Cubic Traction Law - Revision history

Nairnj: /* Traction History Variables */

2021-01-03T05:14:42Z

Traction History Variables

← Older revision		Revision as of 05:14, 3 January 2021
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	# Maximum normal opening displacement		# Maximum normal opening displacement
	# Maximum shear opening displacement ~~(absolute value)~~		# Maximum shear opening displacement magnitude

	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.		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.

Nairnj: /* The Traction Law */

2021-01-03T05:08:16Z

The Traction Law

← Older revision		Revision as of 05:08, 3 January 2021
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	[[File:Cubictraction.jpg\|right]]		[[File:Cubictraction.jpg\|right]]

	This [[Traction Laws\|traction law]] assumes use a cubic cohesive law for traction as a function of crack opening displacement (COD). The four parameters in the cubic ~~functino~~ of found by requiring zero traction at δ=0 and at δ=δ<sub>c</sub>, peak stress at σ, and zero slope at δ=δ<sub>c</sub>. Note that the peek stress is always at δ<sub>c</sub>/3. This traction law was first proposed by Needleman.<ref name="cubic"/> It has a convenient smooth shape for numerical calculations and the zero slope at δ<sub>c</sub> may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is		This [[Traction Laws\|traction law]] assumes use a cubic cohesive law for traction as a function of crack opening displacement (COD). The four parameters in the cubic function of found by requiring zero traction at δ=0 and at δ=δ<sub>c</sub>, peak stress at σ, and zero slope at δ=δ<sub>c</sub>. Note that the peek stress is always at δ<sub>c</sub>/3. This traction law was first proposed by Needleman.<ref name="cubic"/> It has a convenient smooth shape for numerical calculations and the zero slope at δ<sub>c</sub> may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is

Nairnj at 05:07, 3 January 2021

2021-01-03T05:07:09Z

← Older revision		Revision as of 05:07, 3 January 2021
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	This laws uses uncoupled mode I and mode II cohesive laws. The failure is handled by the same methods used for the [[Triangular Traction Law]]. This cubic cohesive law can also be used for mode I or mode II laws in coupled mixed-mode modeling<ref name="mmzone"/> by using the [[Mixed Mode Traction Law]].		This laws uses uncoupled mode I and mode II cohesive laws. The failure is handled by the same methods used for the [[Triangular Traction Law]]. This cubic cohesive law can also be used for mode I or mode II laws in coupled mixed-mode modeling<ref name="mmzone"/> by using the [[Mixed Mode Traction Law]].

	== ~~References~~ ==		== Traction Law Properties ==

	This traction law only needs the common traction law properties		This traction law only needs the common traction law properties
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	\|}		\|}

	== Traction ~~Law Properties~~ ==		== Traction History Variables ==

			This material tracks two history variables:

			# Maximum normal opening displacement
			# Maximum shear opening displacement (absolute value)

			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>		<references>
	<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="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="cubic">A. Needleman, "A continuum model for void nucleation by inclusion debonding," <i>J. Appl. Mech.</i>, <b>54</b>, 525–531. (1987)</ref>		<ref name="cubic">A. Needleman, "A continuum model for void nucleation by inclusion debonding," <i>J. Appl. Mech.</i>, <b>54</b>, 525–531. (1987)</ref>
	<references/>		</references>

Nairnj: /* The Traction Law */

2020-12-22T18:09:06Z

The Traction Law

← Older revision		Revision as of 18:09, 22 December 2020
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	[[File:Cubictraction.jpg\|right]]		[[File:Cubictraction.jpg\|right]]

	This [[Traction Laws\|traction law]] assumes use a cubic cohesive law for traction as a function of crack opening displacement (COD). The four parameters in the cubic functino of found by requiring zero traction at δ=0 and at δ=δ<sub>c</sub>, peak stress at σ, and zero slope at δ=δ<sub>c</sub>. Note that the peek stress is always at δ<sub>c</sub>/3. This traction law was first proposed by Needleman. It has a convenient smooth shape for numerical calculations and the zero slope at δ<sub>c</sub> may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is		This [[Traction Laws\|traction law]] assumes use a cubic cohesive law for traction as a function of crack opening displacement (COD). The four parameters in the cubic functino of found by requiring zero traction at δ=0 and at δ=δ<sub>c</sub>, peak stress at σ, and zero slope at δ=δ<sub>c</sub>. Note that the peek stress is always at δ<sub>c</sub>/3. This traction law was first proposed by Needleman.<ref name="cubic"/> It has a convenient smooth shape for numerical calculations and the zero slope at δ<sub>c</sub> may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is

Nairnj: /* Traction Law Properties */

2020-12-22T18:04:26Z

Traction Law Properties

← Older revision		Revision as of 18:04, 22 December 2020
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	<references>		<references>
			<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="cubic">A. Needleman, "A continuum model for void nucleation by inclusion debonding," <i>J. Appl. Mech.</i>, <b>54</b>, 525–531. (1987)</ref>		<ref name="cubic">A. Needleman, "A continuum model for void nucleation by inclusion debonding," <i>J. Appl. Mech.</i>, <b>54</b>, 525–531. (1987)</ref>
	<references/>		<references/>

Nairnj at 18:03, 22 December 2020

2020-12-22T18:03:23Z

← Older revision		Revision as of 18:03, 22 December 2020
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	[[File:Cubictraction.jpg\|right]]		[[File:Cubictraction.jpg\|right]]

	This [[Traction Laws\|traction law]] assumes use a cubic cohesive law for traction as a function of crack opening displacement (COD). The four parameters in the cubic functino of found by requiring zero traction at δ=0 and at δ=δ<sub>c</sub>, peak stress at σ, and zero slope at δ=δ<sub>c</sub>. Note that the peek stress is always at δ<sub>c</sub>/3. This traction law was first proposed by Needleman.~~<ref name="cubic">A. Needleman, "A continuum model for void nucleation by inclusion debonding," <i>J. Appl. Mech.</i>, <b>54</b>, 525–531. (1987)</ref>~~ It has a convenient smooth shape for numerical calculations and the zero slope at δ<sub>c</sub> may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is		This [[Traction Laws\|traction law]] assumes use a cubic cohesive law for traction as a function of crack opening displacement (COD). The four parameters in the cubic functino of found by requiring zero traction at δ=0 and at δ=δ<sub>c</sub>, peak stress at σ, and zero slope at δ=δ<sub>c</sub>. Note that the peek stress is always at δ<sub>c</sub>/3. This traction law was first proposed by Needleman. It has a convenient smooth shape for numerical calculations and the zero slope at δ<sub>c</sub> may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is


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	== Failure ==		== Failure ==

	The failure ~~criterion under pure more or possible mixed-mode conditions~~ is ~~identical to~~ the ~~one~~ used in the [[Triangular Traction Law~~#Failure\|triangular traction~~ law]].		This laws uses uncoupled mode I and mode II cohesive laws. The failure is handled by the same methods used for the [[Triangular Traction Law]]. This cubic cohesive law can also be used for mode I or mode II laws in coupled mixed-mode modeling<ref name="mmzone"/> by using the [[Mixed Mode Traction Law]].

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

			<references>
			<ref name="cubic">A. Needleman, "A continuum model for void nucleation by inclusion debonding," <i>J. Appl. Mech.</i>, <b>54</b>, 525–531. (1987)</ref>
	<references/>		<references/>

Nairnj: /* Traction Law Properties */

2020-12-22T18:01:43Z

Traction Law Properties

← Older revision		Revision as of 18:01, 22 December 2020
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	The failure criterion under pure more or possible mixed-mode conditions is identical to the one used in the [[Triangular Traction Law#Failure\|triangular traction law]].		The failure criterion under pure more or possible mixed-mode conditions is identical to the one used in the [[Triangular Traction Law#Failure\|triangular traction law]].

	== ~~Traction Law Properties~~ ==		== References ==

	This traction law only needs the common traction law properties		This traction law only needs the common traction law properties

Nairnj: /* Traction Law Properties */

2020-12-22T18:01:29Z

Traction Law Properties

← Older revision		Revision as of 18:01, 22 December 2020
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	\| ([[Common Traction Law Properties\|other]]) \|\| Properties common to all traction laws \|\| varies \|\| varies		\| ([[Common Traction Law Properties\|other]]) \|\| Properties common to all traction laws \|\| varies \|\| varies
	\|}		\|}

			== Traction Law Properties ==

			<references/>

Nairnj: /* The Traction Law */

2020-12-22T18:01:08Z

The Traction Law

← Older revision		Revision as of 18:01, 22 December 2020
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	[[File:Cubictraction.jpg\|right]]		[[File:Cubictraction.jpg\|right]]

	This [[Traction Laws\|traction law]] assumes use a cubic ~~function~~ for traction as a function of crack ~~opending~~ displacement (COD). ~~This~~ cubic ~~relation is choosen such that the slope is~~ zero at δ<sub>c</sub> and the ~~peak~~ always ~~occurs~~ at δ<sub>c</sub>. This traction law was first proposed by Needleman. It has a convenient smooth shape for numerical calculations and the zero slope at δ<sub>c</sub> may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is		This [[Traction Laws\|traction law]] assumes use a cubic cohesive law for traction as a function of crack opening displacement (COD). The four parameters in the cubic functino of found by requiring zero traction at δ=0 and at δ=δ<sub>c</sub>, peak stress at σ, and zero slope at δ=δ<sub>c</sub>. Note that the peek stress is always at δ<sub>c</sub>/3. This traction law was first proposed by Needleman.<ref name="cubic">A. Needleman, "A continuum model for void nucleation by inclusion debonding," <i>J. Appl. Mech.</i>, <b>54</b>, 525–531. (1987)</ref> It has a convenient smooth shape for numerical calculations and the zero slope at δ<sub>c</sub> may be desirable. There is no physical basis to claim it is more realistic than other traction laws. The resulting function is

Nairnj: /* The Traction Law */

2020-01-08T19:01:18Z

The Traction Law

← Older revision		Revision as of 19:01, 8 January 2020
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	These relations assume J<sub>Ic</sub> in J/m<sup>2</sup>, σ in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]], and δ<sub>c</sub> in [[ConsistentUnits Command#Legacy and Consistent Units\|length units]].		These relations assume J<sub>Ic</sub> in J/m<sup>2</sup>, σ in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]], and δ<sub>c</sub> in [[ConsistentUnits Command#Legacy and Consistent Units\|length units]].

	Besides specifying area and toughness properties, the cubic traction law has no other adjustable parameters. The initial slope and peak location ~~of give~~ once the area is specified. Thus unlike most other [[Traction Laws\|traction laws]], this law has fewer parameters, which can be helpful when studying role of traction ~~law~~ on failure simulations.		Besides specifying area and toughness properties, the cubic traction law has no other adjustable parameters. The initial slope and peak location are given once the area is specified. Thus unlike most other [[Traction Laws\|traction laws]], this law has fewer parameters, which can be helpful when studying role of traction laws on failure simulations.

	== Failure ==		== Failure ==