Nonlinear Hardening 2 - Revision history

Nairnj at 21:46, 25 April 2017

2017-04-25T21:46:12Z

← Older revision		Revision as of 21:46, 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 instead of 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 1\|nonlinear hardening law]] is also available.		An alternate [[Nonlinear Hardening 1\|nonlinear hardening law]] is also available.

Nairnj: /* Hardening Law Properties */

2017-04-25T21:45:49Z

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: /* Hardening Law Properties */

2017-04-25T21:43:19Z

Hardening Law Properties

← Older revision		Revision as of 21:43, 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 21:42, 25 April 2017

2017-04-25T21:42:44Z

← Older revision		Revision as of 21:42, 25 April 2017
Line 4:		Line 4:
	<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 instead of hardening. The amount of softening can be limited by the <tt>yieldMin</tt> property.

	An alternate [[Nonlinear Hardening 1\|nonlinear hardening law]] is also available.		An alternate [[Nonlinear Hardening 1\|nonlinear hardening law]] is also available.

Nairnj at 21:53, 2 June 2015

2015-06-02T21:53:06Z

← Older revision		Revision as of 21:53, 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 18:51, 22 May 2013

2013-05-22T18:51:13Z

← Older revision		Revision as of 18:51, 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 at 18:21, 22 May 2013

2013-05-22T18:21:51Z

← Older revision		Revision as of 18:21, 22 May 2013
Line 3:		Line 3:
	<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 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.

	An alternate [[Nonlinear Hardening 1\|nonlinear hardening law]] is also available.		An alternate [[Nonlinear Hardening 1\|nonlinear hardening law]] is also available.
Line 26:		Line 26:
	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 = \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.

Nairnj: Created page with "In this nonlinear hardening law, the yield stress is given by $\sigma_y = \sigma_{Y0}(1+K\alpha^n)$ where $\sigma_{Y0}$ is initial ..."

2013-05-21T20:21:22Z

Created page with "In this nonlinear hardening law, the yield stress is given by <math>\sigma_y = \sigma_{Y0}(1+K\alpha^n)</math> where <math>\sigma_{Y0}</math> is initial ..."

New page

In this nonlinear [[Hardening Laws|hardening law]], the yield stress is given by

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

where <math>\sigma_{Y0}</math> is initial yield stress, α is cumulative plastic strain, and K and n are dimensionless hardening law coefficients.

An alternate [[Nonlinear Hardening 1|nonlinear hardening law]] is also available.

== Hardening Law Properties ==

The material parameters in this [[Hardening Laws|hardening law]] are defined with the following properties:

{| class="wikitable"
|-
! 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.
|-
| Khard || The dimensionless parameter K for nonlinear hardening.
|-
| 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.
|}

== History Data ==

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

Nonlinear Hardening 2 - Revision history

Nairnj at 21:46, 25 April 2017

Nairnj: /* Hardening Law Properties */

Nairnj: /* Hardening Law Properties */

Nairnj at 21:42, 25 April 2017

Nairnj at 21:53, 2 June 2015

Nairnj at 18:51, 22 May 2013

Nairnj at 18:21, 22 May 2013

Nairnj: Created page with "In this nonlinear hardening law, the yield stress is given by \sigma_y = \sigma_{Y0}(1+K\alpha^n) where \sigma_{Y0} is initial ..."

Nairnj: Created page with "In this nonlinear hardening law, the yield stress is given by $\sigma_y = \sigma_{Y0}(1+K\alpha^n)$ where $\sigma_{Y0}$ is initial ..."