Difference between revisions of "Linear Softening"
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<math>sG_c = \int_0^{\delta_{max}} f(\delta,s) = {\delta_{max}\over 2} \quad{\rm or}\quad \delta_{max} = 2sG_c</math> | <math>sG_c = \int_0^{\delta_{max}} f(\delta,s) = {\delta_{max}\over 2} \quad{\rm or}\quad \delta_{max} = 2sG_c</math> | ||
The area (or energy dissipation term) is | |||
| | ||
<math>A(\delta,s) = {\delta\over 2}</math> | <math>A(\delta,s) = {\delta\over 2}</math> | ||
The stability condition is: | |||
<math>\max\bigl(f'(\delta,s)\bigr) = {1\over 2sG_c}</math> | <math>\max\bigl(f'(\delta,s)\bigr) = {1\over 2sG_c}</math> | ||
Revision as of 10:47, 27 December 2016
The Softening Law
A linear softening law has the following values:
[math]\displaystyle{ f(\delta,s) = 1 - {\delta\over 2sG_c} }[/math]
where
[math]\displaystyle{ sG_c = \int_0^{\delta_{max}} f(\delta,s) = {\delta_{max}\over 2} \quad{\rm or}\quad \delta_{max} = 2sG_c }[/math]
The area (or energy dissipation term) is
[math]\displaystyle{ A(\delta,s) = {\delta\over 2} }[/math]
The stability condition is:
[math]\displaystyle{ \max\bigl(f'(\delta,s)\bigr) = {1\over 2sG_c} }[/math]
where s is the softening scaling term and Gc is toughness of the law (and the law's only property). The critical cracking strain, which depends on mesh size and crack orientation, is given by
[math]\displaystyle{ \delta_{max} = 2sG_c }[/math]
Softening Law Properties
Only one property is needed to define a linear softening law:
| Property | Description | Units | Default |
|---|---|---|---|
| Gc | The toughness associated with the this softening law | energy release units | none |
Note that softening materials