Advances in Imposing Nonconforming Neumann Boundary Conditions in the Material Point Method

Due to the material point method's hybrid Lagrangian-Eulerian formulation, both conforming and nonconforming boundaries often exist throughout a simulation. Imposing nonconforming boundary conditions in the MPM remains a challenge due to the material boundary continually updating throughout a simulation. Regardless of the computational challenges, imposing Neumann boundary conditions is vital for modeling a wide variety of geotechnical problems. Recently, two variations of the MPM, the CutMesh MPM and the virtual stress boundary (VSB) method, have been proposed for imposing nonconforming Neumann boundary conditions. The current study uses two benchmark problems to directly compare the numerical performance of these newly developed variations of the MPM. For very simple problems, the CutMesh MPM has lower error than the VSB method, but as problem geometry becomes more complex, both methods produce comparable results.