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 overcome 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 briefly reviewed. In addition, the split-based formulation proposed by Zienkiewicz et al. (International Journal for Numerical Methods in Engineering 1998; 43:565–583) is described 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.