A low-regularity finite element approach for dielectric viscoelastic Kirchhoff–Love shells

Abstract 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.