The material point method (MPM) is a meshfree method that can alleviate the issue of mesh-distortion confronted in the FEM for large deformation problems. We develop a serious of models based on the MPM to simulate granular flows.
(1) Coupling of the MPM and the DEM for granular flows impacting simulations
We adopt the MPM to model granular flows and the deformable DEM to model blocks. Each block is treated as comprising nine material points to couple the MPM and DEM, and the acceleration of grid nodes arising from the contacts between granular material and blocks is projected to the discrete element nodes working as body forces. Some results are shown below (click the figure to see the animation).
(2) Two-phases MPM
We use two set material points representing solid and fluid, respectively to consider the hydro-mechanical coupling problems. An experiment is conducted as a reference for validation. The results are shown below.
Sliding surface in the experiment Plastic strain distributions in simulations
(3) Hierarchy multi-scale modelling framework for granular materials using the MPM and DEM
Under this multi-scale framework, each material point is connected with a representative volume element consisting of an assembly of spheres. We abandon the phenomenological constitutive laws of granular materials and directly extract the constitutive relationships for each RVE using the DEM. Thus, we can link the macroscopic behaviors (such as plastic strain) and the microscopic mechanisms (such as force chains).
Schematic of the modelling scheme Connections of the macroscopic plastic strain and local packings
Displacements of the collapse of the granular pile simulated using the multiscale modelling scheme.
(4) Simulations of debris flows
We incorporate the domain terrain to simulate the process of a debris flow. The process is shown as flows (click the figure to see the animation)
The process of debris flow (simulated by others using our code)