Physics-Based Simulation

Summary

We have successfully implemented a minimal yet complete 2D Material Point Method (MPM) simulation featuring two colliding elastic blocks. This setup showcases the core pipeline of MPM, including particle sampling, data structure initialization, PIC-based transfer schemes, and elastic deformation based on the StVK constitutive model in Hencky strain space.

Despite its simplicity, this example captures key aspects of MPM. It serves as a clean and extensible foundation for building more sophisticated MPM systems.

In the next lecture, we build upon this framework by incorporating the APIC transfer scheme, Drucker-Prager plasticity, and SDF-based boundary handling to simulate 2D sand interacting with a static sphere collider, enabling realistic modeling of granular materials with frictional contact.