Sebastian Platzer

The modeling and simulation of thin dielectric viscoelastic structures experiencing large deformations presents significant challenges. In this work, we introduce a shell formulation that captures the essential kinematic and constitutive features of these structures under transient electric loading. The formulation includes elastic and viscous membrane strains, curvature, as well as thickness deformation and the variation of the electric field through the thickness. A thermodynamically consistent model is developed and discretized using low-regularity shell elements within a variational framework. The proposed method is validated through several computational examples. The results demonstrate a high level of accuracy in capturing the transient large-strain behavior of dielectric elastomer shells even for very coarse discretizations.

The finite element simulation of thin viscoelastic membranes is a challenging problem. On the one hand, geometric dimensions of the membrane are adverse to classical finite element formulations, which require the thickness of the structure to be resolved. On the other hand, both material and geometric nonlinearities need to be considered in the large-strain regime. In the present paper, a Kirchhoff–Love shell formulation including thickness deformation is deduced for incompressible viscoelastic membranes at finite strain. For this formulation, a mixed shell element with low regularity is proposed to discretize a viscoelastic shell formulation based on a multiplicative split of the deformation gradient. The formulation is tested against full three-dimensional formulations in a variety of examples. Excellent accordance of results in quasi-static as well as dynamic simulations is observed.