Mixed Material Point Methods
for Stiff Elastoplasticity

Gilles Daviet

NVIDIA Spatial Intelligence Lab, Physics Research Group

ACM Transactions on Graphics — SIGGRAPH 2026

Paper Supplemental video BibTeX Code
A large cuboid of sand, comprising 49 million particles, falls onto a model city and creates intricate patterns as it rushes through narrow streets and around high-rise structures. Thanks to the compact stencils of our mixed discretization, the simulation runs at 4 seconds per frame on a single GPU.

Abstract

We present a family of mixed Material Point Methods well suited to CFL-rate simulation of stiff elastoviscoplastic materials, up to the incompressible limit. Our work builds on the mixed discretization from Daviet and Bertails-Descoubes [2016a] and extends it to handle finite-strain viscoelasticity and more general flow rules, allowing the simulation of a much wider range of materials. Our implicit integration scheme yields a well-posed, symmetric optimization problem with compact stencils, together with an efficient GPU solver. We demonstrate our method on a variety of examples ranging from granular materials and snow to elastic solids, including two-way coupling with rigid-body solvers.

Twisting beam simulated with different mixed discretization variants
We explore the performance/accuracy characteristics of various velocity–stress discretization pairs supported by our mixed formulation and show that trilinear velocities are often competitive, here illustrated on a twisting elastic beam.

Two-way coupling with rigid-body solvers

Integrated as a first-party module in the Newton physics engine, our solver is designed for tight coupling with rigid-body simulators: grains push back on articulated characters and rigid obstacles, and vice versa.

One-way coupling: the robot is unaffected by the terrain.
Two-way coupling: the robot adjusts its stride as it walks.
Two-way coupled interactive sandbox.
Our formulation natively supports incompressible fluids.

Stiff elastoplasticity

Beyond granular and fluid flows, our implicit mixed formulation supports stiff elastoplastic materials, up to the near-incompressible limit.

Snow avalanche: fracture propagation in an elastoplastic snowpack.
A concrete Armadillo fractures under an industrial press.

More examples

Many additional results are shown in the full supplemental video and parameter exploration video (MP4).

BibTeX

@article{daviet2026mixed,
  author    = {Daviet, Gilles},
  title     = {Mixed Material Point Methods for Stiff Elastoplasticity},
  journal   = {ACM Transactions on Graphics},
  volume    = {45},
  number    = {4},
  articleno = {151},
  numpages  = {19},
  year      = {2026},
  month     = jul,
  publisher = {ACM},
  doi       = {10.1145/3811345}
}