A local grid refinement scheme for B-spline material point method

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.