Material Point Method

A continuum simulation method where particles carry the material's state while forces are computed on a background grid.

The material point method is a hybrid Eulerian-Lagrangian numerical method: an object is discretized into a large number of “material points,” with each particle carrying mass, velocity, stress, and the rest of its full state; at each step, this information is mapped onto a fixed background grid to solve the momentum equation, and the results are mapped back onto the particles. It traces back to the particle-in-cell (PIC) method Harlow introduced in 1957, and was developed into its current form starting in 1993 by Sulsky and colleagues. Compared with the finite element method, it avoids repeatedly re-meshing, making it well suited to materials that undergo large deformation, fracture, or flow, such as snow, sand, mud, and plasticine — Disney's Frozen used it to simulate snow. The cost is heavy memory and computation. In embodied AI it's used for deformable-object manipulation simulation, and simulators such as Genesis have a built-in MPM solver.

ExampleThe PlasticineLab benchmark uses a differentiable MLS-MPM (Moving Least Squares Material Point Method) to simulate plasticine, letting an agent learn to pinch and mold it into a target shape.

Also called

MPM

Related

Deformable-Body Simulation · Finite Element Method · Smoothed Particle Hydrodynamics · Differentiable Simulation · Genesis · Deformable Object Manipulation

Sources

Material point method - Wikipedia
PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics (arXiv 2104.03311)
Genesis 文档：What is Genesis (Chinese)