Exploring MPM materials and coupling

The Material Point Method (MPM) represents materials with particles that can deform, compact, and flow. Stiffness, yielding, friction, and viscosity determine how these materials respond to forces and collisions.

In this tutorial, we compare material parameters in simple impact scenes, explore the nearly rigid limit, and reconstruct a fluid surface from particles. We then use a walking G1 robot to see how particle reaction forces affect rigid-body motion. Each comparison helps isolate a different part of the simulation so you can adapt the settings to your own scene.

For an introduction to spawning MPM objects and configuring the Newton solver, see Implicit MPM. The comparisons below illustrate qualitative behavior; they are starting points for experiments rather than calibrated material models.

Running the tutorials

The material and rigid-body tutorials launch Kit by default, requiring the isaacsim extra. The surface-reconstruction tutorial launches Newton GL by default. Use --viz to select another visualizer; Newton RTX also requires uv run --extra ovrtx.

Comparing material parameters

The material_parameters.py tutorial shows how one parameter changes a material’s response to impact. The stiffness and compressibility presets drop spheres onto plates. The other presets drop blocks onto horizontal cylinders, where you can observe spreading, fragmentation, and the shape left after impact.

Elastic stiffness with --press_spheres:

Watch the embedded video Start with the elastic stiffness comparison:

uv run --extra isaacsim python scripts/tutorials/08_mpm/material_parameters.py \
  --preset young_modulus --viz kit

The three specimens share the same geometry, initial velocities, particle mass, solver settings, and seeded particle layout. Their Young’s moduli are 100 kPa, 300 kPa, and 1 MPa. Compare how much each sphere compresses and how it recovers after impact. Yielding is disabled in this preset to isolate the elastic response.

Each preset defines the varied field and the values that remain fixed. material_values_for_variant() combines these with the common material settings before passing them to MPMParticleMaterialCfg:

def material_values_for_variant(index: int) -> dict[str, float]:
    """Combine the common material settings with the selected variant's value."""
    material_values = {
        "density": DENSITY,
        "young_modulus": 1.0e7,
        "poisson_ratio": 0.3,
        "friction": 0.68,
        "yield_pressure": 1.0e12,
        **PRESET.fixed,
    }
    if PRESET.field != "particle_jitter_fraction":
        material_values[PRESET.field] = PRESET.values[index]
    return material_values

Choose a preset according to the behavior you want to explore:

The default solver voxel size is 25 mm, with two particles per voxel axis (eight per interior voxel). Material comparisons reuse the same random offsets to avoid confusing a change in packing with a change in material response. Only particle_jitter compares aligned particles with jittered particles. Use --variant_index 0, 1, or 2 to inspect a single specimen; the jitter preset has two variants.

To apply sustained compression, add --press_spheres to either sphere preset:

uv run --extra isaacsim python scripts/tutorials/08_mpm/material_parameters.py \
  --preset poisson_ratio --press_spheres --viz kit

The plates descend after a two-second settling period and hold the spheres under compression. Compare the lateral expansion and volume response while keeping Young’s modulus fixed. Let the simulation continue after loading so you can distinguish transient motion from the settled shape.

See MPM Solver for the preset values and guidance on checking resolution, timestep, and convergence before interpreting material behavior.

Approaching the rigid-body limit

The rigid_body_equivalence.py tutorial compares spheres, cubes, and capsules on two identical inclines. MJWarp simulates rigid bodies on the left; Newton MPM simulates particle versions on the right. Corresponding objects share their color, initial placement relative to the ramp, outer dimensions, and total mass.

Watch the embedded video

uv run --extra isaacsim python scripts/tutorials/08_mpm/rigid_body_equivalence.py \
  --viz kit

The MPM objects use a large finite stiffness and pressure-yield threshold to approximate a rigid material. Compare their rolling, sliding, and shape retention with the rigid bodies. MPM remains a discretized continuum, so a large stiffness does not guarantee exact rigid-body motion: grid resolution, particle sampling, timestep, and solver convergence still matter.

Use --mpm_young_modulus and --mpm_yield_pressure to explore the transition to a softer or yielding material. Keep --voxel_size, --mpm_substeps, and --solver_iterations fixed when comparing material values, then vary them separately to check the numerical approximation.

Reconstructing a fluid surface

The surface_reconstruction.py tutorial drops a water blob into a shallow pool. It shows how to turn the particle positions into a continuous surface for rendering, while leaving the particle simulation unchanged.

Watch the embedded video

uv run python scripts/tutorials/08_mpm/surface_reconstruction.py \
  --surface_preset balanced --viz newton_gl

Run the same scene again with another --surface_preset:

Look at the splash sheets, small surface features, and the pool as it settles. Use --fluid_render_mode both to inspect the mesh alongside the source particles. The reconstruction grid is separate from the MPM solver grid; changing it affects surface detail and extraction cost rather than particle motion. Individual --surface_* options override the selected preset.

The tutorial constructs newton.geometry.ParticleSurface after sim.reset() and passes it to ParticleSurfaceRenderer. The simulation loop calls the renderer’s update() before sim.render() so the viewers receive the mesh for the current particle state. See Implicit MPM for this integration pattern.

Comparing one-way and two-way coupling

The mpm-g1-coupling example uses a trained G1 walking policy to cross shallow sand, snow, and clay strips on a rigid runway. The robot starts on the bare runway before reaching the particles. This comparison shows how material resistance affects a controller trained for rigid terrain.

Run the two-way comparison from a source checkout:

uv run --extra isaacsim --extra rsl-rl isaaclab example mpm-g1-coupling \
  --coupling two_way --viz kit

Then repeat it with --coupling one_way. Both modes let the robot displace particles. Two-way coupling returns particle reaction forces to the robot; one-way coupling sets proxy feedback relaxation to zero from the initial state. Compare the robot’s progress and balance as well as the displaced particles. The policy may slow down, become stuck, or fall when it encounters the material.

By default, the example exposes the robot’s full collision geometry to MPM. Use --proxy_bodies feet or --proxy_bodies lower_legs to explore how the choice of coupled geometry affects interaction. Both --proxy_mode choices, lagged and staggered, support feedback; the scheduling mode alone does not select one-way coupling. See Coupled Solvers for the proxy configuration and feedback controls.

The example requires CUDA and downloads the published Isaac-Velocity-Flat-G1 policy unless you supply --checkpoint. It is also available in the installed package:

uvx --from 'isaaclab[isaacsim,rsl-rl]' isaaclab example mpm-g1-coupling \
  --coupling two_way --viz kit