Abstract Summary
The Material Point method is a suitable numerical method to simulate large deformations that often occur 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. In our work, we present the moving least square approximation for the 2P-MPM to better handle these problems. 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 as well as dry soil, to simulate complex geotechnical problems. The performed computations of wave propagation as well as large deformations using the proposed methods show improved convergence behavior as well as increased efficiency.
