Tensile Instability and Artificial Stresses in Impact Problems in SPH

The smooth particle hydrodynamics (SPH) is a meshless computational technique that is popular in the modeling of impact and penetration problems. However, SPH is liable to a tensile instability that manifests itself as a bunching of nodes and formation of artificial voids and no generally accepted formulation exists to counter this instability. We examine the performance of two methods that have been proposed to deal with the tensile instability— the Monaghan artificial stresses and the Godunov-type SPH. The impact and penetration of 0.5 cm radii steel spheres on 2 mm thick aluminium plate at 3.1 km/s is chosen for comparison. We show that the artificial void formation in St-Al impact is suppressed but not eliminated by using Monaghan stresses while the void formation is entirely eliminated by using Godunov-type formulation of SPH that was proposed by Parshikov and Medin.