A low-order locking-free hybrid discontinuous Galerkin element formulation for large deformations

Instead of using conventional shape functions in the interior, the deformation gradient F is assumed constant within the element. Furthermore, F is connected to the skeleton degrees of freedom via the weak form. This leads to a very simple formulation and implementation. The element is tested for several computational examples from the literature. Special choices of the penalty parameter are investigated, which are partially derived analytically. It is found that the element is free of volumetric and shear locking. Moreover, the convergence is similar to that of other well-known locking-free finite element formulations.