Tait Liquid Material - Revision history

Nairnj: /* Examples */

2018-11-07T21:42:56Z

Examples

← Older revision		Revision as of 21:42, 7 November 2018
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	== Examples ==		== Examples ==

	The following commands are for water.		The following commands are for water for scripted or <tt>XML</tt> input files

			Material "matID","Water","TaitLiquid"
			K 2200
			viscosity 1
			alpha 70
			rho 1
			Cv 418.13
			kCond 0.58
			Done

	<Material Type="27" Name="Water">		<Material Type="27" Name="Water">
	<K>2200</K>		<K>2200</K>

Nairnj: /* Pressure-Dependent Properties */

2017-09-22T18:03:32Z

Pressure-Dependent Properties

← Older revision		Revision as of 18:03, 22 September 2017
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	<math>K(P,T) = {p + CK_0\over C} {J\over J_{res}} =K_0 {J\over J_{res}}\qquad {\rm and} \qquad \beta(P,T) = \beta_0</math>		<math>K(P,T) = {p + CK_0\over C} {J\over J_{res}} =K_0 {J\over J_{res}}\exp\left({1\over C}\left(1 - {J\over J_{res}}\right)\right) \qquad {\rm and} \qquad \beta(P,T) = \beta_0</math>

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

Nairnj: /* Pressure-Dependent Properties */

2017-09-22T18:02:38Z

Pressure-Dependent Properties

← Older revision		Revision as of 18:02, 22 September 2017
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	<math>K(P,T) = {p + CK_0\over C} {J\over J_{res}} \qquad {\rm and} \qquad \beta(P,T) = \beta_0</math>		<math>K(P,T) = {p + CK_0\over C} {J\over J_{res}} =K_0 {J\over J_{res}}\qquad {\rm and} \qquad \beta(P,T) = \beta_0</math>

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

Nairnj: /* Material Properties */

2017-02-10T01:14:26Z

Material Properties

← Older revision		Revision as of 01:14, 10 February 2017
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	\| K \|\| Zero-pressure, bulk modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none		\| K \|\| Zero-pressure, bulk modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none
	\|-		\|-
	\| viscosity \|\| Liquid viscosity at one shear rate \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|viscosity units]] \|\| none		\| viscosity \|\| Liquid viscosity at one shear rate (note that legacy units are cP = 1 mPa-sec) \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|viscosity units]] \|\| none
	\|-		\|-
	\| logshearrate \|\| log of shear rate corresponding to a viscosity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|1/(time units]] \|\| none		\| logshearrate \|\| log of shear rate corresponding to a viscosity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|1/(time units]] \|\| none

Nairnj: /* History Variables */

2016-06-08T23:50:27Z

History Variables

← Older revision		Revision as of 23:50, 8 June 2016
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	# J or the volumetric strain (''i.e.'', the determinant of the deformation gradient, but when initial pressure is set, it will be the product of the determinant of the tracked deformation gradient and the volume change caused by the initial pressure).		# J or the volumetric strain (''i.e.'', the determinant of the deformation gradient, but when initial pressure is set, it will be the product of the determinant of the tracked deformation gradient and the volume change caused by the initial pressure).
	# Jres or the volume change that would occur due to free thermal expansion.		# Jres or the volume change that would occur due to free thermal expansion.
	# The shear rate seen by the particle, which is equal to <math>2\|{\rm dev}\nabla\vec v\|</math>		# The shear rate seen by the particle, which is equal to <math>2\|{\rm dev}\nabla(\vec v)\|</math>

	== Notes ==		== Notes ==

Nairnj: /* History Variables */

2016-06-08T23:48:56Z

History Variables

← Older revision		Revision as of 23:48, 8 June 2016
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	== History Variables ==		== History Variables ==

	This material ~~uses~~ history #~~1 to store~~ the volumetric strain (''i.e.'', the determinant of the deformation gradient, but when initial pressure is set, it will be the product of the determinant of the tracked deformation gradient and the volume change caused by the initial pressure).		This material tracks three history variables:

			# J or the volumetric strain (''i.e.'', the determinant of the deformation gradient, but when initial pressure is set, it will be the product of the determinant of the tracked deformation gradient and the volume change caused by the initial pressure).
			# Jres or the volume change that would occur due to free thermal expansion.
			# The shear rate seen by the particle, which is equal to <math>2\|{\rm dev}\nabla\vec v\|</math>

	== Notes ==		== Notes ==

Nairnj: /* Material Properties */

2016-06-08T23:45:31Z

Material Properties

← Older revision		Revision as of 23:45, 8 June 2016
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	If one <tt>viscosity</tt> is given and no <tt>logshearrate</tt>, the material has constant viscosity. If multiple <tt>logshearrate</tt> and <tt>viscosity</tt> commands are used, each pair defines points for piecewise linear representation of viscosity as a function of log shear rate. You must enter an equal number of <tt>logshearrate</tt> and <tt>viscosity</tt> commands with monotonically increasing shear rates. The liquid's viscosity will be interpolated within the provided points. Shear rates below the minimum or above the maximum provided shear rates will be equal to the viscosity at the minimum or maximum shear rate, respectively.		If one <tt>viscosity</tt> is given and no <tt>logshearrate</tt>, the material has constant viscosity. If multiple <tt>logshearrate</tt> and <tt>viscosity</tt> commands are used, each pair defines points for piecewise linear representation of viscosity as a function of log shear rate. You must enter an equal number of <tt>logshearrate</tt> and <tt>viscosity</tt> commands with monotonically increasing shear rates. The liquid's viscosity will be interpolated within the provided points. Shear rates below the minimum or above the maximum provided shear rates will be equal to the viscosity at the minimum or maximum shear rate, respectively.

	Note that when initial pressure is set, the mass of each particle will be adjusted to fill the initial particle volume under the set pressure. ~~THe~~ particle deformation tracked during the simulation will be the deformation relative to the initial state under pressure. The particle's relative volume, which is tracked in [[#History Variables\|history variable 1]], will be relative to the pressure-free state and thus will include volume change due to the initial pressure.		Note that when initial pressure is set, the mass of each particle will be adjusted to fill the initial particle volume under the set pressure. The particle deformation tracked during the simulation will be the deformation relative to the initial state under pressure. The particle's relative volume, which is tracked in [[#History Variables\|history variable 1]], will be relative to the pressure-free state and thus will include volume change due to the initial pressure.

	== History Variables ==		== History Variables ==

Nairnj: /* Material Properties */

2016-05-04T17:16:49Z

Material Properties

← Older revision		Revision as of 17:16, 4 May 2016
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	\| K \|\| Zero-pressure, bulk modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none		\| K \|\| Zero-pressure, bulk modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none
	\|-		\|-
	\| viscosity \|\| Liquid viscosity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|~~voscosity~~ units]] \|\| none		\| viscosity \|\| Liquid viscosity at one shear rate \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|viscosity units]] \|\| none
			\|-
			\| logshearrate \|\| log of shear rate corresponding to a viscosity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|1/(time units]] \|\| none
	\|-		\|-
	\| alpha \|\| Linear thermal expansion coefficient (β<sub>0</sub> = 3α) \|\| ppm/K \|\| 0		\| alpha \|\| Linear thermal expansion coefficient (β<sub>0</sub> = 3α) \|\| ppm/K \|\| 0
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	\| ([[Common Material Properties\|other]]) \|\| Properties common to all materials \|\| varies \|\| varies		\| ([[Common Material Properties\|other]]) \|\| Properties common to all materials \|\| varies \|\| varies
	\|}		\|}

			If one <tt>viscosity</tt> is given and no <tt>logshearrate</tt>, the material has constant viscosity. If multiple <tt>logshearrate</tt> and <tt>viscosity</tt> commands are used, each pair defines points for piecewise linear representation of viscosity as a function of log shear rate. You must enter an equal number of <tt>logshearrate</tt> and <tt>viscosity</tt> commands with monotonically increasing shear rates. The liquid's viscosity will be interpolated within the provided points. Shear rates below the minimum or above the maximum provided shear rates will be equal to the viscosity at the minimum or maximum shear rate, respectively.

	Note that when initial pressure is set, the mass of each particle will be adjusted to fill the initial particle volume under the set pressure. THe particle deformation tracked during the simulation will be the deformation relative to the initial state under pressure. The particle's relative volume, which is tracked in [[#History Variables\|history variable 1]], will be relative to the pressure-free state and thus will include volume change due to the initial pressure.		Note that when initial pressure is set, the mass of each particle will be adjusted to fill the initial particle volume under the set pressure. THe particle deformation tracked during the simulation will be the deformation relative to the initial state under pressure. The particle's relative volume, which is tracked in [[#History Variables\|history variable 1]], will be relative to the pressure-free state and thus will include volume change due to the initial pressure.

Nairnj: /* Shear Stress */

2016-05-04T17:13:49Z

Shear Stress

← Older revision		Revision as of 17:13, 4 May 2016
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	<math>\tau = \eta \left(\nabla \mathbf{v} + \nabla \mathbf{v}^T - {2\over 3}{\rm Tr}(\nabla \mathbf{v})\mathbf{I}\right)</math>		<math>\tau = \eta(\dot\gamma) \left(\nabla \mathbf{v} + \nabla \mathbf{v}^T - {2\over 3}{\rm Tr}(\nabla \mathbf{v})\mathbf{I}\right) = 2 \eta(\dot\gamma) {\rm dev}(\nabla v)</math>

	where <math>\nabla \mathbf{v}</math> is the velocity gradient and <math>\eta</math> is the viscosity. The total stress is given by <math> \mathbf{\sigma} = -p \mathbf{I} + \tau</math>		where <math>\nabla \mathbf{v}</math> is the velocity gradient and <math>\eta(\dot\gamma)</math> is the viscosity at a given shear rate. The total stress is given by <math> \mathbf{\sigma} = -p \mathbf{I} + \tau</math>.

			If the material is assigned only a viscosity, then <math>\eta(\dot\gamma)</math> in independent of shear rate describing a Newtonian fluid. Alternatively, you can enter any arbitrary shear-rate dependence of viscosity for the material. The shear rate is defined by


			<math>\dot\gamma = 2 \|{\rm dev}(\nabla v)\|</math>

	=== Pressure-Dependent Properties ===		=== Pressure-Dependent Properties ===

Nairnj: /* Material Properties */

2015-06-02T22:56:41Z

Material Properties

← Older revision		Revision as of 22:56, 2 June 2015
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	\| K \|\| Zero-pressure, bulk modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none		\| K \|\| Zero-pressure, bulk modulus \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|pressure units]] \|\| none
	\|-		\|-
	\| viscosity \|\| Liquid viscosity ~~(1 Pa-sec = 1000 cP)~~ \|\| cP \|\| none		\| viscosity \|\| Liquid viscosity \|\| [[ConsistentUnits Command#Legacy and Consistent Units\|voscosity units]] \|\| none
	\|-		\|-
	\| alpha \|\| Linear thermal expansion coefficient (β<sub>0</sub> = 3α) \|\| ppm/K \|\| 0		\| alpha \|\| Linear thermal expansion coefficient (β<sub>0</sub> = 3α) \|\| ppm/K \|\| 0