Abstract
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 tensor. The developed quadrilateral shell element is characterized by a course 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.
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