Preliminary effort in developing the smoothed material point method for impact

The smoothed material point method (SMPM) is being developed for better simulating impact problems, based on the respective strengths of the original material point method (MPM) and the smoothed particle hydrodynamics (SPH). The field variables of each material point (including velocity and stress) are re-calculated by one smoothed reconstruction procedure, while the rest of the solution steps are the same as those in the original MPM algorithm. In this preliminary study, the numerical performances of the original MPM, SPH and the SMPM are examined and compared using one-dimensional transient problems including impact. It is demonstrated that the numerical oscillations can be effectively reduced by the proposed reconstruction, showing the superiority of the SMPM over the original MPM and SPH in terms of solution accuracy and stability. As compared with the SPH, the SMPM exhibits significantly higher efficiency. Numerical results also illustrate that the proposed SMPM possesses the advantages of both the MPM and the SPH, which warrants the further development of the SMPM for general applications.