An Exploration of Accuracy and Convergence of the Degenerate Uniform Strain Hexahedral Element: A Solution to the Unmeshed Void in an All-Hexahedral Mesh

The uniform strain hexahedral element mesh has long been a work horse for getting accurate and convergent answers in high deformation solid mechanics analyses. Obtaining an all-hexahedral mesh can be a difficult and time consuming process thus limiting the element’s use in design phase computations. Unconstrained paving and plastering offers a technique to get an all-hexahedral mesh automatically but still can leave un-meshable voids [1]. While degenerated forms of the uniform strain hexahedral element such as the wedge have been used sparingly, they have garnered limited general acceptance. We present a more exhaustive numerical exploration of the degenerated hexes with the hope of encouraging their use to resolve the un-meshable voids. The results of patch tests are used to numerically demonstrate linear completeness of the degenerate elements. A manufactured solution analysis is then used to show optimal convergence rates for meshes containing degenerate elements. Additionally, applications to a torsion rod and high velocity impact are used to highlight the accuracy and applicability of degenerates for solving more complex problems.