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Simo [70, 71] proposed a damage criterion related to the strain energy density, $$\begin{equation} \Xi\left(\mathbf{U}\right)=\sqrt{2\Psi_{r}\left(\mathbf{U}\right)}\,.\label{eq:dmg-model-Simo} \end{equation}$$ This damage measure is valid for isotropic or anisotropic materials, since the strain energy density $\Psi_{r}$ must satisfy the frame-invariance of Eq.1↓ by construction. Its resulting damage surface normal is $$\begin{equation} \mathbf{N}=\frac{1}{\sqrt{2\Psi_{r}}}\frac{1}{2}\left(\mathbf{S}\cdot\mathbf{U}+\mathbf{U}\cdot\mathbf{S}\right)\,,\label{eq:dmg-model-Simo-N} \end{equation}$$ where we have used the result of Eq.(5.6.5.1-2). The normal reduces to the null tensor in the limit when $\Psi_{r}$ and $\boldsymbol{\sigma}$ tend to zero.