On the dynamic assessment of the Local-Maximum Entropy Material Point Method through an Explicit Predictor–Corrector Scheme

Abstract Material Point Method (MPM) has arisen in the recent years as an alternative to Finite Element Method (FEM) under large deformations. However, the simulation of shock waves propagation in the large deformation regime is still challenging under this approach due to the incapability of the standard MPM time integration scheme to filter spurious noises. To overcome it, we propose in this paper an explicit Predictor–Corrector time integration scheme. Its powerful performance mitigates the presence of spurious oscillations with minimal dissipation in high frequency problems. Other source of numerical noise in MPM occurs when the material points cross computational grid boundaries, being caused by the lack of smoothness of the interpolation functions. This noise results in spurious local variations at the material points, where strain–stress fields are computed. This could lead to inaccurate solutions as well as aborted simulations in the worst cases. To surmount it, we propose in this work the Local Maximum-Entropy (LME) approximation schemes as a robust substitute of the traditional shape function in MPM. The performance of both improvements is validated by the high quality results of the numerical examples.