Theory Manual Version 3.4
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Subsection 7.1.6: Augmented Lagrangian Method Up Section 7.1: Sliding Interfaces Subsection 7.1.8: Alternative Formulations

### 7.1.7 Automatic Penalty Calculation

The determination of the penalty factor can be a difficult task, since a good value may depend on both material parameters and geometrical factors. In FEBio the value of this penalty factor can be determined automatically. In this case FEBio will calculate a penalty factor for each facet using the following formula. Here, is the effective Young's modulus along the facet normal, the surface area of the facet, the volume of the element to which this facet belongs and a user defined scale factor. The parameter is evaluated from the elasticity tensor and the facet unit normal according to where is the compliance tensor.
Subsection 7.1.6: Augmented Lagrangian Method Up Section 7.1: Sliding Interfaces Subsection 7.1.8: Alternative Formulations