Isotropic, Hyperelastic-Plastic Material - Revision history

Nairnj: /* Material Properties */

2018-05-16T16:33:09Z

Material Properties

← Older revision		Revision as of 16:33, 16 May 2018
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	\| G1 (or G) \|\| Low-strain shear modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none		\| G1 (or G) \|\| Low-strain shear modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none
	\|-		\|-
	\| UJOption \|\| Set to 0, 1, or 2, to select the energy term from [[#Constitutive Law\|~~above~~]]. \|\| none \|\| 0		\| UJOption \|\| Set to 0, 1, or 2, to select the energy term from [[Mooney Material#Constitutive Law\|Mooney Material]]. \|\| none \|\| 0
	\|-		\|-
	\| alpha \|\| Thermal expansion coefficient \|\| ppm/K \|\| 0		\| alpha \|\| Thermal expansion coefficient \|\| ppm/K \|\| 0

Nairnj: /* Examples */

2017-04-19T17:05:41Z

Examples

← Older revision		Revision as of 17:05, 19 April 2017
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	alpha 60		alpha 60
	rho 1.2		rho 1.2
			Hardening "Linear"
	yield 72		yield 72
	Ep 1000		Ep 1000

Nairnj at 21:58, 2 June 2015

2015-06-02T21:58:29Z

← Older revision		Revision as of 21:58, 2 June 2015
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	! Property !! Description !! Units !! Default		! Property !! Description !! Units !! Default
	\|-		\|-
	\| K \|\| Low-strain bulk modulus \|\| ~~MPa~~ \|\| none		\| K \|\| Low-strain bulk modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none
	\|-		\|-
	\| G1 (or G) \|\| Low-strain shear modulus \|\| ~~MPa~~ \|\| none		\| G1 (or G) \|\| Low-strain shear modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none
	\|-		\|-
	\| UJOption \|\| Set to 0, 1, or 2, to select the energy term from [[#Constitutive Law\|above]]. \|\| none \|\| 0		\| UJOption \|\| Set to 0, 1, or 2, to select the energy term from [[#Constitutive Law\|above]]. \|\| none \|\| 0

Nairnj: /* Material Properties */

2015-03-12T15:53:53Z

Material Properties

← Older revision		Revision as of 15:53, 12 March 2015
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	\| UJOption \|\| Set to 0, 1, or 2, to select the energy term from [[#Constitutive Law\|above]]. \|\| none \|\| 0		\| UJOption \|\| Set to 0, 1, or 2, to select the energy term from [[#Constitutive Law\|above]]. \|\| none \|\| 0
	\|-		\|-
	\| alpha \|\| Thermal expansion coefficient \|\| ppm/M \|\| 0		\| alpha \|\| Thermal expansion coefficient \|\| ppm/K \|\| 0
	\|-		\|-
	\| Hardening \|\| This command selects the [[Hardening Laws\|hardening law]] by its name or number. It should be before entering any yielding properties. \|\| none \|\| none		\| Hardening \|\| This command selects the [[Hardening Laws\|hardening law]] by its name or number. It should be before entering any yielding properties. \|\| none \|\| none

Nairnj: /* History Variables */

2014-07-01T17:22:37Z

History Variables

← Older revision		Revision as of 17:22, 1 July 2014
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	== History Variables ==		== History Variables ==

	The selected [[Hardening Laws\|hardening law]] will create one or more history variables. This material uses the next history variable (after the hardening laws history variables) to store the volumetric change (''i.e.'', ''J'' or the determinant of the deformation gradient). The total strain is stored in the elastic strain variable, while the plastic strain stores the left Cauchy Green tensor.		The selected [[Hardening Laws\|hardening law]] will create one or more history variables. This material uses the next history variable (after the hardening laws history variables) to store the volumetric change (''i.e.'', ''J'' or the determinant of the deformation gradient). The total strain is stored in the elastic strain variable, while the plastic strain stores the elastic left Cauchy Green tensor.

	== Examples ==		== Examples ==

Nairnj: /* Material Properties */

2014-03-19T21:50:28Z

Material Properties

← Older revision		Revision as of 21:50, 19 March 2014
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	\| K \|\| Low-strain bulk modulus \|\| MPa \|\| none		\| K \|\| Low-strain bulk modulus \|\| MPa \|\| none
	\|-		\|-
	\| G1 \|\| Low-strain shear modulus \|\| MPa \|\| none		\| G1 (or G) \|\| Low-strain shear modulus \|\| MPa \|\| none
	\|-		\|-
	\| UJOption \|\| Set to 0, 1, or 2, to select the energy term from [[#Constitutive Law\|above]]. \|\| none \|\| 0		\| UJOption \|\| Set to 0, 1, or 2, to select the energy term from [[#Constitutive Law\|above]]. \|\| none \|\| 0

Nairnj: /* Examples */

2013-12-31T22:45:04Z

Examples

← Older revision		Revision as of 22:45, 31 December 2013
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	== Examples ==		== Examples ==

	These commands model polymer as an isotropic hyperelastic-plastic material with a particular linear isotropic hardening ~~(using scripted or XML commands)~~:		These commands model a polymer as an isotropic hyperelastic-plastic material with a particular linear isotropic hardening:

	Material "polymer","polymer","HEIsotropic"		Material "polymer","polymer","HEIsotropic"
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	Ep 1000		Ep 1000
	Done		Done

	~~<Material Type="24" Name="Polymer">~~
	~~<K>5166.67</K>~~
	~~<G1>1107.14</G1>~~
	~~<alpha>60</alpha>~~
	~~<rho>1.2</rho>~~
	~~<yield>72</yield>~~
	~~<Ep>1000</Ep>~~
	~~</Material>~~

	== References ==		== References ==
	<references/>		<references/>

Nairnj: /* History Variables */

2013-12-31T18:43:56Z

History Variables

← Older revision		Revision as of 18:43, 31 December 2013
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	== History Variables ==		== History Variables ==

	The selected [[Hardening Laws\|hardening law]] will create one or more history variables. This material uses the next history variable (after the hardening laws history variables)\ to store the volumetric ~~strain~~ (''i.e.'', the determinant of the deformation gradient). The total strain is stored in the elastic strain variable, while the plastic strain stores the left Cauchy Green tensor.		The selected [[Hardening Laws\|hardening law]] will create one or more history variables. This material uses the next history variable (after the hardening laws history variables) to store the volumetric change (''i.e.'', ''J'' or the determinant of the deformation gradient). The total strain is stored in the elastic strain variable, while the plastic strain stores the left Cauchy Green tensor.

	== Examples ==		== Examples ==

Nairnj: /* Constitutive Law */

2013-12-31T18:42:10Z

Constitutive Law

← Older revision		Revision as of 18:42, 31 December 2013
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	<math> L_{v} \mathbf{B}^e = \mathbf{F} {\delta\over t} (\mathbf{\bar C}{^{p-1}}) \mathbf{F^T} = - {2\over 3} {\gamma} {\rm Tr}(\mathbf{B}_{e}) )\mathbf{n} \qquad {\rm with} \qquad \mathbf{n} = {\mathbf{\tau^{d}}\over \|\|\mathbf{\tau^{d}}\|\|} </math>		<math> L_{v} \mathbf{B}^e = \mathbf{F} {\delta\over t} (\mathbf{\bar C}{^{p-1}}) \mathbf{F^T} = - {2\over 3} {\gamma} {\rm Tr}(\mathbf{B}_{e})\mathbf{n} \qquad {\rm with} \qquad \mathbf{n} = {\mathbf{\tau^{d}}\over \|\|\mathbf{\tau^{d}}\|\|} </math>

	Where ''L<sub>v</sub>'' is the Lie derivative of the deviatoric part of the elastic left Cauchy-Green strain tensor <math>\bigl(\mathbf{\bar B}_{e}\bigr)</math>. It represents the plastic strain rate that is a tensor normal to the yield surface in the stress space; '''n''' is a normal to the yield surface and γ is the consistency parameter also called the plastic multiplicator. In addition, a isotropic hardening law is needed. It is represented by the rate equation, as in the linear theory:		Where ''L<sub>v</sub>'' is the Lie derivative of the deviatoric part of the elastic left Cauchy-Green strain tensor <math>\bigl(\mathbf{\bar B}_{e}\bigr)</math>. It represents the plastic strain rate that is a tensor normal to the yield surface in the stress space; '''n''' is a normal to the yield surface and γ is the consistency parameter also called the plastic multiplicator. In addition, a isotropic hardening law is needed. It is represented by the rate equation, as in the linear theory:

Nairnj: /* Constitutive Law */

2013-12-31T18:40:39Z

Constitutive Law

← Older revision		Revision as of 18:40, 31 December 2013
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	<math> {d {\alpha}\over dt } = ~~(2/3)^~~{1\~~over 2~~} {\~~gamma~~} </math>		<math> {d {\alpha}\over dt } ={\gamma} \sqrt{2\over3} </math>

	== Material Properties ==		== Material Properties ==