Skip to content

CDF Weibull

Module: solid

Category: materialprop

Type string: "CDF Weibull"

Parameters

Name Description Default Units
Dmax Dmax 1 []
alpha alpha 1 []
mu mu 1 []
ploc ploc 0 []

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.

FigDamageCDFWeibull.png

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>