Contact Interface Time Step

The contact interface time step is calculated in two different ways. First, based on stiffness and second, based on the velocity of the secondary nodes.

The contact interface time step based on stiffness is only calculated with TYPE7, TYPE10, TYPE11, TYPE19, TYPE21, TYPE24 and TYPE25. No matter which time step method is used, nodes that are involved in contacts have an increased stiffness which make it necessary to calculate a nodal contact interface time step using the nodal mass, interface stiffness and element stiffness.(1)

Δ t_{i n t e r n o d a l} = \sqrt{\frac{2 M_{n o d a l}}{\sum (K_{i n t e r f a c e} + K_{e l e m e n t})}}

Where,

$M_{n o d a l}$: Nodal mass
$K_{i n t e r f a c e}$: Interface stiffness
$K_{e l e m e n t}$: Element stiffness

The kinematic contact time step of interfaces TYPE7, TYPE11 and TYPE19 is used to make sure that a secondary node does not penetrate past a main segment during one cycle:(2)

Δ t_{k i n} = \frac{1}{2} [\frac{G a p - p}{\frac{d p}{d t}}]

Where,

$G a p$: Contact gap
$p$: Penetration amount
$\frac{d p}{d t}$: Relative velocity of the penetrating secondary node (or line for TYPE11 contact) with respect to the main segment (or line for TYPE11 contact).