Improved double-point material point method for dynamic geotechnical problems

Abstract The Material Point method is a suitable numerical method to simulate large deformations often occurring in geotechnical engineering. The Double-Point MPM (2P-MPM) extends the simulations for water-saturated materials. In the present work, a coupled dynamic formulation is used to account for coupled wave propagation in porous media in addition to large deformations. The computational cost of 2P-MPM is expensive because information between material points and grid nodes must be approximated at each time step. In conventional 2P-MPM formulations, linear shape functions are used for this approximation, leading to well-known grid crossing and loss of contact problems. We use the moving least square approximation for the 2P-MPM to handle these problems better. In addition, a parallelization approach is shown to improve the computation time, especially for large boundary value problems. The developed methods can be combined with non-saturated materials, such as fluids and dry soil, to simulate complex geotechnical issues. The performed computations of wave propagation and large deformations using the proposed methods show improved convergence behavior and increased efficiency.