Linear Hardening - Revision history

Nairnj: /* Hardening Law Properties */

2021-04-29T16:58:15Z

Hardening Law Properties

← Older revision		Revision as of 16:58, 29 April 2021
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	\| Ep \|\| The plastic modulus. This modulus is the slope of total stress as a function of plastic strain during uniaxial, 3D loading. The default of 0.0 results in an elastic-perfectly plastic material or a material with no hardening. It must be non-negative, but you can enter softening by using negative <tt>Khard</tt>. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0		\| Ep \|\| The plastic modulus. This modulus is the slope of total stress as a function of plastic strain during uniaxial, 3D loading. The default of 0.0 results in an elastic-perfectly plastic material or a material with no hardening. It must be non-negative, but you can enter softening by using negative <tt>Khard</tt>. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0
	\|-		\|-
	\| Khard \|\| Alternatively, you can enter this dimensionless parameter for hardening. It is only used if E<sub>p</sub> is not entered and when entered, it is ~~convert~~ to E<sub>p</sub> using E<sub>p</sub> = <math>\sigma_{Y0}K</math>. K can be positive (hardening) or negative (softening) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0		\| Khard \|\| Alternatively, you can enter this dimensionless parameter for hardening. It is only used if E<sub>p</sub> is not entered and when entered, it is converted to E<sub>p</sub> using E<sub>p</sub> = <math>\sigma_{Y0}K</math>. K can be positive (hardening) or negative (softening) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0
	\|-		\|-
	\| 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		\| 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 and Softening */

2021-04-29T16:57:34Z

Hardening and Softening

← Older revision		Revision as of 16:57, 29 April 2021
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	=== Hardening and Softening ===		=== Hardening and Softening ===

	As implied by the name "Linear Hardening", the law normally models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening will be unstable if ~~is crosses~~ entire cross section of a material under ~~applied~~ load, but is usually stable otherwise ~~or when~~ localized to a yield ~~zone~~. To prevent non-physical negative values at large plastic strain, the softened yield stress must be limited to a minimum yield stress value (the default minimum is zero).		As implied by the name "Linear Hardening", the law normally models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening will be unstable if yielding material points cross an entire cross section of a material under load, but is usually stable otherwise. It other words, is can be used to model localized to yield zones. To prevent non-physical negative values at large plastic strain, the softened yield stress must be limited to a minimum yield stress value (the default minimum is zero).

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj: /* Hardening and Softening */

2017-04-25T21:46:46Z

Hardening and Softening

← Older revision		Revision as of 21:46, 25 April 2017
Line 8:		Line 8:
	=== Hardening and Softening ===		=== Hardening and Softening ===

	As implied by the name "Linear Hardening", the law normally models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening will be unstable if is crosses entire cross section of a material under applied load, but is usually stable otherwise or when localized to a yield zone. To prevent non-physical negative values ~~are~~ large plastic strain, the softened yield stress must be limited to a minimum yield stress value (the default minimum is zero).		As implied by the name "Linear Hardening", the law normally models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening will be unstable if is crosses entire cross section of a material under applied load, but is usually stable otherwise or when localized to a yield zone. To prevent non-physical negative values at large plastic strain, the softened yield stress must be limited to a minimum yield stress value (the default minimum is zero).

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj: /* Hardening and Softening */

2017-04-25T21:02:57Z

Hardening and Softening

← Older revision		Revision as of 21:02, 25 April 2017
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	=== Hardening and Softening ===		=== Hardening and Softening ===

	As implied by the name "Linear Hardening", the law normally models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p=\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening will be unstable if is crosses entire cross section of a material under applied load, but is usually stable otherwise or when localized to a yield zone. To prevent non-physical negative values are large plastic strain, the softened yield stress must be limited to a minimum yield stress value (the default minimum is zero).		As implied by the name "Linear Hardening", the law normally models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening will be unstable if is crosses entire cross section of a material under applied load, but is usually stable otherwise or when localized to a yield zone. To prevent non-physical negative values are large plastic strain, the softened yield stress must be limited to a minimum yield stress value (the default minimum is zero).

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj: /* Hardening Law Properties */

2017-04-25T21:00:42Z

Hardening Law Properties

← Older revision		Revision as of 21:00, 25 April 2017
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	! Property !! Description !! Units !! Default		! 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. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| Very 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]] \|\| Very Large
	\|-		\|-
	\| Ep \|\| The plastic modulus. This modulus is the slope of total stress as a function of plastic strain during uniaxial, 3D loading. The default of 0.0 results in an elastic-perfectly plastic material or a material with no hardening. It must be non-negative, but you can enter softening by using negative <tt>Khard</tt>. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0		\| Ep \|\| The plastic modulus. This modulus is the slope of total stress as a function of plastic strain during uniaxial, 3D loading. The default of 0.0 results in an elastic-perfectly plastic material or a material with no hardening. It must be non-negative, but you can enter softening by using negative <tt>Khard</tt>. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0
	\|-		\|-
	\| Khard \|\| Alternatively, you can enter this dimensionless parameter for hardening. It is only used if E<sub>p</sub> is not entered and when entered, it is convert to E<sub>p</sub> using E<sub>p</sub> = <math>\sigma_{Y0}K</math>. K can be positive (hardening) or negative (softening) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0		\| Khard \|\| Alternatively, you can enter this dimensionless parameter for hardening. It is only used if E<sub>p</sub> is not entered and when entered, it is convert to E<sub>p</sub> using E<sub>p</sub> = <math>\sigma_{Y0}K</math>. K can be positive (hardening) or negative (softening) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0
			\|-
			\| 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 and Softening */

2017-04-25T20:58:58Z

Hardening and Softening

← Older revision		Revision as of 20:58, 25 April 2017
Line 8:		Line 8:
	=== Hardening and Softening ===		=== Hardening and Softening ===

	As implied by the name "Linear Hardening", the law ~~normal~~ models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p=\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening ~~behavior tends to lead to~~ unstable ~~simulations~~, but ~~it can~~ be ~~used when yielding~~ is ~~localized or maybe with addition of effecting damping~~.		As implied by the name "Linear Hardening", the law normally models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p=\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening will be unstable if is crosses entire cross section of a material under applied load, but is usually stable otherwise or when localized to a yield zone. To prevent non-physical negative values are large plastic strain, the softened yield stress must be limited to a minimum yield stress value (the default minimum is zero).

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj at 16:46, 19 April 2017

2017-04-19T16:46:31Z

← Older revision		Revision as of 16:46, 19 April 2017
Line 8:		Line 8:
	=== Hardening and Softening ===		=== Hardening and Softening ===

	As implied by the name "Linear Hardening", the law normal models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words <math>E_p> 0<\math> and <math>K\ge0</math>. ~~The~~ law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p<\math>, however, has to be done by ~~enterin~~ a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0} <\math>. Softening behavior tends to lead to unstable simulations, but it can be used when yielding is localized or maybe with addition of effecting damping.		As implied by the name "Linear Hardening", the law normal models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words, <math>E_p=\ge 0</math> and <math>K\ge0</math>. This law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p</math>, however, has to be done by entering a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0}</math>. Softening behavior tends to lead to unstable simulations, but it can be used when yielding is localized or maybe with addition of effecting damping.

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj: /* Hardening and Softening */

2017-04-19T16:42:12Z

Hardening and Softening

← Older revision		Revision as of 16:42, 19 April 2017
Line 8:		Line 8:
	=== Hardening and Softening ===		=== Hardening and Softening ===

	As implied by the name "Linear Hardening", the law normal models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words <math>E_p~~\ge0~~<\math> and <math>K\ge0</math>. The law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p<\math>, however, has to be done by enterin a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0} <\math>. Softening behavior tends to lead to unstable simulations, but it can be used when yielding is localized or maybe with addition of effecting damping.		As implied by the name "Linear Hardening", the law normal models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words <math>E_p> 0<\math> and <math>K\ge0</math>. The law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p<\math>, however, has to be done by enterin a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0} <\math>. Softening behavior tends to lead to unstable simulations, but it can be used when yielding is localized or maybe with addition of effecting damping.

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj at 16:41, 19 April 2017

2017-04-19T16:41:15Z

← Older revision		Revision as of 16:41, 19 April 2017
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	where <math>\sigma_{Y0}</math> is initial yield stress, E<sub>p</sub> is the plastic modulus, α is cumulative equivalent plastic strain, and K is a hardening coefficient.		where <math>\sigma_{Y0}</math> is initial yield stress, E<sub>p</sub> is the plastic modulus, α is cumulative equivalent plastic strain, and K is a hardening coefficient.

			=== Hardening and Softening ===

			As implied by the name "Linear Hardening", the law normal models a response where the yield strength increases with plastic strain <math>\alpha</math>. In other words <math>E_p\ge0<\math> and <math>K\ge0</math>. The law can also be used to model linear softening by entering a negative modulus. Entry of a negative <math>E_p<\math>, however, has to be done by enterin a negative <math>K</math>. This entry will result in <math>E_p=K \sigma_{Y0} <\math>. Softening behavior tends to lead to unstable simulations, but it can be used when yielding is localized or maybe with addition of effecting damping.

	== Hardening Law Properties ==		== Hardening Law Properties ==

Nairnj: /* Hardening Law Properties */

2017-04-19T16:35:28Z

Hardening Law Properties

← Older revision		Revision as of 16:35, 19 April 2017
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	! Property !! Description !! Units !! Default		! 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. \|\| ~~Stress~~ \|\| Very Large		\| 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. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| Very Large
	\|-		\|-
	\| Ep \|\| The plastic modulus ~~(enter in [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]])~~. This modulus is the slope of total stress as a function of plastic strain during uniaxial, 3D loading. The default is 0.0 ~~which~~ results in an elastic-perfectly plastic material or a material with no ~~work~~ hardening. \|\| ~~Stress~~ \|\| 0.0		\| Ep \|\| The plastic modulus. This modulus is the slope of total stress as a function of plastic strain during uniaxial, 3D loading. The default of 0.0 results in an elastic-perfectly plastic material or a material with no hardening. It must be non-negative, but you can enter softening by using negative <tt>Khard</tt>. \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0
	\|-		\|-
	\| Khard \|\| Alternatively, you can enter this dimensionless parameter for hardening. It is only used if E<sub>p</sub> is not entered and when entered, it is convert to E<sub>p</sub> using E<sub>p</sub> = <math>\sigma_{Y0}K</math>. \|\| ~~Stress~~ \|\| 0.0		\| Khard \|\| Alternatively, you can enter this dimensionless parameter for hardening. It is only used if E<sub>p</sub> is not entered and when entered, it is convert to E<sub>p</sub> using E<sub>p</sub> = <math>\sigma_{Y0}K</math>. K can be positive (hardening) or negative (softening) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| 0.0
	\|}		\|}