Large-displacement landslides based on affine velocity matrix-improved material point method

In order to overcome the numerical noise problem of the material point method, the momentum mapping scheme of the affine particle-in-cell method is applied to the classical material point method, that is, in the process of momentum mapping, an additional affine velocity matrix is maintained, and then the velocity field represented by the affine velocity matrix and velocity vector of material point is constructed. It is proved that the affine velocity matrix is the first-order approximation of velocity gradient. The affine velocity matrix greatly simplifies the solving process of spin rate and rate of deformation as well as the computation process in a single time step, so that the computational efficiency is doubled. The Taichi programming language, which can be used for GPU parallel computing, is used for algorithm programming, which improves the solution efficiency hundreds of times. The effectiveness of the improved algorithm to overcome numerical noise, the numerical accuracy and the computational efficiency of the program are verified by simulating the natural stacking of sand columns and the stacking of aluminum rods. By simulating the landslide of a typical shape slope, the applicability and advantages of the algorithm and program in landslide analysis are verified.