A solid-shell formulation based on the assumed natural inhomogeneous strains for modeling the viscoelastic response of electro-active polymers

In this paper, an advanced low-order solid-shell formulation is presented for modeling electro-active polymers (EAPs). This advanced finite element is of great importance due to the fact that EAPs actuators are typically designed as shell-like formations, in which the application of standard finite element formulation will lead to various locking pathologies (e.g. shear locking, trapezoidal locking, volumetric locking, etc.). Thus, for alleviating the various locking pathologies, both the assumed natural inhomogeneous strains (ANIS) and the enhanced assumed strain (EAS) methods are adopted for modifying the strain measure. Within the modified kinematics, a strain energy function that accounts for the elastic and the viscoelastic response as well as the electromechanical coupling is adopted. The developed formulation is implemented in the finite-element software Abaqus for further numerical applications, in which the developed ANIS solid-shell is compared with the classical assumed natural strains solid-shell and the mixed finite element formulation.