Command manual

This command is used to define a randomly distributed initial damage. A distribution function $f(D)$ describes the number of defects per unit volume of matter.

$f(D) = \left\{ \begin{array}{cc} a \cdot e^{-b D} & D \leq D_{max} \\ 0 & D > D_{max} \end{array} \right.$

Note that the maximum initial damage cannot be larger than $D_{max}$. The number of defects $N$ per unit volume of matter in the range $D_0$ to $D_{max}$ can be calculated by integrating $f(D)$ from $D_0$ to $D_{max}$:

$N = \displaystyle{\int_{D_0}^{D_{max}}} f(D) \mathrm{d} D$

Based on the assumed damage distribution $f(D)$ one can show that the probability $p$ of having at least one initial defect larger than or equal to $D_0$ in a volume $v$ is:

$p = 1 - \mathrm{e}^{-N \cdot v}$

This probability expression can be used to assign an initial damage level to each integration point in the model. The damage level is obtained by solving the expression for $D_0$ (given a random number $p$ and an integration point volume $v$).

Some failure models work with multiple damage variabeles. The parameter did can then be used to specify which damage variable to initialize.

The initial yield stress can only be set for MAT_METAL and MAT_JC.