An angular momentum conserving affine-particle-in-cell method

Summary Large deformation soil behavior underpins the operation and performance for a wide range of key geotechnical structures and needs to be properly considered in their modeling, analysis, and design. The material point method (MPM) has gained increasing popularity recently over conventional numerical methods such as finite element method (FEM) in tackling large deformation problems. In this study, we present a novel hierarchical coupling scheme to integrate MPM with discrete element method (DEM) for multiscale modeling of large deformation in geomechanics. The MPM is employed to treat a typical boundary value problem that may experience large deformation, and the DEM is used to derive the nonlinear material response from small strain to finite strain required by MPM for each of its material points. The proposed coupling framework not only inherits the advantages of MPM in tackling large deformation engineering problems over the use of FEM (eg, no need for remeshing to avoid mesh distortion in FEM), but also helps avoid the need for complicated, phenomenological assumptions on constitutive material models for soil exhibiting high nonlinearity at finite strain. The proposed framework lends great convenience for us to relate rich grain‐scale information and key micromechanical mechanisms to macroscopic observations of granular soils over all deformation levels, from initial small‐strain stage en route to large deformation regime before failure. Several classic geomechanics examples are used to demonstrate the key features the new MPM/DEM framework can offer on large deformation simulations, including biaxial compression test, rigid footing, soil‐pipe interaction, and soil column collapse.

Summary This paper presents algorithm improvements that reduce the numerical noise and increase the numerical stability of the material point method formulation. Because of the linear mapping required in each time step of the material point method algorithm, a possible mismatch between the number of material points and grid nodes leads to a loss of information. These null‐space related errors may accumulate and affect the numerical solution. To remove the null‐space errors, the presented algorithm utilizes a null‐space filter. The null‐space filter shown removes the null‐space errors, resulting from the rank deficient mapping and the difference between the number of material points and the number of nodes. The presented algorithm enhancements also include the use of the explicit generalized‐α integration method, which helps optimizing the numerical algorithmic dissipation. This paper demonstrates the performance of the improved algorithms in several numerical examples.

In this paper, a new formulation of material point method (MPM) to model coupled soil deformation and pore fluid flow problems is presented within the framework of the theory of porous media. The saturated porous medium is assumed to be consisting of incompressible pore fluid and deformable soil skeleton made up of incompressible solid grains. The main difference of the proposed MPM algorithm is the implicit treatment of pore‐water pressure which satisfies its incompressibility internal constraint. The resulting solid‐fluid coupled equations are solved by using a splitting algorithm based on the Chorin's projection method. The splitting algorithm helps to mitigate numerical instabilities at the incompressibility limit when equal‐order interpolation functions are used. The key strengths of the proposed semi‐implicit coupled MPM formulation is its capability to reduce pressure oscillations as well as to increase the time step size, which is independent of the fluid incremental strain level and the soil permeability. The proposed semi‐implicit MPM is validated by comparing the numerical results with the analytical solutions of several numerical tests, including 1D and 2D plane‐strain consolidation problems. To demonstrate the capability of the proposed method in simulating practical engineering problems involving large deformations, a hydraulic process leading to slope failure is studied, and the numerical result is validated by the monitored data.