Viscoelastic Kirchhoff–Love shells at finite strains: constitutive modeling and mixed low-regularity finite elements

Abstract 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.