Linear Softening - Revision history

Nairnj: /* The Softening Law */

2021-07-09T17:46:26Z

The Softening Law

← Older revision		Revision as of 17:46, 9 July 2021
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	<math>\max\bigl(-f'(\delta,s)\bigr) = {1\over \delta_{max}} = {1\over 2sG_c}</math>		<math>\max\bigl(-f'(\delta,s)\bigr) = {1\over \delta_{max}} = {1\over 2sG_c}
			\qquad\implies\qquad \eta=2</math>

	== Softening Law Properties ==		== Softening Law Properties ==

2021-07-09T17:42:55Z

The Softening Law

← Older revision		Revision as of 17:42, 9 July 2021
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	<math>A(\delta,s) = {\delta\over 2}</math>		<math>\Omega(\delta,s) = {\delta\over 2}</math>

	The stability condition is:		The stability condition is:

2017-09-04T21:16:34Z

The Softening Law

← Older revision		Revision as of 21:16, 4 September 2017
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	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).		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 critical cracking strain, <math>\delta_{max}</math>, which depends on mesh size and crack orientation, is calculated ~~above~~ and is not a law property to be provided.		The critical cracking strain, <math>\delta_{max}</math>, which depends on mesh size and crack orientation, is calculated from ''s'' and ''G<sub>c</sub>'' and is not a law property to be provided.

	The area (or energy dissipation term) is		The area (or energy dissipation term) is

2017-09-04T21:15:49Z

The Softening Law

← Older revision		Revision as of 21:15, 4 September 2017
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	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).		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 critical cracking strain, which depends on mesh size and crack orientation, is calculated above and is not a law property to be provided.		The critical cracking strain, <math>\delta_{max}</math>, which depends on mesh size and crack orientation, is calculated above and is not a law property to be provided.

	The area (or energy dissipation term) is		The area (or energy dissipation term) is

2016-12-27T18:51:19Z

Softening Law Properties

← Older revision		Revision as of 18:51, 27 December 2016
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	\| Gc \|\| The toughness associated with the this softening law \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|energy release units]] \|\| none		\| Gc \|\| The toughness associated with the this softening law \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|energy release units]] \|\| none
	\|}		\|}

	~~Note that softening materials~~

2016-12-27T18:51:00Z

The Softening Law

← Older revision		Revision as of 18:51, 27 December 2016
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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>

			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 critical cracking strain, which depends on mesh size and crack orientation, is calculated above and is not a law property to be provided.

	The area (or energy dissipation term) is		The area (or energy dissipation term) is
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	<math>\max\bigl(-f'(\delta,s)\bigr) = {1\over \delta_{max}} = {1\over 2sG_c}</math>		<math>\max\bigl(-f'(\delta,s)\bigr) = {1\over \delta_{max}} = {1\over 2sG_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). The critical cracking strain, which depends on mesh size and crack orientation, is calculated above and is not a law property to be provided.

	== Softening Law Properties ==		== Softening Law Properties ==

2016-12-27T18:50:05Z

The Softening Law

← Older revision		Revision as of 18:50, 27 December 2016
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	<math>\max\bigl(f'(\delta,s)\bigr) = {1\over 2sG_c}</math>		<math>\max\bigl(-f'(\delta,s)\bigr) = {1\over \delta_{max}} = {1\over 2sG_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). The critical cracking strain, which depends on mesh size and crack orientation, is calculated above and is not a law property to be provided.		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 critical cracking strain, which depends on mesh size and crack orientation, is calculated above and is not a law property to be provided.

2016-12-27T18:49:31Z

The Softening Law

← Older revision		Revision as of 18:49, 27 December 2016
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	<math>f(\delta,s) = 1 - {\delta\over \delta_{max} } = 1 - {\delta\over 2sG_c} </math>		<math>f(\delta,s) = 1 - {\delta\over \delta_{max} } = 1 - {\delta\over 2sG_c} </math>

	~~where~~		which follows from

2016-12-27T18:49:17Z

The Softening Law

← Older revision		Revision as of 18:49, 27 December 2016
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	<math>f(\delta,s) = 1 - {\delta\over ~~2sG_c~~} = 1 - {\delta\over ~~\delta_{max}~~ }</math>		<math>f(\delta,s) = 1 - {\delta\over \delta_{max} } = 1 - {\delta\over 2sG_c} </math>

	where		where

2016-12-27T18:48:38Z

The Softening Law

← Older revision		Revision as of 18:48, 27 December 2016
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	<math>f(\delta,s) = 1 - {\delta\over 2sG_c}</math>		<math>f(\delta,s) = 1 - {\delta\over 2sG_c} = 1 - {\delta\over \delta_{max} }</math>

	where		where