Development on the smoothed material point method for extremely large deformation and impact with elastoplastic models

• A Smoothed Material Point Method (SMPM) is presented to solve the large deformation and impact problem. • The proposed method is developed by combining the smoothed reconstruction with the conventional MPM. • The presented SMPM can be reduce the unphysical oscillations without artificial viscosity. • The presented SMPM shows enhanced numerical stability over the classical MPM. • This presented SMPM exhibits higher accuracy and also maintains good convergence when simulating impact and large deformation problems involving elastic and elastoplastic models, as compared with the classical MPM. A Smoothed Material Point method (SMPM) is developed by introducing the smoothed reconstruction into the classical MPM algorithm, so that the unphysical numerical oscillation can be reduced without artificial viscosity. The accuracy order of the smoothed reconstruction has been derived in this work. In the context of engineering problems, the proposed algorithm is applied with von-Mises and Johnson-Cook elastoplastic constitutive models to simulate extreme loading responses in both two and three dimensions cases. Three typical numerical examples, including two-dimensional elastic collision, three-dimensional extremely compressive loading of copper block and impact of Taylor bar, have been simulated by the SMPM and MPM algorithms to demonstrate the advantages of the proposed method. According to the error analysis, all the SMPM simulations without artificial viscosity obtain more accurate results than the MPM with artificial viscosity. Furthermore, in the simulation of extremely large deformations involving ideal and hardening elastoplastic models, the SMPM algorithm also demonstrates stronger numerical stability than the classical MPM. Therefore, the SMPM proposed here has more advantages than the classical MPM in terms of accuracy and stability. The research work in this paper showcases the application prospects of the SMPM algorithm in problems of extremely large deformation and impact.