An improved material point method using moving least square shape functions

In this study, moving least square (MLS) shape functions are employed to reduce the cell-crossing error occurred in conventional material point method (MPM) when material particles pass through grid cell boundaries. The level of smoothness of MLS shape functions for mapping information from material particles to a background grid can be controlled by the support size of MLS weight functions. A simple method is proposed to reduce the computational cost for evaluating MLS shape functions at material particles by interpolating pre-computed MLS shape function values at sampling points in a grid cell. Numerical results show that the present method is very effective to reduce the cell-crossing error in MPM computations.