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.

在这项研究中，移动最小二乘（MLS）形状函数用于减少当传统的材料点方法（MPM）中发生的跨材料网格物体穿过网格边界时的网格交叉误差。用于将信息从物料粒子映射到背景网格的MLS形状函数的平滑度可以通过MLS权重函数的支持大小来控制。提出了一种简单的方法，通过在网格单元中的采样点内插预先计算的MLS形状函数值来减少评估材料粒子上MLS形状函数的计算成本。数值结果表明，该方法在减小MPM计算中单元交叉误差方面非常有效。