Simulating stiff materials in applications where deformations are either not
significant or else can safely be ignored is a fundamental task across fields.
Rigid body modeling has thus long remained a critical tool and is, by far,
the most popular simulation strategy currently employed for modeling stiff
solids. At the same time, rigid body methods continue to pose a number of
well known challenges and trade-offs including intersections, instabilities,
inaccuracies, and/or slow performances that grow with contact-problem
complexity. In this paper we revisit the stiff body problem and present
ABD, a simple and highly effective affine body dynamics framework, which
significantly improves state-of-the-art for simulating stiff-body dynamics.
We trace the challenges in rigid-body methods to the necessity of linearizing
piecewise-rigid 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 of both worlds: 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
we build it upon, 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-orders on the CPU and an order more when utilizing
the GPU, obtaining 10, 000× speedups) over prior IPC-based methods, while
maintaining simulation quality and nonintersection of trajectories. At the
same time ABD has comparable or faster timings when compared to state-ofthe-art rigid body libraries optimized for performance without guarantees,
and successfully and efficiently solves challenging simulation problems
where both classes of prior rigid body simulation methods fail altogether.