An improved convected particle domain interpolation material point method for large deformation geotechnical problems

A novel material point method called the improved convected particle domain interpolation (ICPDI) is proposed in this paper to simulate large-deformation problems in geotechnical engineering. The ICPDI framework is based on the existing convected particle domain interpolation (CPDI) and employs an adaptive orthogonal improved interpolating moving least square (AOIIMLS) shape functions. The AOIIMLS shape functions prevent computational instability problems caused by singular or ill-conditioned matrices through avoiding the direct solving of inverse matrices. Additionally, ICPDI adopts the velocity gradient to calculate the velocity field in particle domains and reduces cell-crossing errors by using AOIIMLS shape functions. To reconstruct the velocity function in the background grid, the velocities of the material points and four related corner points are employed through AOIIMLS shape functions. The bar axis-aligned vibration, ring radial expansion, slope elasto-plastic slumping, and post-failure tunnel collapse behavior examples are used to verify the accuracy and effectiveness of ICPDI by comparing the results with other numerical methods and experiments. Numerical simulation results show that ICPDI outperforms the material point method (MPM) and CPDI in terms of computational accuracy and convergence while reducing cell-crossing errors. Consequently, this study demonstrates the capability of ICPDI in simulations of large-deformation geotechnical problems.