A local grid refinement scheme for the material point method with B‐spline basis functions (BSMPM) is developed based on the concept of bridging domain approach. The fine grid is defined in the local large‐deformation regions to accurately capture the complex material responses, whereas other spatial domains are discritized by coarse grids. In the overlapping domain between the fine and coarse grids, the constraint of particle displacements obtained with different grids is enforced using the Lagrange multiplier method to eliminate the spurious stress reflection at the fine/coarse grid interface. Representative numerical examples have shown that the BSMPM simulations with the proposed local grid refinement scheme could provide the solutions in good agreement with those obtained with the uniformly fine grid, and that no significant spurious stress reflection is induced at the fine/coarse grid interface, even for the bridging domain size as small as the cell size of the fine grid. It is also found that the proposed local grid refinement method can significantly reduce the BSMPM computational time compared with the cases for uniformly fine grids. A multitime‐step algorithm is presented and shown to considerably enhance the efficiency of the present local grid refinement scheme with no compromise in accuracy.

中文翻译：

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B样条材料点方法的局部网格细化方案

基于桥接域方法的概念，针对具有B样条基函数（BSMPM）的材料点方法，开发了一种局部网格细化方案。在局部大变形区域中定义了精细网格，以准确捕获复杂的材料响应，而其他空间域则由粗糙网格来区分。在细网格和粗网格之间的重叠域中，使用拉格朗日乘数法强制使用不同网格获得的粒子位移约束，以消除细/粗网格界面处的杂散应力反射。代表性的数值示例表明，采用建议的局部网格细化方案进行的BSMPM仿真可以提供与采用均等精细网格获得的解具有良好一致性的解决方案，并且即使对于与细网格的像元大小一样小的桥接域，在细/粗网格界面上也不会引起明显的杂散应力反射。还发现，与均匀精细网格的情况相比，所提出的局部网格细化方法可以显着减少BSMPM的计算时间。提出并展示了一种多时步算法，该算法大大提高了当前局部网格细化方案的效率，而不会影响准确性。