Exponential Softening - Revision history

Nairnj: /* Softening Law Properties */

2021-07-20T20:15:38Z

Softening Law Properties

← Older revision		Revision as of 20:15, 20 July 2021
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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
	\|-		\|-
	\| min \|\| Minimum <math>f(\delta,s)</math> or law is failed if gets below this value \|\| none \|\| 0.01		\| min \|\| Minimum <math>f(\delta,s)</math> or law is failed if it gets below this value \|\| none \|\| 0.01
	\|}		\|}

2021-07-09T17:48:24Z

Minimum f(\delta,s)

← Older revision		Revision as of 17:48, 9 July 2021
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	=== Minimum <math>f(\delta,s)</math> ===		=== Minimum <math>f(\delta,s)</math> ===

	This law requires selection of minimum value for <math>f(\delta,s)</math> below which the material point is marked as failed. If we define the minimum value as ''c'', this choice effective ~~defines a~~ maximum cracking strain:		This law requires selection of minimum value for <math>f(\delta,s)</math> below which the material point is marked as failed. If we define the minimum value as ''c'', this choice defines an effective maximum cracking strain as:

2021-07-09T17:47:38Z

The Softening Law

← Older revision		Revision as of 17:47, 9 July 2021
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	<math>\max\bigl(-f'(\delta,s)\bigr) = k = {1\over sG_c}</math>		<math>\max\bigl(-f'(\delta,s)\bigr) = k = {1\over sG_c} \qquad\implies\qquad \eta=1</math>

	=== Minimum <math>f(\delta,s)</math> ===		=== Minimum <math>f(\delta,s)</math> ===

2021-07-09T17:47:07Z

The Softening Law

← Older revision		Revision as of 17:47, 9 July 2021
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	<math>A(\delta,s) = sG_c - e^{-\delta/(sG_c)}\left(sG_c+{\delta\over2}\right)</math>		<math>\Omega(\delta,s) = sG_c - e^{-\delta/(sG_c)}\left(sG_c+{\delta\over2}\right)</math>

	The stability condition is:		The stability condition is:

2020-11-14T00:56:01Z

Softening Law Properties

← Older revision		Revision as of 00:56, 14 November 2020
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	== Softening Law Properties ==		== Softening Law Properties ==

	Only ~~one property is~~ needed to define an exponential softening law:		Only two properties are needed to define an exponential softening law:

	{\| class="wikitable"		{\| class="wikitable"

2020-11-14T00:49:42Z

Minimum f(\delta,s)

← Older revision		Revision as of 00:49, 14 November 2020
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	=== Minimum <math>f(\delta,s)</math> ===		=== Minimum <math>f(\delta,s)</math> ===

	~~In this~~ law~~, it is desirable to define and~~ minimum value for <math>f(\delta,s)</math>. If we define the minimum value as ''c'', this choice effective defines a maximum cracking strain:		This law requires selection of minimum value for <math>f(\delta,s)</math> below which the material point is marked as failed. If we define the minimum value as ''c'', this choice effective defines a maximum cracking strain:


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	<math>\delta_{max} = 4.60517 s G_c</math>		<math>\delta_{max} = 4.60517 s G_c</math>

	Note that [[Linear Softening\|linear softening]] has 2 in place of 4.60517 for finding maximum cracking strain.		Note that [[Linear Softening\|linear softening]] has 2 in place of 4.60517 for finding maximum cracking strain. Without a minimum value, exponential softening would never fail. If you want to prevent failures, set the minimum value to a very small number (but it cannot be zero).

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

2017-09-03T00:58:37Z

Minimum f(\delta,s)

← Older revision		Revision as of 00:58, 3 September 2017
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	<math>\delta_{max} = -{\ln c \over k} = -s G_c \ln c</math>		<math>\delta_{max} = -{\ln c \over k} = -s G_c \ln c</math>

	For example, picking c = -0.~~001~~ gives		For example, picking ''c'' = 0.01 gives


	<math>\delta_{max} = 6.~~907755~~ s G_c</math>		<math>\delta_{max} = 4.60517 s G_c</math>

	Note that [[Linear Softening\|linear softening]] has 2 in place of 6.~~907755~~ for finding maximum cracking strain.		Note that [[Linear Softening\|linear softening]] has 2 in place of 4.60517 for finding maximum cracking strain.

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

2017-09-03T00:56:58Z

Softening Law Properties

← Older revision		Revision as of 00:56, 3 September 2017
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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
	\|-		\|-
	\| min \|\| Minimum <math>f(\delta s)</math> or law is failed if gets below this value \|\| none \|\| 0.01		\| min \|\| Minimum <math>f(\delta,s)</math> or law is failed if gets below this value \|\| none \|\| 0.01
	\|}		\|}

2017-09-03T00:56:45Z

Softening Law Properties

← Older revision		Revision as of 00:56, 3 September 2017
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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
			\|-
			\| min \|\| Minimum <math>f(\delta s)</math> or law is failed if gets below this value \|\| none \|\| 0.01
	\|}		\|}

2017-09-03T00:54:36Z

Minimum f(\delta,s)

← Older revision		Revision as of 00:54, 3 September 2017
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	<math>\delta_{max} = 6.907755 s G_c</math>		<math>\delta_{max} = 6.907755 s G_c</math>

	Note that [[~~LInear~~ Softening\|linear softening]] has 2 in place of 6.907755 for finding maximum cracking strain.		Note that [[Linear Softening\|linear softening]] has 2 in place of 6.907755 for finding maximum cracking strain.

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