CDF Simo

Module: solid

Category: materialprop

Type string: "CDF Simo"

Parameters

Name	Description	Default	Units
Dmax	Dmax	1	[]
a	a	0	[]
b	b	0	[]

Description

The material type for Simo's c.d.f. [#Simo87] is CDF Simo.

For this material the c.d.f. is given by

\[ F\left(\Xi\right)=1-\beta-\left(1-\beta\right)\frac{\alpha}{\Xi}\left(1-e^{-\Xi/\alpha}\right)\,. \]

Note that

\[ \lim\limits_{\Xi\to\infty}F\left(\Xi\right)=1-\beta \]

represents the maximum allowable damage. Therefore, \(\beta\) regulates the maximum allowable damage, whereas \(\alpha\) controls the rate at which \(F\left(\Xi\right)\) increases with increasing \(\Xi\).

Figure 1. Illustration of the CDF Simo cumulative distribution function.

Example:

<damage type="CDF Simo">
  <a>0.1</a>
  <b>0</b>
  <Dmax>1</Dmax>
</damage>