An assumed strain approach avoiding artificial thickness straining for a non‐linear 4‐node shell element

A quadrilateral degenerated C0 shell element is presented which relies on extensible director kinematics and which incorporates unmodified three‐dimensional constitutive models. It is shown that the direct interpolation of the extensible director field causes severe locking behaviour in the case of thin shell structures. An assumed strain interpolation is proposed to overcome the thin‐shell defect. Due to this modification the shell element is able to accommodate large rotations without a rotation tensor, even for very thin shells. Several large deformation examples confirm that the developed shell element is competitive with more elaborate formulations which use rotational degrees of freedom.