Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications

This papers summarizes two linear tetrahedral FE formulations that have been recently proposed to over- come volumetric locking in nearly incompressible explicit dynamic applications. In particular, the average nodal pressure (ANP) technique described by Bonet and Burton (Communications in Numerical Methods in Engineering 1998; 14:437{449) is brie y reviewed. In addition, the split-based formulation proposed by Zienkiewicz et al. (International Journal for Numerical Methods in Engineering 1998; 43:565{583) is de- scribed here in terms of a time integration of the nodal Jacobian. This will make it simple to compare both techniques and will enable a new combined method to be presented. The paper will then discuss the stability constraints that each technique places on the timestep size. A von-Neuman stability analysis on simple 1-D uniform meshes will show that the ANP element permits the use of much larger timesteps than the split based formulations. Finally, numerical examples corroborating in 3-D this analytical conclusions will be presented.