  Fast, accurate, and generalizable simulations are a key enabler of modern
advances in robot design and control. However, existing simulation frameworks
in robotics either model rigid environments and mechanisms only, or if they
include flexible or soft structures, suffer significantly in one or more of
these performance areas. To close this "sim2real" gap, we introduce DisMech, a
simulation environment that models highly dynamic motions of rod-like soft
continuum robots and structures, quickly and accurately, with arbitrary
connections between them. Our methodology combines a fully implicit discrete
differential geometry-based physics solver with fast and accurate contact
handling, all in an intuitive software interface. Crucially, we propose a
gradient descent approach to easily map the motions of hardware robot
prototypes to control inputs in DisMech. We validate DisMech through several
highly-nuanced soft robot simulations while demonstrating an order of magnitude
speed increase over previous state of the art. Our real2sim validation shows
high physical accuracy versus hardware, even with complicated soft actuation
mechanisms such as shape memory alloy wires. With its low computational cost,
physical accuracy, and ease of use, DisMech can accelerate translation of
sim-based control for both soft robotics and deformable object manipulation.
