diff --git a/docs/examples/example_neohooke.md b/docs/examples/example_neohooke.md
index 2dbdd16..a092e72 100644
--- a/docs/examples/example_neohooke.md
+++ b/docs/examples/example_neohooke.md
@@ -9,7 +9,7 @@ parent: Examples
This is a very basic example on how to implement a nearly-incompressible version of the Neo-Hookean material model in a commercial FEM package (HYPELA2 for Marc). As no special two- or three-field variational principle is used in this example, it is not suitable for nearly-incompressible material behaviour. Otherwise the elements tend to show excessive volumetric locking during deformation and hence, wrong results are calculated.
-The strain energy density function per unit reference volume is additively splitted into an isochoric and volumetric contribution, see $$\eqref{eq:psi}$$. The first one is assumed to be proportional to the first invariant of the isochoric part of the right Cauchy-Green deformation tensor whereas the volumetric part is only a function of the volumetric ratio (the determinant of the deformation gradient).
+The strain energy density function per unit reference volume is additively splitted into an isochoric and volumetric contribution, see Eq. $$\eqref{eq:psi}$$. The first one is assumed to be proportional to the first invariant of the isochoric part of the right Cauchy-Green deformation tensor whereas the volumetric part is only a function of the volumetric ratio (the determinant of the deformation gradient), see Eq. $$\eqref{eq:psi-nh}$$.
$$
\begin{equation}
@@ -25,25 +25,53 @@ $$
\end{equation}
$$
-&space;=&space;\text{C}_{10}&space;(\text{I}_\mathbf{\hat&space;C}-3)&space;+&space;\frac{\kappa}{2}&space;(J-1)^2 "\psi(\mathbf{C}) = \text{C}_{10} (\text{I}_\mathbf{\hat C}-3) + \frac{\kappa}{2} (J-1)^2")
+We get the second Piola-Kirchhoff stress with the derivative of the strain energy density function per unit reference volume with respect to one half of the right Cauchy-Green deformation tensor as shown in Eq. $$\eqref{eq:pk2-nh}$$.
-We get the second Piola-Kirchhoff stress with the derivative of the helmholtz free energy per unit reference volume with respect to one half of the right Cauchy-Green deformation tensor:
-
-}{\partial&space;\frac{1}{2}\mathbf{C}} "\mathbf{S} = \frac{\partial \psi(\mathbf{C})}{\partial \frac{1}{2}\mathbf{C}}")
+$$
+\begin{equation}
+ \mathbf{S} = \frac{\partial \psi(\mathbf{C})}{\partial \frac{1}{2}\mathbf{C}}
+ \label{eq:pk2}
+\end{equation}
+$$
-&space;\mathbf{C}^{-1}&space;+&space;\kappa&space;(J-1)&space;J&space;\mathbf{C}^{-1} "\mathbf{S} = 2\text{C}_{10} \ \text{dev}(\hat{\mathbf{C}}) \mathbf{C}^{-1} + \kappa (J-1) J \mathbf{C}^{-1}")
+$$
+\begin{equation}
+ \mathbf{S} = 2\text{C}_{10} \ \text{dev}(\hat{\mathbf{C}}) \mathbf{C}^{-1} + \kappa (J-1) J \mathbf{C}^{-1}
+ \label{eq:pk2-nh}
+\end{equation}
+$$
-By evaluating the derivative of the stress with respect to one half of the right Cauchy-Green deformation tensor we get the material elasticity tensor:
+By evaluating the derivative of the stress with respect to one half of the right Cauchy-Green deformation tensor we get the material elasticity tensor, see Eq. $$\eqref{eq:c4-nh}$$,
-
+$$
+\begin{equation}
+ \mathbb{C} = \frac{\partial \mathbf{S}}{\partial\frac{1}{2}\mathbf{C}}
+ \label{eq:c4}
+\end{equation}
+$$
-&space;\&space;\mathbb{I}&space;-&space;\mathbf{1}&space;\otimes&space;\mathbf{C}^{-1}&space;-&space;\mathbf{C}^{-1}&space;\otimes&space;\mathbf{1}&space;+&space;\frac{1}{3}&space;\text{tr}(\mathbf{C})&space;\&space;\mathbf{C}^{-1}&space;\otimes&space;\mathbf{C}^{-1})&space;+&space;\left(\kappa&space;(J-1)&space;J&space;+&space;\kappa&space;J^2\right)&space;\&space;\mathbf{C}^{-1}&space;\otimes&space;\mathbf{C}^{-1}&space;-&space;2&space;\kappa&space;(J-1)&space;J&space;\&space;\mathbb{I} "\mathbb{C} = 2\text{C}_{10} J^{-2/3} \frac{2}{3} \ (\text{tr}(\mathbf{C}) \ \mathbb{I} - \mathbf{1} \otimes \mathbf{C}^{-1} - \mathbf{C}^{-1} \otimes \mathbf{1} + \frac{1}{3} \text{tr}(\mathbf{C}) \ \mathbf{C}^{-1} \otimes \mathbf{C}^{-1}) + \left(\kappa (J-1) J + \kappa J^2\right) \ \mathbf{C}^{-1} \otimes \mathbf{C}^{-1} - 2 \kappa (J-1) J \ \mathbb{I}")
+$$
+\begin{equation}
+ \mathbb{C} = 2\text{C}_{10} J^{-2/3} \frac{2}{3} \ (\text{tr}(\mathbf{C}) \ \mathbb{I} - \mathbf{1} \otimes \mathbf{C}^{-1} - \mathbf{C}^{-1} \otimes \mathbf{1} + \frac{1}{3} \text{tr}(\mathbf{C}) \ \mathbf{C}^{-1} \otimes \mathbf{C}^{-1}) + \left(\kappa (J-1) J + \kappa J^2\right) \ \mathbf{C}^{-1} \otimes \mathbf{C}^{-1} - 2 \kappa (J-1) J \ \mathbb{I}
+ \label{eq:c4-nh}
+\end{equation}
+$$
-with the fourth order identity tensor
+with the fourth order identity tensor in Eq. $$\eqref{eq:i4}$$.
-
+$$
+\begin{equation}
+ \mathbb{I}= \mathbf{C}^{-1} \odot \mathbf{C}^{-1}
+ \label{eq:i4}
+\end{equation}
+$$
-
+$$
+\begin{equation}
+ \mathbf{C}^{-1} = \mathbb{I} : \mathbf{C}
+ \label{eq:i4-projection}
+\end{equation}
+$$
The two equations are now implemented in a Total Lagrange user subroutine with the help of this Tensor module as follows:
@@ -114,4 +142,4 @@ The two equations are now implemented in a Total Lagrange user subroutine with
end
```
-There are also examples for a [basic understandig of the tensor toolbox](examples/script_umat.f), the implementation of the [St.Venant Kirchhoff material](example_stvenantkirchhoff.md) and a [full featured MSC.Marc Neo-Hookean material HYPELA2 user subroutine](examples/hypela2_nh_ttb.f).
+There are also examples for a [basic understandig of the tensor toolbox](examples/script_umat.f), the implementation of the [St.Venant Kirchhoff material](example_stvenantkirchhoff.md) and a [full featured Marc Neo-Hookean material HYPELA2 user subroutine](examples/hypela2_nh_ttb.f).