The previous section explains that the time step can be seriously reduced during contact since
stiffness is added to all penetrated nodes. Moreover, to prevent any node from going through
the main segment during one cycle, a kinematic time step is also computed. If the node
impact velocity is high enough to pass through the segment on one cycle, Radioss reduces the time step in order to apply the penalty force when
the node is in the gap distance. If
$p$
is the penetration distance, then
$dp/dt$
is the penetration speed and the kinematic time step is
necessary time for the node to go over half of the distance between the node and the
segment. The nodal time step is also computed to ensure the numerical stability. The
smallest time step is then used for the simulation.

Nodal time step during contact:

(1)
$$d{t}_{nodal}=\sqrt{\frac{2{M}_{nodal}}{{\displaystyle \sum \left({K}_{\mathrm{int}erface}+{K}_{element}\right)}}}$$

Kinematic time step:

(2)
$$d{t}_{kin}=\frac{1}{2}\left[\frac{Gap-p}{\raisebox{1ex}{$dp$}\!\left/ \!\raisebox{-1ex}{$dt$}\right.}\right]$$

Note: Regarding the impact velocities in automobile crash simulations, kinematic
time step cannot be activated. Its activation may be due to an incoherency in the
model.

If for some reason a node is highly penetrated, either the nodal time step or the kinematic time
step may be very low. Then, it is possible to release this node from the interface using the
option

/DT/INTER/DEL in the Engine file. All nodes reaching

$d{t}_{\mathrm{min}}$
will be removed from the interface.

Note: This
option may be useful in order to keep a decent time step during contact, but if the number
of released nodes is too large, poor results can be expected. Take note of the following
message displayed in the Engine output
file:

**WARNING MINIMUM TIME STEP XXX IN INTERFACE 1
REMOVE SECONDARY NODE XXX FROM INTERFACE