MLS-based SPH in LS-DYNA® for Increased Accuracy and Tensile Stability

Two important limitations of the Smoothed Particle Hydrodynamics are low accuracy and tensile instability. While the former can be somewhat alleviated by employing very fine discretizations and renormalized formulations, the latter can only be slightly mitigated with heavy use of artificial viscosity. In addition, renormalized formulations can be unsuitable for extreme deformations and impact simulations, and excessive artificial viscosity can severely alter the physics of the problem being modeled. A new formulation based on a Moving Least-Squares approximation and an improved nodal integration scheme is presented in this paper. The method is shown to be much more stable in tension, and very accurate. Extensive comparisons with traditional SPH and with experimental data are presented.