$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$

Cumulative distribution functions provide the function $F\left(\Xi\right)$ that determines the evolution of the damage variable $D$ based on the maximum value of the failure criterion $\Xi$ up until the current time.