Implementing Dynamic Boundary Conditions with the Material Point Method

The material point method (MPM) is gaining an increasing amount of attention due to its capacity to solve geotechnical problems involving large deformations. Large deformations in geotechnics usually involve the failure process and therefore dynamic analyses are often carried out. However, simulating the (infinite) continuous domain using typical Dirichlet (fixed) boundary conditions induces spurious reflections, causing (1) unrealistic stress increments at the domain boundary and (2) the appearance of multiple unnatural stress waves in the domain. Aiming to eliminate this numerical artifact in MPM, two solutions for absorbing boundary conditions found in FEM are implemented and investigated; these are (1) a viscous boundary condition and (2) a viscoelastic boundary condition. The use of such dynamic boundary conditions in MPM is scarce and no validation of them has yet been presented in the literature. In this paper, these absorbing conditions are implemented alongside recent mapping and integration techniques, improving numerical stability and accuracy.