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# Contact stiffness calculation

Contact treatment is internally represented by linear springs between the slave nodes and the nearest master segments. The stiffness of these springs determines the force that will be applied to the slave nodes and the master nodes.

There are currently two methods of calculating the contact spring stiffness and they are briefly discussed below.

## Penalty-based approach (SOFT = 0 in Optional Card A in *CONTACT_)

This method is the default method and uses the size of the contact segment and its material properties to determine the contact spring stiffness. As this method depends on the material constants and the size of the segments, it works effectively when the material stiffness parameters between the contacting surfaces are of the same order-of-magnitude. In cases where dissimilar materials come into contact, the contact might break down, as the stiffness, which is roughly the minimum of the slave and master stiffness, may be too small. This frequently happens with soft dense foams contact metal materials. Consequently, for crash analysis we do not recommend the option, `SOFT=0`, unless prior experience shows that no problems occur.

## Soft constraint-based approach (SOFT = 1 & 2 on Optional Card A in *CONTACT_)

This non-default method calculates the stiffness of the linear contact springs based on the nodal masses that come into contact and the global time step size. The resulting contact stiffness is independent of the material constants and is well suited for treating contact between bodies of dissimilar materials. The stiffness is found by taking the nodal mass divided by the square of the time step size with a scale factor to ensure stability. Generally, for the case of metals contacting metals the resulting penalty stiffness for `SOFT=0` or `SOFT=1` is similar. For the case where soft dense foams contact metal, the option, `SOFT=1` often gives interface stiffness that are one or two orders-of-magnitude greater. The `SOFT=1` option is recommended for impact analysis where dissimilar materials come into contact.

The `SOFT=2` option uses mass and time step based penalty stiffness as in `SOFT=1`. `SOFT=2` invokes a segment-based contact algorithm which has it origins in Pinball contact developed by Belytschko and his co-workers. With this contact algorithm, contact between segments is treated ratherthan using the usual node-to-segment treatment. When two 4-noded segments come into contact, forces are applied to eight nodes to resist segment penetration. This treatment has the effect of distributing forces more realistically and sometimes is quite effective for very stubborn contact problems. The `SOFT=2` option is available for SMP as well as MPP calculations. Beam contact is not handled by `SOFT=2` type contact. Further, `SOFT=2` is available only for surface-to-surface and single surface contacts and not for nodes-to-surface contacts. The optional parameter EDGE on Optional Card Ashould be used cautiously when segment-edge-to-segment-edge contact is anticipated and `SOFT` is set to 2.

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