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adtzlr committed Sep 27, 2023
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The following example discusses the implementation of a Saint Venant-Kirchhoff material in a very simple and readable user subroutine. The Saint Venant-Kirchhoff material is possibly the simplest example for a hyperelastic material but suffers from practical relevance beyond the small strain range [1]. Anyway, it's a good starting point because stress tensor and elasticity matrix are of the same form as the linear elasticity formulation, except that Green-Lagrange strains are used.

## Kinematics
Starting from the Deformation Gradient, we calculate the Green-Lagrange strain tensor in Eq. $$\eqref{eq:gl-strain}$$ with the right Cauchy Green Deformation Tensor, see Eq. $$\eqref{eq:cauchy-green}$$.
Starting from the Deformation Gradient, we calculate the Green-Lagrange strain tensor in Eq. $$\eqref{eq:gl-strain}$$ with the right Cauchy-Green deformation tensor, see Eq. $$\eqref{eq:cauchy-green}$$.

$$
\begin{equation}
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