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.

Figure 1. Interface Force Variation in Interface TYPE7
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:(1)
F n = K S P+C dP dt { K S = K 0 Gap GapP C=VI S S 2 K S M
The instantaneous stiffness is then computed as:(2)
K t = F P = K 0 Ga p 2 ( GapP ) 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.


  1. Even if an elementary time step is chosen for the simulation, a nodal time step is automatically computed if there is an interface TYPE7. The lowest time step is applied for the simulation.
  2. Contrary to interface TYPE5, a Stfac smaller than 1.0 produces a large penetration at the first touch and results in high interface stiffness and reaction force. To avoid high penetration, a Stfac greater than or equal to 1.0 is recommended.

    Figure 2. Force versus Penetration Curves

    Although, increasing the initial stiffness leads to a smaller time step at the beginning of the penetration, it will increase the time step if penetration is large.