A reduced mixed finite-element formulation for modeling the viscoelastic response of electro-active polymers at finite deformation

Abstract

In this work, a parameter identification procedure has been held for characterizing the widely used dielectric elastomer VHB. The calibration procedure has been performed using various experimental data found in previous works including uniaxial and multiaxial tests. Unlike the uniaxial tests, the multiaxial tests yield inhomogeneous deformation fields and, therefore, the finite-element method is adopted to obtain numerical solutions for the multiaxial tests. Here, a numerical scheme has been developed using the reduced mixed finite-element formulation, which eliminates the possible volumetric locking in electro-active polymers and enhances the computational efficiency as the static condensation is circumvented. The objective function, which calculates the discrepancy between the results obtained from the computational model and the measured experimental data, has been formulated taking into account the different types of experiments. The material parameters have been extracted when the objective function reached a minimum value, which is obtained by applying an iterative procedure using the fminsearch in Matlab. Within the extracted parameters and the developed finite-element formulation, number of simulations showing the efficiency of the computational model have been performed.

A Convex Multi-Variable based computational framework for multilayered electro-active polymers

“…, where E ijk (or E IJK ) symbolises the third-order alternating tensor components and the use of repeated indices implies summation 6 .…”

“…With the aim of modelling more complex deformation scenarios, the use of computational methods constructed on the basis of variational principles is nowadays acknowledged as the preferred method of choice. Building upon the early works of Toupin [73,74] and those of Dorfmann, Ogden, MacMeeking, Suo and co-workers in [21,22,49,71], recent contributions in the field of computational electro-mechanics can be found in [6,23,40,75,76]. In these works, the constitutive behaviour of a single-phase electro-mechanical material is encoded within a carefully (phenomenologically) defined energy functional which depends upon appropriate strain measures, a Lagrangian electric variable and, if dissipative effects are considered, an electromechanical internal variable [47].…”

Finite element modeling of electro‐viscoelasticity in fiber reinforced electro‐active polymers

“…Locking phenomena or artificial stiffening occurs in finite elements due to the nearly incompressible behavior of rubber‐like materials, especially when the structural response is bending dominated. Motivated by the latter aspects, mixed finite elements have been used in References 27 and 28 to simulate electro‐viscoelastic experiments and the response of electro‐elastic bodies surrounded by free space, respectively.…”

On the computational modelling of nonlinear electro-elasticity in heterogeneous bodies at finite deformations

“…A computational framework of electro-elasticity using the micro-sphere network model is presented in [25]. The Yeoh hyperelastic material model has been employed to predict the response of EAP in [29]. A Gent electro-elastic model is used in [30,31].…”