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Section 8.4: Guidelines for Contact Problems Up Section 8.4: Guidelines for Contact Problems Subsection 8.4.2: Augmented Lagrangian Method

### 8.4.1 The penalty method

The penalty method enforces contact by “penalizing” (in an energy sense) any deviation from the contact constraint. In other words, when the two contacting surfaces penetrate, a force is generated proportional to the distance of penetration, which has the effect that the surfaces will now repell each other. The strength of this repelling force is controlled by the user through the penalty factor.
The obvious downside of this method is that some penetration is necessary to generate the contact force. The larger the penalty factor, the smaller this penetration needs to be and thus the better the contact constraint is enforced. However, choosing the penalty factor too large may cause the problem to become unstable since the contact force (and corresponding stiffness) will dominate the other forces in the model. Choosing a good penalty factor can thus be often difficult and may require several attempts before getting it “right”. To help with choosing a penalty factor, FEBio offers the auto_penalty option for many of its contact interfaces which will estimate a good penalty factor based on element size and initial material stiffness. However, even then it may still take a few tries before getting the penalty factor good enough.
Section 8.4: Guidelines for Contact Problems Up Section 8.4: Guidelines for Contact Problems Subsection 8.4.2: Augmented Lagrangian Method