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

A robust and computationally efficient finite element framework for coupled electromechanics

“…The accuracy of the proposed finite element formulation is at first verified by studying an example with an analytical solution that has been previously studied in Hennan et al [32], Liu et al [114], Sharma and Joglekar [73,74]. We consider a plane-strain model (2D) and a 3D model with the original side length L mm, as shown in Fig.…”

“…Although P2/P1, Q2/Q1 and BT2/BT1 elements have been used widely for incompressible solids mechanics problems, the adaption of the Q2/P1 element to solid mechanics problems is scarce when compared to its usage for incompressible fluid flow problems. To the best of the authors' knowledge, extensive studies on the adaptation of these elements to coupled electromechanics are either sparse or non-existent; literature on computational electromechanics is predominantly restricted to the Q1/P0 and Q1-F -bar elements [32,46,60,67,74,90,123]. Thanks to the advantages of Bézier elements over Lagrange elements for explicit dynamics simulations and their ease of mesh generation over NURBS [111,112], our primary choice of finite elements in this work is the one based on Bézier elements.…”

“…To enhance actuations, EAPs are frequently filled with high electric permittivity fillers which are further cured under an electric field during the curing process that results in anisotropic EAP composites, see Kashani et al [43], Carpi et al [14] and Kumar et al [44] for experimental evidences, and refer to Keip and coworkers [45,70] and Ullah et al [71,72] for homogenization-based simulation frameworks. In order to capture the underlying inhomogeneous behaviour of particle-filled EAPs, Bustamante [8], Hossain and Steinmann [33], Hossain [34], Sharma and Joglekar [73,74], Bustamante and Shariff [11] and Shariff et al [81] proposed mathematical formulations of electro-elasticity that incorporated transverse and dispersion-type anisotropy. All the constitutive modelling frameworks mentioned above are based on the so-called phenomenological approach.…”

“…In contrary, exploiting the micro-mechanics of polymeric chain orientations and deformations under mechanical and electromechanical coupled loads, Itskov et al [39], Cohen et al [15,16], Brighenti et al [4], and Thylander et al [87,88] proposed micro-mechanically-motivated electro-elastic models at finite strains with physically meaningful material parameters. Other efforts in formulating constitutive modelling of electro-elasticity are due to Gao et al [30], Zhao and Suo [98], Henann et al [32], Ask et al [1], Büschel et al [12], Nedjar [60], Wang et al [99], Sharma and Joglekar [74], Wang et al [99], Thylander [87], Vogel et al [90,91], Saxena et al [76,77], Skatulla et al [83], and Zäh and Miehe [97].…”

“…Since dielectric elastomers are mainly made of thin structures, a solid shell finite element formulation using a mixed variational principle of Hu-Washizu type is proposed by Klinkel et al [46]. In order to ameliorate volumetric-locking, a common phenomenon in nearly incompressible rubber-like materials, Hennan et al [32] extended the classical F -bar element method proposed by de Souza Neto et al [25] to the case of electro-elastic coupled problem while Sharma and Joglekar [74] extended the J-bar method [123] for simulating the nearly incompressible electro-viscoelasticity. Very recently, in a series of papers, Gil and co-workers [31,62] proposed a new constitutive framework with finite element implementations for large strain electromechanics based on the so-called convex multi-variable strain energies.…”