A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains

In this paper a finite shell element for large deformations is presented based on extensible director kinematics. The essential feature is an interface to arbitrary three-dimensional material laws. The non-linear Lagrangian formulation is based on the three-field variational principle, parametrized with the displacement vector, enhanced Green-Lagrangian strain tensor and second Piola Kirchhoff stress tenser. The developed quadrilateral shell element is characterized by a coarse mesh accuracy and distortion insensitivity compared with bilinear displacement approaches. Furthermore, plane stress response is approximately recovered in the asymptotic case of vanishing thickness. A number of example problems investigating large deformation as well as finite strain applications are presented. Compressible and incompressible hyperelastic materials of the St. Venant-Kirchhoff, Neo-Hookean and Mooney-Rivlin type are particularly used.