Comparison of Neo-Hookean Materials - Revision history

Nairnj: /* Elastic Energy Functions */

2023-01-30T01:09:22Z

Elastic Energy Functions

← Older revision		Revision as of 01:09, 30 January 2023
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	<math>W = {\lambda\over 2}(J_E-1)^2 + G\sum_k (\lambda_k-1)^2</math><br>		<math>W = {\lambda\over 2}(J_E-1)^2 + G\sum_k (\lambda_k-1)^2</math><br>
	To use this neo-Hookean material, the material properties must set either <tt> CritComp</tt> or <tt> CritTens</tt> to less than zero and set <tt>Elastic</tt> ~~is 0~~.		To use this neo-Hookean material, the material properties must set either <tt> CritComp</tt> or <tt> CritTens</tt> to less than zero and set <tt>Elastic</tt> to zero.
	</li>		</li>
	</ul>		</ul>

Nairnj: /* Stress Strain Response */

2020-03-25T16:13:43Z

Stress Strain Response

← Older revision		Revision as of 16:13, 25 March 2020
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	The following figure plots stress vs. strain from compression to tension for the above neo-Hookean materials. For the [[Mooney Material]], one plot uses G<sub>2</sub>=0 while the second uses G<sub>1</sub>=G<sub>2</sub>. Although all are the same in the small strain limit the differences at large strain are significant. The [[Mooney Material]] softens at high strain while the [[Neo-Hookean Material]] and [[Clamped Neo-Hookean Material]] (or "Co-Rotated" material) get stiffer at higher strain. The choice of material model should be based on corresponding response of an actual material.		The following figure plots stress vs. strain from compression to tension for the above neo-Hookean materials. For the [[Mooney Material]], one plot uses G<sub>2</sub>=0 while the second uses G<sub>1</sub>=G<sub>2</sub>. Although all are the same in the small strain limit the differences at large strain are significant. The [[Mooney Material]] softens at high strain while the [[Neo-Hookean Material]] and [[Clamped Neo-Hookean Material]] (or "Co-Rotated" material) get stiffer at higher strain. The choice of material model should be based on corresponding response of an actual material.

	[[File:NewHookean.png\|center]]		[[File:NewHookean.png\|center\|600px]]

Nairnj at 16:04, 25 March 2020

2020-03-25T16:04:02Z

← Older revision		Revision as of 16:04, 25 March 2020
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	# [[Clamped Neo-Hookean Material]]		# [[Clamped Neo-Hookean Material]]

	The first is always a neo-Hookean material. The second has three properties for bulk modulus (K) and two shear modulus (G<sub>1</sub> and G<sub>2</sub>). It can be considered as a neo-Hookeen material that reduces to small strain material with same bulk modulus and shear modulus G = G<sub>1</sub>+ G<sub>2</sub>. The subclasses of [[Mooney Material]] use elastic part of that material with G=G<sub>1</sub> abd G<sub>2</sub>=0. The [[Isotropic, Hyperelastic-Plastic Mie-Grüneisen Material]] (but not plotted here yet). The third allows plastic deformation by limiting the amount of elongation in tension or compression. By turning off the clamping, the [[Clamped Neo-Hookean Material\|clamped neo-Hookean material]] represents a modified corotated elasticity law.		The first is always a neo-Hookean material. The second has three properties for bulk modulus (K) and two shear modulus (G<sub>1</sub> and G<sub>2</sub>). It can be considered as a neo-Hookeen material that reduces to small strain material with same bulk modulus and shear modulus G = G<sub>1</sub>+ G<sub>2</sub>. The subclasses of [[Mooney Material]] use elastic part of that material with G=G<sub>1</sub> abd G<sub>2</sub>=0. The [[Isotropic, Hyperelastic-Plastic Mie-Grüneisen Material]] has different elaastic behavior in compression (but not plotted here yet). The third allows plastic deformation by limiting the amount of elongation in tension or compression. By turning off the clamping, the [[Clamped Neo-Hookean Material\|clamped neo-Hookean material]] represents a modified corotated elasticity law.

	== Elastic Energy Functions ==		== Elastic Energy Functions ==

Nairnj: /* Introduction */

2020-03-25T16:02:16Z

Introduction

← Older revision		Revision as of 16:02, 25 March 2020
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	# [[Clamped Neo-Hookean Material]]		# [[Clamped Neo-Hookean Material]]

	The first is always a neo-Hookean material. The second has three properties for bulk modulus (K) and two shear modulus (G<sub>1</sub> and G<sub>2</sub>). It can be considered as neo-~~Hooken~~ that ~~reduce~~ to small strain material with same bulk modulus and shear modulus G = G<sub>1</sub>+ G<sub>2</sub>. The subclasses of [[Mooney Material]] use elastic part of that material with G=G<sub>1</sub> abd G<sub>2</sub>=0. The [[Isotropic, Hyperelastic-Plastic Mie-Grüneisen Material]] (but not plotted here yet). The third allows plastic deformation by limiting the amount of elongation in tension or compression. By turning off the clamping, the [[Clamped Neo-Hookean Material\|clamped neo-Hookean material]] represents a modified corotated elasticity law.		The first is always a neo-Hookean material. The second has three properties for bulk modulus (K) and two shear modulus (G<sub>1</sub> and G<sub>2</sub>). It can be considered as a neo-Hookeen material that reduces to small strain material with same bulk modulus and shear modulus G = G<sub>1</sub>+ G<sub>2</sub>. The subclasses of [[Mooney Material]] use elastic part of that material with G=G<sub>1</sub> abd G<sub>2</sub>=0. The [[Isotropic, Hyperelastic-Plastic Mie-Grüneisen Material]] (but not plotted here yet). The third allows plastic deformation by limiting the amount of elongation in tension or compression. By turning off the clamping, the [[Clamped Neo-Hookean Material\|clamped neo-Hookean material]] represents a modified corotated elasticity law.

	== Elastic Energy Functions ==		== Elastic Energy Functions ==

Nairnj: /* Introduction */

2020-03-25T16:01:08Z

Introduction

← Older revision		Revision as of 16:01, 25 March 2020
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	== Introduction ==		== Introduction ==

	The definition of an isotropic, neo-Hookean is an elastic material that depends ot two elastic constants and in the limit of small deformations is identical to a [[Isotropic Material\|small-strain, linear-elastic, Hookean material]]. The currently available [[Material Models\|MPM Materials]] that a neo-Hookean material options are:		The definition of an isotropic, neo-Hookean material is an elastic material that depends ot two elastic constants and in the limit of small deformations is identical to a [[Isotropic Material\|small-strain, linear-elastic, Hookean material]]. The currently available [[Material Models\|MPM Materials]] that a neo-Hookean material options are:

	# [[Neo-Hookean Material]]		# [[Neo-Hookean Material]]

Nairnj: /* Introduction */

2020-03-25T16:00:50Z

Introduction

← Older revision		Revision as of 16:00, 25 March 2020
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	# [[Neo-Hookean Material]]		# [[Neo-Hookean Material]]
	# [[Mooney Material]]		# [[Mooney Material]]
			#* [[Isotropic, Hyperelastic-Plastic Material]]
			#* [[Isotropic, Hyperelastic-Plastic Mie-Grüneisen Material]]
	# [[Clamped Neo-Hookean Material]]		# [[Clamped Neo-Hookean Material]]

	The first is always a neo-Hookean material. The second has three properties for bulk modulus (K) and two shear modulus (G<sub>1</sub> and G<sub>2</sub>). Is can be considered as neo-Hooken that reduce to small strain material with same bulk modulus and shear modulus G = G<sub>1</sub>+ G<sub>2</sub>. The third allows plastic deformation by limiting the amount of elongation in tension or ~~compressure~~. By turning off the clamping, the [[Clamped Neo-Hookean Material\|clamped neo-Hookean material]] represents a modified corotated elasticity law.		The first is always a neo-Hookean material. The second has three properties for bulk modulus (K) and two shear modulus (G<sub>1</sub> and G<sub>2</sub>). It can be considered as neo-Hooken that reduce to small strain material with same bulk modulus and shear modulus G = G<sub>1</sub>+ G<sub>2</sub>. The subclasses of [[Mooney Material]] use elastic part of that material with G=G<sub>1</sub> abd G<sub>2</sub>=0. The [[Isotropic, Hyperelastic-Plastic Mie-Grüneisen Material]] (but not plotted here yet). The third allows plastic deformation by limiting the amount of elongation in tension or compression. By turning off the clamping, the [[Clamped Neo-Hookean Material\|clamped neo-Hookean material]] represents a modified corotated elasticity law.

	== Elastic Energy Functions ==		== Elastic Energy Functions ==

Nairnj: /* Stress Strain Response */

2018-07-20T18:43:37Z

Stress Strain Response

← Older revision		Revision as of 18:43, 20 July 2018
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	== Stress Strain Response ==		== Stress Strain Response ==

	The following figure plots stress vs. strain from compression to tension for the above neo-Hookean materials. For the [[Mooney Material]], one plot uses G<sub>2</sub>=0 while the second uses G<sub>1</sub>=G<sub>2</sub>. Although all are the same in the small strain limit the differences ~~are~~ large strain are significant. The [[Mooney Material]] softens at high strain while the [[Neo-Hookean Material]] and [[Clamped Neo-Hookean Material]] (or "Co-Rotated" material) get stiffer at higher strain. The choice of material model should be based on corresponding response of an actual material.		The following figure plots stress vs. strain from compression to tension for the above neo-Hookean materials. For the [[Mooney Material]], one plot uses G<sub>2</sub>=0 while the second uses G<sub>1</sub>=G<sub>2</sub>. Although all are the same in the small strain limit the differences at large strain are significant. The [[Mooney Material]] softens at high strain while the [[Neo-Hookean Material]] and [[Clamped Neo-Hookean Material]] (or "Co-Rotated" material) get stiffer at higher strain. The choice of material model should be based on corresponding response of an actual material.

	[[File:NewHookean.png\|center]]		[[File:NewHookean.png\|center]]

Nairnj at 23:08, 16 November 2017

2017-11-16T23:08:42Z

← Older revision		Revision as of 23:08, 16 November 2017
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			__TOC__
	== Introduction ==		== Introduction ==

Nairnj: /* Stress Strain Response */

2017-11-16T23:04:50Z

Stress Strain Response

← Older revision		Revision as of 23:04, 16 November 2017
Line 35:		Line 35:
	The following figure plots stress vs. strain from compression to tension for the above neo-Hookean materials. For the [[Mooney Material]], one plot uses G<sub>2</sub>=0 while the second uses G<sub>1</sub>=G<sub>2</sub>. Although all are the same in the small strain limit the differences are large strain are significant. The [[Mooney Material]] softens at high strain while the [[Neo-Hookean Material]] and [[Clamped Neo-Hookean Material]] (or "Co-Rotated" material) get stiffer at higher strain. The choice of material model should be based on corresponding response of an actual material.		The following figure plots stress vs. strain from compression to tension for the above neo-Hookean materials. For the [[Mooney Material]], one plot uses G<sub>2</sub>=0 while the second uses G<sub>1</sub>=G<sub>2</sub>. Although all are the same in the small strain limit the differences are large strain are significant. The [[Mooney Material]] softens at high strain while the [[Neo-Hookean Material]] and [[Clamped Neo-Hookean Material]] (or "Co-Rotated" material) get stiffer at higher strain. The choice of material model should be based on corresponding response of an actual material.

	[[File:~~NeoHookean~~.png~~\|600px\|thumb~~\|center]]		[[File:NewHookean.png\|center]]

Nairnj: /* Stress Strain Response */

2017-11-16T23:03:21Z

Stress Strain Response

← Older revision		Revision as of 23:03, 16 November 2017
Line 35:		Line 35:
	The following figure plots stress vs. strain from compression to tension for the above neo-Hookean materials. For the [[Mooney Material]], one plot uses G<sub>2</sub>=0 while the second uses G<sub>1</sub>=G<sub>2</sub>. Although all are the same in the small strain limit the differences are large strain are significant. The [[Mooney Material]] softens at high strain while the [[Neo-Hookean Material]] and [[Clamped Neo-Hookean Material]] (or "Co-Rotated" material) get stiffer at higher strain. The choice of material model should be based on corresponding response of an actual material.		The following figure plots stress vs. strain from compression to tension for the above neo-Hookean materials. For the [[Mooney Material]], one plot uses G<sub>2</sub>=0 while the second uses G<sub>1</sub>=G<sub>2</sub>. Although all are the same in the small strain limit the differences are large strain are significant. The [[Mooney Material]] softens at high strain while the [[Neo-Hookean Material]] and [[Clamped Neo-Hookean Material]] (or "Co-Rotated" material) get stiffer at higher strain. The choice of material model should be based on corresponding response of an actual material.

	[[File:~~NewHookean~~.png\|600px\|center]]		[[File:NeoHookean.png\|600px\|thumb\|center]]