# Contact stiffness influenced by time step size

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The contact stiffness is not affected by the time step size, when SOFT=0 (*CONTACT, Optional Card A). It can be affected, if SOFT=1 and it is definitely affected when SOFT=2 is set.

When SOFT=1, contact stiffness is calculated as follows:

k = max[SLSFAC*SFS*k0, SOFSCL*k1] where

• k is the penalty stiffness
• SLSFAC is user input on *CONTROL_CONTACT
• SFS is user input on *CONTACT (Card 3)
• SOFSCL is user input on *CONTACT (Optional Card A)
• k0 is the stiffness calculated from material bulk modulus and element dimensions. This is the stiffness used when SOFT=0 (see Section 23.7 in the LS-DYNA Theory Manual).
• k1 is the stiffness calculated from nodal masses and the solution time step (analogous to how Courant time step is determined based on mass and stiffness).
• k1 is proportional to 1/(time step)^2. Thus, if the time step is cut in half, the contact stiffness increases by a factor of 4.

When SOFT=2, contact stiffness is calculated in similar fashion to k1 above and can be scaled by SLSFAC and by SFS. So again, the contact stiffness is proportional to 1/(time step)^2.

Time step can affect contact behavior aside from contact stiffness. The bucket sorting interval is based on a number of time steps. Thus, if the time step is reduced, there will be less time between bucket sorts. Also, the incremental penetrations will likely be smaller if the time step is reduced.