Case Study: 2D Sand with a Sphere Collider*

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

So far, we have introduced all core components necessary to build a complete and physically plausible MPM simulation system—including material discretization, time integration, and data transfer schemes.

In this case study, we put these components together to simulate two colliding elastic blocks in 2D. We start by setting up the simulation with material properties and data structure definitions. Then, we implement the Particle-In-Cell (PIC) Transfer to handle momentum exchange between particles and the grid.

This example serves as a quick-start demonstration of the MPM pipeline using elastic materials, without plasticity or complex boundary conditions.

For implementation, we use NumPy and Taichi as our programming framework. Taichi provides efficient parallelism on both CPU and GPU, and more importantly, it supports sparse data structures, which are critical for high-performance MPM grid computations.

The executable Python project for this section can be found at https://github.com/phys-sim-book/solid-sim-tutorial under the 10_mpm_elasticity folder.