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For this criterion, the damage measure takes the form $$\begin{equation} \Xi\left(\mathbf{U}\right)=\sigma_{1}\,,\label{eq:dmg-model-MNS} \end{equation}$$ where $\sigma_{1}$ is the maximum principal stress (under the assumption that the three principal stresses of $\boldsymbol{\sigma}$ are ordered such that $\sigma_{1}\ge\sigma_{2}\ge\sigma_{3}$ ). To evaluate the damage surface normal, we may use Eqs.(5.6.5.4-4)-(5.6.5.4-5) where $$\begin{equation} \frac{\partial\Xi}{\partial\boldsymbol{\sigma}}=\frac{\partial\sigma_{1}}{\partial\boldsymbol{\sigma}}=\mathbf{n}_{1}\otimes\mathbf{n}_{1}\,.\label{eq:dmg-MNS-tangent} \end{equation}$$ Here, $\mathbf{n}_{1}$ is a unit vector along the principal direction of maximum normal stress (the eigenvector of $\boldsymbol{\sigma}$ corresponding to the eigenvalue $\sigma_{1}$ ).