Difference between revisions of "Exponential Softening"
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<math>\max\bigl(f'(\delta,s)\bigr) < {1\over sG_c}</math> | <math>\max\bigl(f'(\delta,s)\bigr) < {1\over sG_c}</math> | ||
where s is the [[Softening Laws#Normalized Softening Law|softening scaling term]] and G<sub>c</sub> is toughness of the law (and the law's only property). This law never fails, although the traction asymptotically approaches zero. The exponential decay rate, | where s is the [[Softening Laws#Normalized Softening Law|softening scaling term]] and G<sub>c</sub> is toughness of the law (and the law's only property). This law never fails, although the traction asymptotically approaches zero. The exponential decay rate, ''k'', is | ||
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Revision as of 14:02, 25 December 2016
The Softening Law
An exponential softening law has the following values:
[math]\displaystyle{ f(\delta,s) = e^{-\delta/(sG_c)} }[/math]
[math]\displaystyle{ A(\delta,s) = cG_c - e^{-\delta/(sG_c)}\left(sG_c+{\delta\over2}\right) }[/math]
[math]\displaystyle{ \max\bigl(f'(\delta,s)\bigr) \lt {1\over sG_c} }[/math]
where s is the softening scaling term and Gc is toughness of the law (and the law's only property). This law never fails, although the traction asymptotically approaches zero. The exponential decay rate, k, is
[math]\displaystyle{ k = sG_c }[/math]
Softening Law Properties
Only one property is needed to define an exponential softening law:
| Property | Description | Units | Default |
|---|---|---|---|
| Gc | The toughness associated with the this softening law | energy release units | none |
Note that softening materials