Affine Body Dynamics: Fast, Stable Intersection-free Simulation of Stiff Materials

by   Lei Lan, et al.

Simulating stiff materials in applications where deformations are either not significant or can safely be ignored is a pivotal task across fields. Rigid body modeling has thus long remained a fundamental tool and is, by far, the most popular simulation strategy currently employed for modeling stiff solids. At the same time, numerical models of a rigid body continue to pose a number of known challenges and trade-offs including intersections, instabilities, inaccuracies, and/or slow performances that grow with contact-problem complexity. In this paper we revisit this problem and present ABD, a simple and highly effective affine body dynamics framework, which significantly improves state-of-the-art stiff simulations. We trace the challenges in the rigid-body IPC (incremental potential contact) method to the necessity of linearizing piecewise-rigid (SE(3)) trajectories and subsequent constraints. ABD instead relaxes the unnecessary (and unrealistic) constraint that each body's motion be exactly rigid with a stiff orthogonality potential, while preserving the rigid body model's key feature of a small coordinate representation. In doing so ABD replaces piecewise linearization with piecewise linear trajectories. This, in turn, combines the best from both parties: compact coordinates ensure small, sparse system solves, while piecewise-linear trajectories enable efficient and accurate constraint (contact and joint) evaluations. Beginning with this simple foundation, ABD preserves all guarantees of the underlying IPC model e.g., solution convergence, guaranteed non-intersection, and accurate frictional contact. Over a wide range and scale of simulation problems we demonstrate that ABD brings orders of magnitude performance gains (two- to three-order on the CPU and an order more utilizing the GPU, which is 10,000x speedups) over prior IPC-based methods with a similar or higher simulation quality.


page 2

page 3

page 4

page 5

page 6

page 8

page 12

page 13


Data-Augmented Contact Model for Rigid Body Simulation

Accurately modeling contact behaviors for real-world, near-rigid materia...

Linear-Time Contact and Friction Dynamics in Maximal Coordinates using Variational Integrators

Simulation of contact and friction dynamics is an important basis for co...

Modeling and simulation of heat source trajectories through phase-change materials

The modeling and simulation of heat source trajectories through phase-ch...

Non-Smooth Newton Methods for Deformable Multi-Body Dynamics

We present a framework for the simulation of rigid and deformable bodies...

Midas: A Multi-Joint Robotics Simulator with Intersection-Free Frictional Contact

We introduce Midas, a robotics simulation framework based on the Increme...

An Unconditionally Stable First-Order Constraint Solver for Multibody Systems

This article describes an absolutely stable, first-order constraint solv...

Towards Dynamic Simulation Guided Optimal Design of Tumbling Microrobots

Design of robots at the small scale is a trial-and-error based process, ...

Please sign up or login with your details

Forgot password? Click here to reset