The Lemaitre damage material model was developed by Lemaitre for an isotropic linear elastic virgin material with stress-strain law as follows
\begin{equation}
\label{eq:22}
\sigma_{ij}=(1-D)C_{ijkl}\epsilon_{kl} \quad D\in[0,1]
\end{equation}
where $D$ represents the extent of damage with the damage evolution law
\begin{equation}
\label{eq:23}
D(\bar{\epsilon})=1-(1-A)\epsilon_{D_{0}}\bar{\epsilon}^{-1}-Ae^{-B(\bar{\epsilon}-\epsilon_{D_{0}})}
\end{equation}
where $A$ and $B$ are the characteristic parameters of the material, $\epsilon_{D_{0}}$ is the initial damage threshold strain and $\bar{\epsilon}$ is the effective strain defined by
\begin{equation}
\label{eq:24}
\bar{\epsilon}=\sqrt{\sum_{i=1}^{3}{\epsilon_{i}^{2}}H(\epsilon_{i})}
\end{equation}
with $H$ is the Heaviside function given by
\begin{equation}
\label{eq:25}
H(x)=\left\{ \begin{array}{11}
$0$ & \textrm{if $x > 0$}\\
1 & \textrm{if $x < 0$}
\end{array} \right
\end{equation}
Sorry, here I am writting all equations by TEX and I will be very happy to get your related comments for this material model.
Thanks for your attention!