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For this criterion, the damage measure takes the form $$\begin{equation} \Xi\left(\mathbf{U}\right)=\frac{\sigma_{1}-\sigma_{3}}{2}\,,\label{eq:dmg-model-MSS} \end{equation}$$ where $\sigma_{1}$ and $\sigma_{3}$ are the maximum and minimum principal normal stresses (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 $$\begin{equation} \frac{\partial\Xi}{\partial\boldsymbol{\sigma}}=\frac{1}{2}\left(\mathbf{n}_{1}\otimes\mathbf{n}_{1}-\mathbf{n}_{3}\otimes\mathbf{n}_{3}\right)\,.\label{eq:dmg-MSS-tangent} \end{equation}$$ Here, $\mathbf{n}_{1}$ and $\mathbf{n}_{3}$ are unit vectors along the principal directions of maximum and minimum normal stress, respectively.