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It may be assumed that damage occurs when the strain energy density $\Psi_{r}$ achieves a certain threshold $\Psi_{m}$ . In that case, the constitutive model for the damage measure is $$\begin{equation} \Xi\left(\mathbf{U}\right)=\Psi_{r}\left(\mathbf{U}\right)\,.\label{eq:dmg-model-SED} \end{equation}$$ 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. The resulting damage surface normal is $$\begin{equation} \mathbf{N}=\frac{\partial\Psi_{r}}{\partial\mathbf{U}}=\frac{1}{2}\left(\mathbf{S}\cdot\mathbf{U}+\mathbf{U}\cdot\mathbf{S}\right)\,,\label{eq:dmg-model-SED-N} \end{equation}$$ where $\mathbf{S}=\partial\Psi_{r}/\partial\mathbf{E}=J\mathbf{F}^{-1}\cdot\boldsymbol{\sigma}\cdot\mathbf{F}^{-T}$ is the second Piola-Kirchhoff stress associated with the material.