Finite deformation analysis of electro-active shells

In this contribution, a novel nonlinear formulation for the finite deformation analysis of shell-like structures made of dielectric polymers and subject to electrical loading is developed. The kinematics of mechanical deformation is described via a seven-parameter shell model. Moreover, a second-order Taylor expansion, containing three parameters, is proposed to approximate the electrical potential through the thickness of the shell. The combined mechanical and electrical parameters constitute a ten-parameter electro-shell model. After developing the variational formulation of the problem, a nonlinear finite element formulation for the numerical solution of the coupled electromechanical problem is also developed. The formulation is further enriched by the enhanced assumed strain method to alleviate locking in thin shells. Finally, the applicability of the proposed formulation in several benchmark examples is demonstrated. In particular, it is shown that the formulation can capture the results available in the literature with high accuracy.