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

Abstract

In this work, a hybrid discontinuous Galerkin (dG) quadrilateral element formulation is presented. As usual in hybrid formulations, the interior of the elements is treated separately from the skeleton, which represents the element boundaries. These are kinematically decoupled, i.e., displacement jumps can occur between the skeleton and the interior of the elements. The global degrees of freedom (dofs) are defined on the skeleton as the displacements at the corners, which allows the implementation into existing finite element codes. As usual in hybrid dG-formulations, the degrees of freedom in the interior are condensed out on the element level, leading to the same number of global degrees of freedom as for continuous bilinear elements.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.