# Interface Stiffness

Like the other interface types, when using the penalty method, the interface has spring stiffness as a secondary node penetrates the gap; however, the reaction force is computed with much better approximation. The force variation versus penetration of a node is nonlinear, due to the increasing stiffness.

The interface stiffness (K) is not constant, it increases with the penetration. Moreover, there is a viscous damping acting on the rate of penetration. The contact force is then computed as:

${F}_{n}={K}_{S}P+C\frac{dP}{dt}\left\{\begin{array}{c}{K}_{S}={K}_{0}\frac{Gap}{Gap-P}\\ C=VI{S}_{S}\sqrt{2{K}_{S}M}\end{array}$

The instantaneous stiffness is then computed as:

${K}_{t}=\frac{\partial F}{\partial P}={K}_{0}\frac{Ga{p}^{2}}{{\left(Gap-P\right)}^{2}}$

Nodal time step can be seriously affected if penetration is large. The stiffness, used to compute the nodal time step takes into account the interface stiffness.

There are two ways to decrease the interface stiffness:
• Increasing the gap
• Increasing the initial stiffness (through the use of the flag Stfac)

Both methods allow absorbing more energy by contact and smoothing the impact. Increasing the gap will allow nodes to slow down over a larger distance, therefore the penetration is reduced.