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Implementation: MarmotMaterialHyperElastic
Derived abstract base class for simple, purely hyperelastic materials to be used for finite elements based on the total lagrangian kinematic description (TL elements). The second Piola - Kirchhoff stress tensor \( S \) will be derived by
\[ \displaystyle S = \frac{\partial f(\boldsymbol{E},t )}{\partial \boldsymbol{E}} \]
with the Green - Lagrange strain tensor \( \boldsymbol{E} \)
\[ \displaystyle E = \frac{1}{2}\,\left(\boldsymbol{F}^T\cdot \boldsymbol{F} - \boldsymbol{I} \right) \]
as work conjugated measure and the variable \( \boldsymbol{F} \) denoting the deformation gradient. The algorithmic tangent will be calculated by
\[ \displaystyle \frac{d \boldsymbol{S}}{d \boldsymbol{E}} \]
The documentation of the available hyperelastic material models in Marmot can be found here