Case Study: 2D Sand with a Sphere Collider*

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

Building on the previous chapter—Two Colliding Elastic Blocks in 2D, where we implemented a minimal Material Point Method (MPM) simulation using the PIC transfer scheme—this case study demonstrates how, with minimal additional effort, we can extend the system to create a more advanced sand simulation.

Unlike the previous chapter, where particles are sampled on a regular grid, here we use Poisson-disk Sampling to initialize the material points. This helps reduce aliasing artifacts and structured noise, producing more physically realistic behavior in granular simulations.

In this case study, the sand is modeled using the Drucker-Prager Elastoplasticity [Klar et al. 2016] constitutive model, allowing us to capture non-recoverable deformation and internal friction—key features in granular material behavior.

We place a Static Sphere Collider inside the domain, which interacts with falling sand particles through frictional contact. The collider boundary is represented using a signed distance function (SDF) and enforces contact constraints and Coulomb friction.

We extend the original PIC scheme by incorporating the APIC Transfer Scheme to achieve improved accuracy and reduced numerical dissipation.

The executable Python project for this section can be found at https://github.com/phys-sim-book/solid-sim-tutorial under the 11_mpm_sand folder.