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 efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element's gradient operator, studies in obtaining a suitable mass lumping and the element's performance in applications are presented. In particular, we examine the eight-node tetrahedral finite element's 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 finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, mean-quadrature tetrahedral finite element is a suitable replacement for the eight-node, mean-quadrature hexahedral finite element and meshes requiring an inordinate amount of user intervention and direction to generate. Copyright (C) 1999 John Wiley & Sons, Ltd. This paper was produced under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.