A suitable low-order, tetrahedral finite element for solids

To use the all-tetrahedral mesh generation capabilities existing today, we have explored the creation of a computationally e cient eight-node tetrahedral nite element (a four-node tetrahedral nite element enriched with four mid-face nodal points). The derivation of the elementʹs gradient operator, studies in obtaining a suitable mass lumping and the elementʹs performance in applications are presented. In particular, we examine the eight-node tetrahedral nite elementʹs behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the eight-node, mean-quadrature hexahedral nite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral nite element and the four-node tetrahedral nite element are included. Given automatic all-tetrahedral meshing, the eight-node, mean-quadrature tetrahedral nite element is a suitable replacement for the eight-node, mean-quadrature hexahedral nite element and meshes requiring an inordinate amount of user intervention and direction to generate. Copyright