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Theory Manual Version 3.6
 Subsection 6.2.4: Linearization Up Subsection 6.2.4: Linearization Subsubsection 6.2.4.2: External Work 

6.2.4.1 Internal Work

The first term in the internal work becomes where is the second Piola-Kirchhoff stress for the solid material. In general, (and thus, ) is only a function of the solid strain, such as the right Cauchy-Green tensor or the Green-Lagrange strain . Therefore, following the standard approach in solid mechanics, the linearization of is where is the material elasticity tensor. Now, the linearization of the first term in is where is the spatial elasticity tensor. Similarly, the second term in produces
 Subsection 6.2.4: Linearization Up Subsection 6.2.4: Linearization Subsubsection 6.2.4.2: External Work