High-Order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes
Zachary Ferguson1, Pranav Jain1, Denis Zorin1, Teseo Schneider2, Daniele Panozzo1
1New York University, 2University of Victoria
ACM SIGGRAPH 2023 Conference Proceedings
High-order armadillo-rollers. Simulation of the armadillo squished by rollers. We use a high-order volumetric mesh (top row) and deform it with quadratic displacement. To solve collision and compute contact forces, we use a dense linear surface mesh (bottom row) and transfer the deformation and contact forces between the two meshes.
Paper

Paper (PDF) Low res (PDF)

Abstract

High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and mesh quality. Thus, we introduce a high-order FE formulation (high-order bases) for elastodynamic simulation on high-order (curved) meshes with contact handling based on the recently proposed Incremental Potential Contact (IPC) model.

Our approach is based on the observation that each IPC optimization step used to minimize the elasticity, contact, and friction potentials leads to linear trajectories even in the presence of nonlinear meshes or nonlinear FE bases. It is thus possible to retain the strong non-penetration guarantees and large time steps of the original formulation while benefiting from the high-order bases and high-order geometry. We accomplish this by mapping displacements and resulting contact forces between a linear collision proxy and the underlying high-order representation.

We demonstrate the effectiveness of our approach in a selection of problems from graphics, computational fabrication, and scientific computing.

Video
Source Code and Data
Results
P1 coarse
(15 s)
P1 reference
(7m 43s)
P2
(32 s)
P3
(58 s)
P1 time budgeted
(57 s)
Bending beam. Squared-section coarse beam pressed by two planes. Linear elements exhibit artificial stiffness as they cannot bend. The reference P1 solution and P3 are rendered in isolation on the right. The results are indistinguishable, but P3 is an order of magnitude faster.
P1 coarse
(2m 47s)
P1 time budgeted
(6h 7m 12s)
P2
(6h 19m 52s)
P1
(2d 14h 13m 0s)
Mat-twist. Simulation of twisting for different bases' order and mesh resolutions. The cross-section (bottom row) shows that the coarse linear mesh (left) has huge artifacts. The coarse P2 bases (middle-right) produce smooth results similar to a dense mesh (right) for a tenth of the time. A “time-budgeted” version shows similar results but exhibits checker patterns around the folds.
Baseline
(2d 13h 19m 0s)
Ours★, P1
(57m 36s)
Ours†, P2
(3h 58m 0s)
Ours‡, P2
(7h 14m 32s)
t = 1.0 s
t = 4.0 s
t = 6.25 s
Coarse FE Mesh
Armadillo-rollers. Armadillo roller simulation for the different variants of our method. Ours★ uses a coarse linear mesh with linear displacement and the original geometry for the collision. Ours† uses a curved mesh with P2 displacement and an upsampled geometry for the collision. Ours‡ uses a curved mesh with P2 displacement and the original geometry for the collision.
BibTex
@inproceedings{Ferguson:2023:HighOrderIPC,
    title     = {High-Order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes},
    author    = {Zachary Ferguson and Pranav Jain and Denis Zorin and Teseo Schneider and Daniele Panozzo},
    year      = 2023,
    booktitle = {{ACM} {SIGGRAPH} 2023 Conference Proceedings},
    publisher = {Association for Computing Machinery},
    address   = {New York, NY, USA},
    series    = {SIGGRAPH '23},
    numpages  = 11,
    location  = {Los Angeles, CA, USA}
}