HYDRO-MECHANICAL COUPLED DUAL DOMAIN MATERIAL POINT METHOD STABILIZED WITH A NULL-SPACE FILTER

The Material Point Method (MPM) is a continuum-based numerical method especially suitable for solving large deformation problems. In this paper, we investigate the null-space errors present in MPM solutions. The paper establishes a null-space stability condition which is used to examine the null-space errors in different versions of the MPM. This analysis shows that a B-splines MPM satisfies the null-space stability condition and therefore reduces greatly the errors associated with the null-space. In contrast, the MPM, the Generalized Interpolation Material Point Method (GIMP) and the Dual Domain Material Point Method (DDMP) show non-trivial null-spaces in the mapping. To remove the null-space errors, this paper utilizes QR factorization method, which is similar to the Single Value Decomposition (SVD) method, but requires fewer computations. This paper simulates several problems with hydro-mechanical coupled Dual Domain Material Point Method (DDMP) formulation both with and without null-space error reduction. The simulations indicate that the null-space filter can improve significantly the accuracy of the pore water pressure for both gravity loading and consolidation in large strain simulation.