A two-steps time discretization scheme using the SPH method for shock wave propagation

The Smoothed Particle Hydrodynamics (SPH) is a meshfree method which has been applied to a wide range of problems. In the present work, a new time integration algorithm using a corrected SPH spatial discretization for small deformations is applied to solve the propagation of shock waves in viscoplastic continua. In the method presented herein the equations are formulated in terms of stress and velocity. A corrected Lagrangian kernel is employed and two different sets of particles are used for the time discretization. Numerical instabilities are not present when using this new SPH formulation. The method proposed here has been proved to be efficient and it provides solutions of good accuracy.