Case Study: Plastic Material Models*
*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 simulate advanced plastic materials.
This case study covers two important plastic material models. First, we demonstrate Drucker-Prager Elastoplasticity through a sand simulation with a sphere collider. Then, we present a viscoplastic material model through a two-bar simulation.
Sand Simulation with Drucker-Prager Model
For the sand simulation, we use Poisson-disk Sampling to initialize the material points, which helps reduce aliasing artifacts and structured noise, producing more physically realistic behavior in granular simulations.
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.
Viscoplastic Material Model
*Author of this section: Žiga Kovačič, Cornell University
Additionally, we demonstrate a viscoplastic material model in 2D Viscoplastic Bars, which extends traditional plasticity with rate-dependent behavior. This model captures materials like toothpaste or highly viscous fluids, where resistance to deformation depends on the rate of loading.
The executable Python project for this section can be found at https://github.com/phys-sim-book/solid-sim-tutorial under the 11_mpm_plastic folder.