Truncated hierarchical B-spline material point method for large deformation geotechnical problems

This article integrates the truncated hierarchical B-spline into the material point method (MPM) to address the large deformation problem in geotechnical engineering. The proposed approach allows the MPM to work with a locally refined hierarchical background grid, by which computational resources could be concentrated in spatial domains of concern. The truncated hierarchical B-spline forms the partition of unity property throughout the computational domain by reducing the support of the basis functions on adjacent hierarchical levels. Two auxiliary data structures beneficial to the hierarchical particle-grid mappings are introduced to facilitate the implementation of the truncated hierarchical B-splines in the framework of MPM. In addition, a particle splitting strategy is employed to eliminate numerical fracture problems that may occur in the case of extremely large deformation. Validation and application examples demonstrate the robustness and stability of the proposed method.