Difference between revisions of "Exponential Softening"
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<math>f(\delta,s | <math>f(\delta,s) = e^{-\delta/(sG_c)}</math> | ||
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<math>A(\delta,s) = {\delta\ | <math>A(\delta,s) = cG_c - e^{-\delta/(sG_c)}\left(sG_c+{\delta\over2}\right)</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). The | 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 | ||
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<math> | <math>k = sG_c</math> | ||
== Softening Law Properties == | == Softening Law Properties == | ||
Only one property is needed to define | Only one property is needed to define an exponential softening law: | ||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 14:52, 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]
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