Difference between revisions of "Exponential Softening"
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<math>A(\delta,s) = cG_c - e^{-\delta/(sG_c)}\left(sG_c+{\delta\over2}\right)</math> | <math>A(\delta,s) = cG_c - e^{-\delta/(sG_c)}\left(sG_c+{\delta\over2}\right)</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 asymmtopically approaches zero. The exponential decay rate, $k$, is | 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 asymmtopically approaches zero. The exponential decay rate, $k$, is | ||
Revision as of 14:01, 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 asymmtopically 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