2. Laws of behavior in Green-Lagrange kinematics

The Green-Lagrange tensor \(E\) can serve as a « kinematic input » to a law of behavior, which then links the evolution of \(E\) to the constraint PK2 (like second Piola Kirchhoff) \(S\):

\(\mathrm{S}=\widehat{\mathrm{S}}(\mathrm{E},\dot{\mathrm{E}})\) eq 2-1

The latter is linked to the Cauchy constraint by the following relationship:

\(\mathrm{\sigma }=\frac{1}{\mathit{det}(\mathrm{F})}\mathrm{F}\mathrm{S}{\mathrm{F}}^{T}\) eq 2-2

This kinematic choice is activated under the keyword factor COMPORTEMENT via the keyword DEFORMATION =” GREEN_LAGRANGE “, for the laws of behavior that allow it, i.e. those for which this kinematic choice is relevant (e.g.: Signorin behavior, RELATION =” ELAS_HYPER”).