CDF Weibull¶
Module: solid
Category: materialprop
Type string: "CDF Weibull"
Parameters¶
| Name | Description | Default | Range | Units |
|---|---|---|---|---|
Dmax |
Dmax | 1 | \([0, 1]\) | |
alpha |
alpha | 1 | \(\ge 0\) | |
mu |
mu | 1 | \(\ge 0\) | |
ploc |
ploc | 0 | \(\in \mathbb{R}\) |
Description¶
The material type for a Weibull c.d.f. is CDF Weibull.
For this material the c.d.f. is given by
\[
F\left(\Xi\right)=1-\exp\left[-\left(\Xi/\mu\right)^{\alpha}\right]\,.
\]
Note that
\[
F\left(\mu\right)=1-e^{-1}\approx0.63\,,
\]
which shows that \(\mu\) is the value of \(\Xi\) at which the fraction \(1-e^{-1}\) of bonds break. Here, \(\alpha\) regulates the rate at which damage increases with increasing \(\Xi\), with higher values of \(\alpha\) producing a more rapid increase.
Figure 1. Illustration of the CDF Weibull cumulative distribution function.
Example:
<damage type="CDF Weibull">
<mu>1</mu>
<alpha>5.0</alpha>
<Dmax>1</Dmax>
</damage>