Transversely Isotropic Material - Revision history

Nairnj: /* Material Properties */

2023-02-03T00:33:06Z

Material Properties

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	\| alphaT \|\| Transverse thermal expansion coefficient \|\| ppm/K \|\| 40		\| alphaT \|\| Transverse thermal expansion coefficient \|\| ppm/K \|\| 40
	\|-		\|-
	\| swapz \|\| Set to >0 to move axial direction from ''z'' axis to the ''y'' axis (or from θ axis to ''Z'' axis in axisymmetric calculations). This property is not allowed in 3D MPM simulations. \|\| none \|\| 0		\| swapz \|\| Set to >0 to move axial direction from ''z'' axis to the ''y'' axis (or from θ axis to ''Z'' axis in axisymmetric calculations). This property is only needed for 2D simulations that want axial direction in the analysis plane (it is not allowed in 3D MPM simulations). \|\| none \|\| 0
	\|}		\|}

Nairnj: /* Material Properties */

2023-01-31T03:56:55Z

Material Properties

← Older revision		Revision as of 03:56, 31 January 2023
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	\| alphaT \|\| Transverse thermal expansion coefficient \|\| ppm/K \|\| 40		\| alphaT \|\| Transverse thermal expansion coefficient \|\| ppm/K \|\| 40
	\|-		\|-
	\| swapz \|\| Set to >0 to move axial direction ~~for~~ ''z'' axis to the ''y'' axis (or from θ axis to ''Z'' axis in axisymmetric calculations. This property is not allowed in 3D MPM simulations. \|\| none \|\| 0		\| swapz \|\| Set to >0 to move axial direction from ''z'' axis to the ''y'' axis (or from θ axis to ''Z'' axis in axisymmetric calculations). This property is not allowed in 3D MPM simulations. \|\| none \|\| 0
	\|}		\|}

Nairnj: /* Material Properties */

2023-01-31T01:45:36Z

Material Properties

← Older revision		Revision as of 01:45, 31 January 2023
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	== Material Properties ==		== Material Properties ==

	~~The properties for [[#Transverse 1\|Transverse 1]] and [[#Transverse 2\|Transverse 2]] are the same, although their initial orientations are different.~~ The properties are		The properties are

	{\| class="wikitable"		{\| class="wikitable"

Nairnj: /* Rotated Material Axes */

2023-01-31T01:44:50Z

Rotated Material Axes

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	As defined, transversely isotropic materials have their axial direction along the ''z'' axis. You can change to any other orientation when defining material points (in MPM) or elements (in FEA) by selecting rotations angles for MPM particles or FEA elements.		As defined, transversely isotropic materials have their axial direction along the ''z'' axis. You can change to any other orientation when defining material points (in MPM) or elements (in FEA) by selecting rotations angles for MPM particles or FEA elements.

	In 2D, however, the only rotation angle that is allowed is about the ''z'' axis, which means the axial direction will always be along the ''z'' axis. To allow simulations with axial direction in the plane of a 2D analysis, set the material <tt>swapz</tt> property greater than zero. When that property is used, the initial material will have its axial direction along the ''y'' axis and the ''x-z'' plane will be isotropic. You can rotate as needed about the ''z'' axis to orient the axial direction anywhere in the ''x-y'' plane.		In 2D, however, the only rotation angle that is allowed is about the ''z'' axis, which means the axial direction will always be along the ''z'' axis. To allow simulations with axial direction in the plane of a 2D analysis, set the material <tt>swapz</tt> property greater than zero. When that property is used, the initial material will have its axial direction along the ''y'' axis and the ''x-z'' plane will be isotropic. You can rotate as needed about the ''z'' axis to orient the axial direction anywhere in the ''x-y'' plane. For axisymmetric calculations, the <tt>swapz</tt> property changes axial direction from θ direction to the ''Z'' direction and the ''r-θ'' plane becomse the isotropic plane. You can reoriented the axial direction as needed in the ''R-Z'' plane.

	~~For axisymmetric calculations~~, the <tt>swapz</tt> ~~property changes axial direction from θ direction~~ to the ~~''Z'' direction and the ''r~~-~~θ'' plane becomse the isotropic~~ plane. ~~You can reoriented the axial direction as needed in the ''R~~-~~Z''~~ plane.		Note that for 2D analyses, the axial direction has to be either in the x-y plane (<tt>swapz=0</tt>) or normal to the x-y plane (<tt>swapz=1</tt> with optional rotations). Any other orientation would induce out-of-plane shear that is not allowed in 2D calculations. To handle such material orientations, you need to use 3D calculations (MPM only).

	The <tt>swapz</tt> property is not allowed in 3D MPM simulations; use material point rotation angles instead to get any desired material orientation.		The <tt>swapz</tt> property is not allowed in 3D MPM simulations; use material point rotation angles instead to get any desired material orientation.

Nairnj: /* Material Properties */

2023-01-31T01:43:03Z

Material Properties

← Older revision		Revision as of 01:43, 31 January 2023
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	\|}		\|}

	~~[[#Transverse 1\|~~Transverse 1]] and ~~[[#~~Transverse 2~~\|Transverse 2]] give identical materials but with different initial orientations~~. ~~You~~ can ~~change to any other orientation when defining~~ material ~~points (in MPM) or elements (in FEA) by selecting rotations angles for particles or elements. In 2D~~, ~~the only rotation angle that is allowed is about the z axis~~. ~~Because there~~ is ~~only one rotation angle, you need both~~ material ~~types to allow you to specify all possible orientations for 2D analysis of transversely isotropic materials~~. ~~In other words, for 2D analysis, the axial direction has to be either in the x-y plane ([[#~~Transverse 2~~\|Transverse 2]]) or normal~~ to ~~the x-y plane ([[#Transverse 1\|Transverse~~ 1~~]]). Any other orientation would induce out-of-plane shear that is not allowed in 2D calculations. To handle such material orientations, you need to use 3D calculations (MPM only)~~.		=== Deprecated Material Properties ===

			Prior to the <tt>swapz</tt> material property, there were two types on transversely isotropic material named "Transverse 1" and "Transverse 2". Although these can still be used as the material type, they are deprecated. The prior "Transverse 1" is identical to this material with <tt>swapz=0</tt>. The prior "Transverse 2" material is identical to this material with <tt>swapz=1</tt>.

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

Nairnj: /* Material Properties */

2023-01-31T01:38:22Z

Material Properties

← Older revision		Revision as of 01:38, 31 January 2023
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	\|-		\|-
	\| alphaT \|\| Transverse thermal expansion coefficient \|\| ppm/K \|\| 40		\| alphaT \|\| Transverse thermal expansion coefficient \|\| ppm/K \|\| 40
			\|-
			\| swapz \|\| Set to >0 to move axial direction for ''z'' axis to the ''y'' axis (or from θ axis to ''Z'' axis in axisymmetric calculations. This property is not allowed in 3D MPM simulations. \|\| none \|\| 0
	\|}		\|}

Nairnj at 01:35, 31 January 2023

2023-01-31T01:35:31Z

← Older revision		Revision as of 01:35, 31 January 2023
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	This transversely isotropic material is a special case of an [[Orthotropic Material\|orthotropic material]] where <math>E_{x}=E_{y}=E_T</math>, <math>E_{z}=E_A</math>, <math>\nu_{xy}=\nu_{yx}=\nu_T</math>, <math>\nu_{xz}=E_T\nu_A/E_A</math>, <math>\nu_{zx}=\nu_A</math>, <math>\nu_{yz}=E_T\nu_A/E_A</math>, <math>\nu_{zy}=\nu_A</math>, <math>G_{xy}=G_T=E_T/(2(1+\nu_T))</math>, <math>G_{xz}=G_{yz}=G_A</math>, <math>\alpha_{x}=\alpha_{y}=\alpha_T</math>, <math>\alpha_{z}=\alpha_A</math>, <math>\beta_{x}=\beta_{y}=\beta_T</math>, and <math>\beta_{z}=\beta_A</math>.		This transversely isotropic material is a special case of an [[Orthotropic Material\|orthotropic material]] where <math>E_{x}=E_{y}=E_T</math>, <math>E_{z}=E_A</math>, <math>\nu_{xy}=\nu_{yx}=\nu_T</math>, <math>\nu_{xz}=E_T\nu_A/E_A</math>, <math>\nu_{zx}=\nu_A</math>, <math>\nu_{yz}=E_T\nu_A/E_A</math>, <math>\nu_{zy}=\nu_A</math>, <math>G_{xy}=G_T=E_T/(2(1+\nu_T))</math>, <math>G_{xz}=G_{yz}=G_A</math>, <math>\alpha_{x}=\alpha_{y}=\alpha_T</math>, <math>\alpha_{z}=\alpha_A</math>, <math>\beta_{x}=\beta_{y}=\beta_T</math>, and <math>\beta_{z}=\beta_A</math>.

	== ~~Transverse 2~~ ==		=== Rotated Material Axes ===

	~~In this~~ transversely isotropic [[Material Models\|MPM material]] (or [[FEA Material Models\|FEA material]]), the isotropic plane is the x-z plane. The axial direction is along the y axis, which is in the plane for 2D analyses. For axisymmetric analyses, the isotropic plane is the r-θ plane and the axial direction is along the ~~z axis. The stiffness and compliance tensors are derived from those [[#Transvers 1\|above]] by interchanging ''y'' (2) and~~ ''z'' ~~(3) entries as well as ''xz'' (5) and ''xy'' (6) entries~~. ~~The thermal and solvent expansion tensors just interchange ''y''~~ (2) ~~and ''z''~~ (3) ~~entries. All properties are set as explained [[#Material Properties\|below]]~~.		As defined, transversely isotropic materials have their axial direction along the ''z'' axis. You can change to any other orientation when defining material points (in MPM) or elements (in FEA) by selecting rotations angles for MPM particles or FEA elements.

	~~The material~~ is ~~only~~ allowed ~~for~~ 2D ~~simulations when~~ the axial direction ~~lies~~ in the ~~analysis~~ ''x-y'' plane.		In 2D, however, the only rotation angle that is allowed is about the ''z'' axis, which means the axial direction will always be along the ''z'' axis. To allow simulations with axial direction in the plane of a 2D analysis, set the material <tt>swapz</tt> property greater than zero. When that property is used, the initial material will have its axial direction along the ''y'' axis and the ''x-z'' plane will be isotropic. You can rotate as needed about the ''z'' axis to orient the axial direction anywhere in the ''x-y'' plane.

			For axisymmetric calculations, the <tt>swapz</tt> property changes axial direction from θ direction to the ''Z'' direction and the ''r-θ'' plane becomse the isotropic plane. You can reoriented the axial direction as needed in the ''R-Z'' plane.

			The <tt>swapz</tt> property is not allowed in 3D MPM simulations; use material point rotation angles instead to get any desired material orientation.

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

Nairnj at 01:20, 31 January 2023

2023-01-31T01:20:14Z

← Older revision		Revision as of 01:20, 31 January 2023
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	In a transversely isotropic [[Material Models\|MPM material]] (or [[FEA Material Models\|FEA material]]), one plane is isotropic while the direction normal to that plane defines a unique axis with different properties. Properties in the isotropic plane are subscripted "T" for transverse plane properties and properties along the unique axis are subscripted "A" for axial properties.		In a transversely isotropic [[Material Models\|MPM material]] (or [[FEA Material Models\|FEA material]]), one plane is isotropic while the direction normal to that plane defines a unique axis with different properties. Properties in the isotropic plane are subscripted "T" for transverse plane properties and properties along the unique axis are subscripted "A" for axial properties.

	== Transverse 1 ==		== Transverse Material Properties ==

	~~In this~~ transversely isotropic [[Material Models\|MPM material]] (or [[FEA Material Models\|FEA material]]), the isotropic plane is the x-y plane, which is the plane for 2D or axisymmetric analyses. The axial direction is along the z axis, which is in the thickness direction for 2D analyses or the hoop direction for axisymmetric ~~anlayses~~. The stiffness and compliance tensors are:		When created, the transversely isotropic [[Material Models\|MPM material]] (or [[FEA Material Models\|FEA material]]), the isotropic plane is the x-y plane, which is the plane for 2D or axisymmetric analyses. The axial direction is along the z axis, which is in the thickness direction for 2D analyses or the hoop direction for axisymmetric analyses. The stiffness and compliance tensors are:

Nairnj: /* Constitutive Law */

2023-01-31T01:15:28Z

Constitutive Law

← Older revision		Revision as of 01:15, 31 January 2023
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	and the order of the shear terms is by the standard convention. The stiffness and compliance tensors contract to 6X6 matrices while all thermal and moisture expansion tensors contract to a vector. When used as an [[FEA Material Models\|FEA material]], the solvent expansion and solvent concentration terms are not used.		and the order of the shear terms is by the standard convention. The stiffness and compliance tensors contract to 6X6 matrices while all thermal and moisture expansion tensors contract to a vector. When used as an [[FEA Material Models\|FEA material]], the solvent expansion and solvent concentration terms are not used.

	In a transversely isotropic [[Material Models\|MPM material]] (or [[FEA Material Models\|FEA material]]), one plane is isotropic while the direction normal to that plane defines a unique axis with different properties. Properties in the isotropic plane are subscripted "T" for transverse plane properties and properties along the unique axis are subscripted "A" for axial properties. You can pick from two types of transversely isotropic materials, which differ only by orientation on the unique axes. The only reason two are needed is for 2D modeling Without two variations, 2D calculations could not model both when the isotropic plane as the analysis plane (use [[#Transverse 1\|Transverse 1]]) and when the axial direction is in the the analysis plane (use [[#Transverse 2\|Transverse 2]]). 3D modeling only needs one (and only [[#Transverse 1\|Transverse 1]] is allowed).		In a transversely isotropic [[Material Models\|MPM material]] (or [[FEA Material Models\|FEA material]]), one plane is isotropic while the direction normal to that plane defines a unique axis with different properties. Properties in the isotropic plane are subscripted "T" for transverse plane properties and properties along the unique axis are subscripted "A" for axial properties.

	== Transverse 1 ==		== Transverse 1 ==

Nairnj: /* Material Properties */

2021-02-17T22:50:30Z

Material Properties

← Older revision		Revision as of 22:50, 17 February 2021
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	<math>-1<\nu_T<1 \qquad ~~-\sqrt~~{~~E_A~~\~~over E_T~~} < \nu_A < \sqrt{~~E_A\over E_T} \qquad~~		<math>-1<\nu_T<1 \qquad {\rm and} \qquad
	{~~E_T\nu_A^2\over~~ E_A~~} < {~~1-\nu_T\over 2}</math>		\|\nu_A\| < \sqrt{{E_A(1-\nu_T)\over 2E_T}}</math>

	The following properties are only allowed in MPM calculations:		The following properties are only allowed in MPM calculations: