonlinear equations by decoupling displacement and electric potential fields. The present formulation is implemented into an in-house finite element program. Firstly, the finite element implementation of the proposed formulation is validated and demonstrated by investigating the effect of viscosity parameter on the electromechanical phenomenon of homogeneously deforming dielectric elastomers, i.e., voltage driven creep and pull-in instability. Further, for an in-homogeneously deforming bi-layered bending actuator, the computational efficiency of the proposed J-bar method employed in conjunction with the staggered solution approach is established over the conventional F-bar and multi-field formulations used with the monolithic solution scheme. Finally, we utilize the proposed formulation for investigating the effect of visco-elasticity on the electromechanical response of complex dielectric elastomeric actuators involving inhomogeneous deformations such as, bilayer bending actuators, grippers, and buckling pumps, when subjected to monotonic and constant electrical loads.