Nonlinear Hardening 1 - Revision history

Nairnj: /* Hardening Law Properties */

2017-04-25T21:45:39Z

Hardening Law Properties

← Older revision		Revision as of 21:45, 25 April 2017
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	\| yield \|\| The initial yield stress. This stress corresponds to the axial stress at yield during uniaxial, 3D loading. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| Large		\| yield \|\| The initial yield stress. This stress corresponds to the axial stress at yield during uniaxial, 3D loading. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| Large
	\|-		\|-
	\| Khard \|\| The hardening parameter K for nonlinear hardening. \|\| ~~Dimensionless~~ \|\| 0		\| Khard \|\| The hardening parameter K for nonlinear hardening. \|\| dimensionless \|\| 0
	\|-		\|-
	\| nhard \|\| The hardening exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use [[Linear Hardening\|linear hardening]] instead. \|\| ~~Dimensionless~~ \|\| 1		\| nhard \|\| The hardening exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use [[Linear Hardening\|linear hardening]] instead. \|\| dimensionless \|\| 1
	\|-		\|-
	\| yieldMin \|\| The minimum yield stress. This minimum only matters when using negative <tt>Khard</tt> or when modeling softening plasticity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0		\| yieldMin \|\| The minimum yield stress. This minimum only matters when using negative <tt>Khard</tt> or when modeling softening plasticity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0

Nairnj: /* Hardening Law Properties */

2017-04-25T21:45:03Z

Hardening Law Properties

← Older revision		Revision as of 21:45, 25 April 2017
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Property !! Description		! Property !! Description !! Units !! Default
	\|-		\|-
	\| yield \|\| The initial yield stress ~~(enter in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]])~~. This stress corresponds to the axial stress at yield during uniaxial, 3D loading.		\| yield \|\| The initial yield stress. This stress corresponds to the axial stress at yield during uniaxial, 3D loading. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| Large
	\|-		\|-
	\| Khard \|\| The ~~dimensionless~~ parameter K for nonlinear hardening.		\| Khard \|\| The hardening parameter K for nonlinear hardening. \|\| Dimensionless \|\| 0
	\|-		\|-
	\| nhard \|\| The ~~dimensionless~~ exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use [[Linear Hardening\|linear hardening]] instead.		\| nhard \|\| The hardening exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use [[Linear Hardening\|linear hardening]] instead. \|\| Dimensionless \|\| 1
	\|-		\|-
	\| yieldMin \|\| The minimum yield stress. This minimum only matters when using negative <tt>Khard</tt> or when modeling softening plasticity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0		\| yieldMin \|\| The minimum yield stress. This minimum only matters when using negative <tt>Khard</tt> or when modeling softening plasticity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0

Nairnj at 21:43, 25 April 2017

2017-04-25T21:43:11Z

← Older revision		Revision as of 21:43, 25 April 2017
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	<math>\sigma_y = \sigma_{Y0}(1+K\alpha)^n</math>		<math>\sigma_y = \sigma_{Y0}(1+K\alpha)^n</math>

	where <math>\sigma_{Y0}</math> is initial yield stress, α is cumulative equivalent plastic strain, and K and n are dimensionless hardening law coefficients. If K < 0, the law is softening ~~and~~ hardening. The amount of softening can be limited by the <tt>yieldMin</tt> property.		where <math>\sigma_{Y0}</math> is initial yield stress, α is cumulative equivalent plastic strain, and K and n are dimensionless hardening law coefficients. If K < 0, the law is softening instead of hardening. The amount of softening can be limited by the <tt>yieldMin</tt> property.

	An alternate [[Nonlinear Hardening 2\|nonlinear hardening law]] is also available.		An alternate [[Nonlinear Hardening 2\|nonlinear hardening law]] is also available.

Nairnj at 21:21, 25 April 2017

2017-04-25T21:21:40Z

← Older revision		Revision as of 21:21, 25 April 2017
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	<math>\sigma_y = \sigma_{Y0}(1+K\alpha)^n</math>		<math>\sigma_y = \sigma_{Y0}(1+K\alpha)^n</math>

	where <math>\sigma_{Y0}</math> is initial yield stress, α is cumulative equivalent plastic strain, and K and n are dimensionless hardening law coefficients.		where <math>\sigma_{Y0}</math> is initial yield stress, α is cumulative equivalent plastic strain, and K and n are dimensionless hardening law coefficients. If K < 0, the law is softening and hardening. The amount of softening can be limited by the <tt>yieldMin</tt> property.

	An alternate [[Nonlinear Hardening 2\|nonlinear hardening law]] is also available.		An alternate [[Nonlinear Hardening 2\|nonlinear hardening law]] is also available.

Nairnj: /* Hardening Law Properties */

2017-04-25T21:20:51Z

Hardening Law Properties

← Older revision		Revision as of 21:20, 25 April 2017
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	\|-		\|-
	\| nhard \|\| The dimensionless exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use [[Linear Hardening\|linear hardening]] instead.		\| nhard \|\| The dimensionless exponent parameter (n) in the nonlinear hardening law. If n=1, it is more efficient to use [[Linear Hardening\|linear hardening]] instead.
			\|-
			\| yieldMin \|\| The minimum yield stress. This minimum only matters when using negative <tt>Khard</tt> or when modeling softening plasticity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0
	\|}		\|}

Nairnj at 21:54, 2 June 2015

2015-06-02T21:54:00Z

← Older revision		Revision as of 21:54, 2 June 2015
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	! Property !! Description		! Property !! Description
	\|-		\|-
	\| yield \|\| The initial yield stress (enter in units ~~of MPa~~). This stress corresponds to the axial stress at yield during uniaxial, 3D loading.		\| yield \|\| The initial yield stress (enter in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]]). This stress corresponds to the axial stress at yield during uniaxial, 3D loading.
	\|-		\|-
	\| Khard \|\| The dimensionless parameter K for nonlinear hardening.		\| Khard \|\| The dimensionless parameter K for nonlinear hardening.

Nairnj at 18:50, 22 May 2013

2013-05-22T18:50:54Z

← Older revision		Revision as of 18:50, 22 May 2013
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	In this nonlinear [[Hardening Laws\|hardening law]], the yield stress is given by		In this nonlinear [[Hardening Laws\|hardening law]], the yield stress is given by


	<math>\sigma_y = \sigma_{Y0}(1+K\alpha)^n</math>		<math>\sigma_y = \sigma_{Y0}(1+K\alpha)^n</math>

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	This [[Hardening Laws\|hardening law]] defines one history variable, which is stored as history variable #1. It stores the the cumulative equivalent plastic strain (absolute) defined as		This [[Hardening Laws\|hardening law]] defines one history variable, which is stored as history variable #1. It stores the the cumulative equivalent plastic strain (absolute) defined as


	<math>\alpha = \sum \sqrt{2\over3}\ \|\|d\varepsilon_p\|\|</math>		<math>\alpha = \sum \sqrt{2\over3}\ \|\|d\varepsilon_p\|\|</math>

	where dε<sub>p</sub> is the incremental plastic strain tensor in one time step.		where dε<sub>p</sub> is the incremental plastic strain tensor in one time step.

Nairnj: /* History Data */

2013-05-22T18:20:53Z

History Data

← Older revision		Revision as of 18:20, 22 May 2013
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	<math>\alpha = \sum \sqrt{2\over3}\ \|\|d\varepsilon_p\|\|</math>		<math>\alpha = \sum \sqrt{2\over3}\ \|\|d\varepsilon_p\|\|</math>

	where ε<sub>p</sub> is the incremental plastic strain tensor in one time step.		where dε<sub>p</sub> is the incremental plastic strain tensor in one time step.

Nairnj: /* History Data */

2013-05-22T18:20:38Z

History Data

← Older revision		Revision as of 18:20, 22 May 2013
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	<math>\alpha = \sum \sqrt{2\over3}\ \|\|d\varepsilon_p\|\|</math>		<math>\alpha = \sum \sqrt{2\over3}\ \|\|d\varepsilon_p\|\|</math>

	where &~~quot;~~epsilon;<sub>p</sub> is the incremental plastic strain tensor in one time step.		where ε<sub>p</sub> is the incremental plastic strain tensor in one time step.

Nairnj: /* History Data */

2013-05-22T18:20:20Z

History Data

← Older revision		Revision as of 18:20, 22 May 2013
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	This [[Hardening Laws\|hardening law]] defines one history variable, which is stored as history variable #1. It stores the the cumulative equivalent plastic strain (absolute) defined as		This [[Hardening Laws\|hardening law]] defines one history variable, which is stored as history variable #1. It stores the the cumulative equivalent plastic strain (absolute) defined as

	<math>\alpha = \~~Sum~~ \sqrt{2\over3}\ \|\|d\varepsilon_p\|\|</math>		<math>\alpha = \sum \sqrt{2\over3}\ \|\|d\varepsilon_p\|\|</math>

	where "epsilon;<sub>p</sub> is the incremental plastic strain tensor in one time step.		where "epsilon;<sub>p</sub> is the incremental plastic strain tensor in one time step.