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Theory Manual Version 3.4
 Subsubsection 6.2.4.1: Internal Work Up Subsection 6.2.4: Linearization Subsection 6.2.5: Discretization 

6.2.4.2 External Work

The linearization of the body force term is The linearization of the traction force term is Note that depends on the nature of the surface traction. For a prescribed traction we have . A contact analysis needs more elaborate derivations (not yet implemented as of FEBio 2.7). In the above expression we used where the unit outward normal is evaluated as
 Subsubsection 6.2.4.1: Internal Work Up Subsection 6.2.4: Linearization Subsection 6.2.5: Discretization