STRESS POINTS FOR TENSION INSTABILITY IN SPH

Abstract

In this work, the stress-point approach, which was developed to address tension instability and improve accuracy in Smoothed Particle Hydrodynamics (SPH) methods, is further extended and applied for one-dimensional (1-D) problems. Details of the implementation of the stress-point method are also given. A stability analysis reveals a reduction in the critical time step by a factor of 1/√2 when the stress points are located at the extremes of the SPH particle. An elementary damage law is also introduced into the 1-D formulation. Application to a 1-D impact problem indicates far less oscillation in the pressure at the interface for coarse meshes than with the standard SPH formulation. Damage predictions and backface velocity histories for a bar appear to be quite reasonable as well. In general, applications to elastic and inelastic 1-D problems are very encouraging. The stress-point approach produces stable and accurate results. © 1997 by John Wiley & Sons, Ltd.