Coupled Traction Law - Revision history

Nairnj at 06:03, 3 January 2021

2021-01-03T06:03:19Z

← Older revision		Revision as of 06:03, 3 January 2021
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	== Property Limitations ==		== Property Limitations ==

	The Höberg model<ref name="hogberg"/> seemingly depends on independent normal and traction law properties that could be entered as for [[Triangular Traction Law\|triangular]] or the [[Exponential Traction Law\|exponential]] cohesive laws. In fact Ref. <ref name="hogberg"/> claims independent properties are allowed. A new analysis of cohesive zone modeling,<ref name="~~mmzone~~"/> however, has revealed that the Högberg model is always invalid for mixed-mode loading unless properties are chosen such that		The Höberg model<ref name="hogberg"/> seemingly depends on independent normal and traction law properties that could be entered as for [[Triangular Traction Law\|triangular]] or the [[Exponential Traction Law\|exponential]] cohesive laws. In fact Ref. <ref name="hogberg"/> claims independent properties are allowed. A new analysis of cohesive zone modeling,<ref name="mixedmode"/> however, has revealed that the Högberg model is always invalid for mixed-mode loading unless properties are chosen such that

Nairnj: /* References */

2021-01-03T06:02:36Z

References

← Older revision		Revision as of 06:02, 3 January 2021
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	<references>		<references>
	<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>
	<ref name="~~mmzone~~">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>in 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>in preparation</i> (2020).</ref>
	<ref name="comanho">P. P. Camanho and C. G. Dàvila, "Mixed-mode decohesion finite elements for the simulation of delamination in composite materials," Technical Report, NASA/TM-2002-211737 (2002).</ref>		<ref name="comanho">P. P. Camanho and C. G. Dàvila, "Mixed-mode decohesion finite elements for the simulation of delamination in composite materials," Technical Report, NASA/TM-2002-211737 (2002).</ref>
	<ref name="comacho">G. T. Camacho and M. Ortiz, "Computational modelling of impact damage in brittle materials," <i>Int. J. Solids Struct.</i>, <b>33</b>, 2899–2938 (1996).</ref>		<ref name="comacho">G. T. Camacho and M. Ortiz, "Computational modelling of impact damage in brittle materials," <i>Int. J. Solids Struct.</i>, <b>33</b>, 2899–2938 (1996).</ref>
	</references>		</references>

Nairnj: /* Traction History Variables */

2021-01-03T05:29:43Z

Traction History Variables

← Older revision		Revision as of 05:29, 3 January 2021
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	# Normal crack opening displacement (u<sub>n</sub>)		# Normal crack opening displacement (u<sub>n</sub>)
	# 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.

	== References ==		== References ==

Nairnj: /* Traction Law Properties */

2021-01-03T05:28:21Z

Traction Law Properties

← Older revision		Revision as of 05:28, 3 January 2021
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	As [[#Property Limitations\|described above]], this implementation lets you select properties that invalidate the method when used to model mixed-mode failure. If you choose invalid properties, a warning is printed in the output files.		As [[#Property Limitations\|described above]], this implementation lets you select properties that invalidate the method when used to model mixed-mode failure. If you choose invalid properties, a warning is printed in the output files.

			== Traction History Variables ==

			This material tracks the following traction history variables

			# Maximum value of λ (or λ<sub>ω</sub> (the value is <0 until initiation of damage)
			# Cumulative work energy
			# Normal crack opening displacement (u<sub>n</sub>)
			# Tangential crack opening displacement (u<sub>t</sub>)

	== References ==		== References ==

Nairnj: /* Alternate Effective Displacement Method */

2021-01-03T05:22:06Z

Alternate Effective Displacement Method

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	<math>\delta_c^{(n)} = \delta_c^{(t)}</math>		<math>\delta_c^{(n)} = \delta_c^{(t)}</math>

	Combining this restriction with the [[#Property Limitations\|Högerg ~~limitations~~]], means this alternate effective displacement model is invalid unless:		Combining this restriction with the [[#Property Limitations\|Högerg limitation]], means this alternate effective displacement model is invalid unless:

Nairnj: /* Alternate Effective Displacement Method */

2021-01-03T05:21:38Z

Alternate Effective Displacement Method

← Older revision		Revision as of 05:21, 3 January 2021
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	<math>\lambda = \sqrt{u_n^2+u_t^2}</math>		<math>\lambda = \sqrt{u_n^2+u_t^2}</math>

	Examples are found in Comanho and Dàvila<ref name="comanho"/> and Comacho and Ortiz<ref name="comacho"/> (these models are implemented in Abaqus cohesive elements). These models are not separately implementeded in [[NairnMPM]] because they are superfluous. ~~Then~~ can be used simply by choosing		Examples are found in Comanho and Dàvila<ref name="comanho"/> and Comacho and Ortiz<ref name="comacho"/> (these models are implemented in Abaqus cohesive elements). These models are not separately implementeded in [[NairnMPM]] because they are superfluous. They can be used with this model simply by choosing

Nairnj: /* Alternate Effective Displacement Method */

2021-01-03T05:21:11Z

Alternate Effective Displacement Method

← Older revision		Revision as of 05:21, 3 January 2021
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	<math>\lambda = \sqrt{u_n^2+u_t^2}</math>		<math>\lambda = \sqrt{u_n^2+u_t^2}</math>

	Examples are found in Comanho and Dàvila<ref name="comanho"/> and Comacho and Ortiz<ref name="comacho"/> (these models are ~~implement~~ in Abaqus cohesive elements). These models are not ~~implemented~~ in [[NairnMPM]] ~~(or in [[OSParticulas]])~~ because they are superfluous. Then can be used simply by choosing		Examples are found in Comanho and Dàvila<ref name="comanho"/> and Comacho and Ortiz<ref name="comacho"/> (these models are implemented in Abaqus cohesive elements). These models are not separately implementeded in [[NairnMPM]] because they are superfluous. Then can be used simply by choosing

Nairnj: /* The Traction Law */

2021-01-03T05:17:51Z

The Traction Law

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	<math>\lambda = \sqrt{\left(\frac{u_n}{\delta_c^{(n)}}\right)^2 +\left(\frac{u_t}{\delta_c^{(t)}}\right)^2}</math>		<math>\lambda = \sqrt{\left(\frac{u_n}{\delta_c^{(n)}}\right)^2 +\left(\frac{u_t}{\delta_c^{(t)}}\right)^2}</math>

	where u is displacement, δ<sub>c</sub> is displacement at failure (see figure), and "n" and "t" refer to normal an tangential directions. In terms of λ, the normal an tangential tractions are:		where u is displacement, δ<sub>c</sub> is displacement at failure (see figure), and "n" and "t" refer to normal an tangential directions. In terms of λ, the normal and tangential tractions are:

Nairnj at 05:17, 3 January 2021

2021-01-03T05:17:05Z

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	__TOC__		__TOC__
	== The Traction Law ==		== The Traction Law ==

	(This documentation is implementation of this law [[OSParticulas]] that is coming soon to [[NairnMPM]]. The current implementation in [[NairnMPM]] is different and should not be used until updated to this new implementation).

	[[File:Exptraction.jpg\|right]]		[[File:Exptraction.jpg\|right]]

Nairnj: /* Traction Law Properties */

2020-12-30T20:42:09Z

Traction Law Properties

← Older revision		Revision as of 20:42, 30 December 2020
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	\| model \|\| Choose whether to model using linear decay (12) or exponential decay (34). The numerical values are material IDs for linear and exponential [[Traction Laws#Traction Law Materials\|traction laws]] \|\| none \|\| 12		\| model \|\| Choose whether to model using linear decay (12) or exponential decay (34). The numerical values are material IDs for linear and exponential [[Traction Laws#Traction Law Materials\|traction laws]] \|\| none \|\| 12
	\|-		\|-
	\| alpha \|\| When using exponential decay (model=34), this parameter selects the α coefficient for the decay rate. Note that when using exponential decay, this implementation first finds law properties assuming triangular traction laws and then ~~adjusts δ<sub>c</sub> such that toughness~~ G<sub>c</sub> (or ~~area under the traction law) of the exponential law matches the input properties for the triangular laws~~. \|\| none \|\| none		\| alpha \|\| When using exponential decay (model=34), this parameter selects the α coefficient for the decay rate. Note that when using exponential decay, this implementation first finds law properties assuming triangular traction laws and then recalculates G<sub>c</sub> based on triangular values or stress and displacements. \|\| none \|\| none
	\|}		\|}