Command manual

This command is used to define randomly distributed initial defects on the surface of a body. The defects are interpreted as equivalent to an initial damage $D$. The probability $P$ of having an initial defect larger or equal to $D$ on a surface $A$ is defined as:

$P(A,D) = \left\{ $$\begin{array}{lcl}1& :& D=0\\ 1-\exp [-A{\left({\displaystyle \frac{1-D}{{\mathrm{\Delta }}_0}}\right)}^m]& :& 0<D\le D_{max}\\ 0& :& D>D_{max}\end{array}$$ \right.$

The variables $\Delta_0, m$ and $D_{max}$ are input parameters that typically need to be tuned to match experimental data with a certain spread.

Typical initial damage probability function $P(A,D)$

The inverse function $D(A,P)$ is used to define the intitial damage level for each integration point near the material surface. In this context $0 \le P \le 1$ is a random number and $A$ is the area represented by the integration point.

$D(A,P) = \left\{ $$\begin{array}{lcl}0& :& P>P(A,0)\\ 1-{\mathrm{\Delta }}_0{\left({\displaystyle \frac{-\ln (1-P)}{A}}\right)}^{1/m}& :& P(A,D_{max})<P\le P(A,0)\\ D_{max}& :& P<P(A,D_{max})\end{array}$$ \right.$

Typical initial damage function $D(A,P)$