Boundary Treatments

*Author of this lecture: Chang Yu, University of California, Los Angeles

During the grid update step, we apply external forces and solve for nodal accelerations and velocities. To model object interactions with the physcal environment, boundary conditions can be enforced at this stage.

In this lecture, we describe how boundary treatments are implemented in MPM. Specifically:

• Boundary Conditions on Grid explains how velocity constraints and external forces are imposed directly on grid nodes to handle Dirichlet and Neumann conditions.
• Frictional Contact on Material Particles focuses on more accurate contact and friction treatments, which are handled at the particle, enabling flexible and more accurate interaction with complex boundaries.

These treatments are essential for producing realistic contact behavior—such as sticking, sliding, and separation—that adheres to the Coulomb friction law.