Mixed Mode Traction Law - Revision history

Nairnj: /* Traction Law Properties */

2023-02-03T20:04:47Z

Traction Law Properties

← Older revision		Revision as of 20:04, 3 February 2023
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	\| (mode II properties) \|\| Enter all properties for the selected mode II law using mode II variables in that law. \|\| (varies) \|\| none		\| (mode II properties) \|\| Enter all properties for the selected mode II law using mode II variables in that law. \|\| (varies) \|\| none
	\|-		\|-
	\| NewtonsMethod \|\| The published update method<ref name="mixedmode"/> appears to work well for most laws, but it is possible that numerical methods might be needed for laws with no initial elastic regime or with a short, very stiff elastic regime. Enter 0 to used default ~~methods~~ or 1 to force use of numerical solution. \|\| Dimensionless \|\| none		\| NewtonsMethod \|\| The published update method<ref name="mixedmode"/> appears to work well for most laws, but it is possible that numerical methods might be needed for laws with no initial elastic regime or with a short, very stiff elastic regime. Enter 0 to used the default method or 1 to force use of a numerical solution. \|\| Dimensionless \|\| none
	\|}		\|}

Nairnj: /* Traction Law Properties */

2023-02-03T20:04:03Z

Traction Law Properties

← Older revision		Revision as of 20:04, 3 February 2023
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	\|}		\|}

	Note that if one law is [[Cubic Traction Law]] and the other is not, the solution will required numerical methods. As a ~~results~~ <tt>NewtonsMethod</tt> will automatically be changed to 1. If both laws are [[Cubic Traction Law\|Cubic Traction Laws]], however, they can be handled by a special-case approach that does not require, or benefit from, numerical methods despite their lack of an initial elastic regime.		Note that if one law is [[Cubic Traction Law]] and the other is not, the solution will required numerical methods. As a result, <tt>NewtonsMethod</tt> will automatically be changed to 1. If both laws are [[Cubic Traction Law\|Cubic Traction Laws]], however, they can be handled by a special-case approach that does not require, or benefit from, numerical methods despite their lack of an initial elastic regime.

	== Traction History Variables ==		== Traction History Variables ==

Nairnj: /* Failure */

2023-02-03T20:03:28Z

Failure

← Older revision		Revision as of 20:03, 3 February 2023
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	The mixed-modeling of this law is done in terms of a single damage parater, ''D'', that is 0 with no damage and reaches 1 at failure. Failure occurs when ''D'' reaches one and both normal and tangential tractions simultaneously reach zero at failure.		The mixed-modeling of this law is done in terms of a single damage parater, ''D'', that is 0 with no damage and reaches 1 at failure. Failure occurs when ''D'' reaches one and both normal and tangential tractions simultaneously reach zero at failure.

	This law does not specify a failure criterion (as needed for [[Triangular Traction Law#Failure\|other laws]]). Instead, the way the cohesive zone fails as a function of mixed-mode ratio is an output of the law. The shape of the ''G<sub>I</sub>'' ''vs.'' ''G<sub>II</sub>'' failure envelope at failure depends on the relative normal and tangential cohesive laws. Calculations show that this proper-~~mixed~~ mode modeling predicts that all such failure envelopes are convex.<ref name="mixedmode"/> Note that prior coupling methods (implemented in [[Coupled Traction Law]]) predict all failure envelopes are linear. In other words, this new model is the only coupled method capable of modeling materials with non-linear failure envelopes.		This law does not specify a failure criterion (as needed for [[Triangular Traction Law#Failure\|other laws]]). Instead, the way the cohesive zone fails as a function of mixed-mode ratio is an output of the law. The shape of the ''G<sub>I</sub>'' ''vs.'' ''G<sub>II</sub>'' failure envelope at failure depends on the relative normal and tangential cohesive laws. Calculations show that this proper mixed-mode modeling predicts that all such failure envelopes are convex.<ref name="mixedmode"/> Note that prior coupling methods (implemented in [[Coupled Traction Law]]) predict all failure envelopes are linear. In other words, this new model is the only coupled method capable of modeling materials with non-linear failure envelopes.

	== Traction Law Properties ==		== Traction Law Properties ==

Nairnj: /* References */

2022-09-12T18:49:34Z

References

← Older revision		Revision as of 18:49, 12 September 2022
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	<references>		<references>
	<ref name="mixedmode">J. A. Nairn and Y. E. Aimene "A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws" <i>~~kin preparation~~</i> (~~2020~~).</ref>		<ref name="mixedmode">J. A. Nairn and Y. E. Aimene "A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws" <i>Engineering Fracture Mechanics</i>, <b>48</b>, 107704 (2021).</ref>

	<ref name="hogberg">J. L. H ögberg, "Mixed mode cohesive law," <i>International Journal of Fracture</i>, <b>141</b>, 549–559 (2006).</ref>		<ref name="hogberg">J. L. H ögberg, "Mixed mode cohesive law," <i>International Journal of Fracture</i>, <b>141</b>, 549–559 (2006).</ref>

Nairnj: /* Traction History Variables */

2022-09-12T18:47:10Z

Traction History Variables

← Older revision		Revision as of 18:47, 12 September 2022
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	# Tangential crack opening displacement (u<sub>t</sub>)		# Tangential crack opening displacement (u<sub>t</sub>)

	These history variables can be [[MPM Archiving Options#ToArchive Command\|archived]] for later plotting. The [[MPM Archiving Options#ToArchive Command\|~~cmdisp~~ archiving option]] can archive total mode I and mode II cumulative dissipated energies. See Ref. <ref name="mixedmode"/> for mode details on ''D'', δ<sub>n</sub>, and δ<sub>t</sub>.		These history variables can be [[MPM Archiving Options#ToArchive Command\|archived]] for later plotting. The [[MPM Archiving Options#ToArchive Command\|czmdisp archiving option]] can archive total mode I and mode II cumulative dissipated energies. See Ref. <ref name="mixedmode"/> for mode details on ''D'', δ<sub>n</sub>, and δ<sub>t</sub>.

	== References ==		== References ==

Nairnj: /* Traction History Variables */

2021-01-03T18:34:31Z

Traction History Variables

← Older revision		Revision as of 18:34, 3 January 2021
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	== Traction History Variables ==		== Traction History Variables ==

	The material tracks to following history variables		The material tracks the following history variables

	# The damage variable ''D'' (it is <0 until initiation if both directions are [[Cubic Traction Law\|cubic laws]])		# The damage variable ''D'' (it is <0 until initiation if both directions are [[Cubic Traction Law\|cubic laws]])

Nairnj: /* Traction Law Properties */

2021-01-03T08:03:53Z

Traction Law Properties

← Older revision		Revision as of 08:03, 3 January 2021
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	\| (mode I properties) \|\| Enter all properties for the selected mode I law using mode I variables in that law. \|\| (varies) \|\| none		\| (mode I properties) \|\| Enter all properties for the selected mode I law using mode I variables in that law. \|\| (varies) \|\| none
	\|-		\|-
	\| modelII \|\| Same as ~~mode I~~ but used to select law for mode II or tangential opening. \|\| Dimensionless \|\| 12		\| modelII \|\| Same as modelI but used to select law for mode II or tangential opening. \|\| Dimensionless \|\| 12
	\|-		\|-
	\| (mode II properties) \|\| Enter all properties for the selected mode II law using mode II variables in that law. \|\| (varies) \|\| none		\| (mode II properties) \|\| Enter all properties for the selected mode II law using mode II variables in that law. \|\| (varies) \|\| none

Nairnj: /* References */

2021-01-03T06:53:17Z

References

← Older revision		Revision as of 06:53, 3 January 2021
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	</references>		</references>

	~~== References ==~~

	~~<references/>~~

Nairnj: /* Traction History Variables */

2021-01-03T06:52:38Z

Traction History Variables

← Older revision		Revision as of 06:52, 3 January 2021
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	The material tracks to following history variables		The material tracks to following history variables

	# The damage variable ''D'' (it is <0 until initiation if both directions are [[Cubic Traction ~~Laws~~\|cubic laws]])		# The damage variable ''D'' (it is <0 until initiation if both directions are [[Cubic Traction Law\|cubic laws]])
	# A damage parameter characterized mode I damage, δ<sub>n</sub>		# A damage parameter characterized mode I damage, δ<sub>n</sub>
	# A damage parameter characterized mode II damage, δ<sub>t</sub>		# A damage parameter characterized mode II damage, δ<sub>t</sub>

Nairnj: /* Traction History Variables */

2021-01-03T06:52:24Z

Traction History Variables

← Older revision		Revision as of 06:52, 3 January 2021
Line 37:		Line 37:
	The material tracks to following history variables		The material tracks to following history variables

	# The damage variable ''D'' (it is <0 until initiation if both directions are cubic)		# The damage variable ''D'' (it is <0 until initiation if both directions are [[Cubic Traction Laws\|cubic laws]])
	# A damage parameter characterized mode I damage, δ<sub>n</sub>		# A damage parameter characterized mode I damage, δ<sub>n</sub>
	# A damage parameter characterized mode II damage, δ<sub>t</sub>		# A damage parameter characterized mode II damage, δ<sub>t</sub>