  Dynamics simulation with frictional contacts is important for a wide range of
applications, from cloth simulation to object manipulation. Recent methods
using smoothed lagged friction forces have enabled robust and differentiable
simulation of elastodynamics with friction. However, the resulting frictional
behavior can be inaccurate and may not converge to analytic solutions. Here we
evaluate the accuracy of lagged friction models in comparison with implicit
frictional contact systems. We show that major inaccuracies near the stick-slip
threshold in such systems are caused by lagging of friction forces rather than
by smoothing the Coulomb friction curve. Furthermore, we demonstrate how
systems involving implicit or lagged friction can be correctly used with
higher-order time integration and highlight limitations in earlier attempts. We
demonstrate how to exploit forward-mode automatic differentiation to simplify
and, in some cases, improve the performance of the inexact Newton method.
Finally, we show that other complex phenomena can also be simulated effectively
while maintaining smoothness of the entire system. We extend our method to
exhibit stick-slip frictional behavior and preserve volume on compressible and
nearly-incompressible media using soft constraints.
