Transversely Isotropic Viscoelastic Material - Revision history

Nairnj: /* Material Properties */

2024-05-01T22:22:32Z

Material Properties

← Older revision		Revision as of 22:22, 1 May 2024
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	\| bTemp<br>bTValue \|\| Enter <tt>(bTemp,bTValue)</tt> pairs for piecewise interpolation of vertical temperature [[Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bTemp</tt> values monotonically increasing \|\| (degrees,none) \|\| none		\| bTemp<br>bTValue \|\| Enter <tt>(bTemp,bTValue)</tt> pairs for piecewise interpolation of vertical temperature [[Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bTemp</tt> values monotonically increasing \|\| (degrees,none) \|\| none
	\|-		\|-
	\| bConc<br>bCValue \|\| Enter <tt>(bConc,bCValue)</tt> pairs for piecewise interpolation of vertical concentration (or moisture) [[Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bConc</tt> values monotonically increasing \|\| none \|\| none		\| bConc<br>bCValue \|\| Enter <tt>(bConc,bCValue)</tt> pairs for piecewise interpolation of vertical concentration (or moisture) [[Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bConc</tt> values monotonically increasing. Enter with actual concentration and not concentration potential. \|\| none \|\| none
	\|-		\|-
	\| [[Transversely Isotropic Material#Material Properties\|TI Properties]] \|\| Enter thermal expansion, solvent expansion, and poroelasticity properties as usual for transversely isotropic materials. \|\| varies \|\| varies		\| [[Transversely Isotropic Material#Material Properties\|TI Properties]] \|\| Enter thermal expansion, solvent expansion, and poroelasticity properties as usual for transversely isotropic materials. \|\| varies \|\| varies

Nairnj: /* Material Properties */

2024-04-18T03:11:42Z

Material Properties

← Older revision		Revision as of 03:11, 18 April 2024
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	\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times (must be positive) \|\| none \|\| 0.0625		\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times (must be positive) \|\| none \|\| 0.0625
	\|-		\|-
	\| bTemp<br>bTValue \|\| Enter <tt>(bTemp,bTValue)</tt> pairs for piecewise interpolation of vertical temperature [[~~Isotropic~~ Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bTemp</tt> values monotonically increasing \|\| (degrees,none) \|\| none		\| bTemp<br>bTValue \|\| Enter <tt>(bTemp,bTValue)</tt> pairs for piecewise interpolation of vertical temperature [[Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bTemp</tt> values monotonically increasing \|\| (degrees,none) \|\| none
	\|-		\|-
	\| bConc<br>bCValue \|\| Enter <tt>(bConc,bCValue)</tt> pairs for piecewise interpolation of vertical concentration (or moisture) [[~~Isotropic~~ Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bConc</tt> values monotonically increasing \|\| none \|\| none		\| bConc<br>bCValue \|\| Enter <tt>(bConc,bCValue)</tt> pairs for piecewise interpolation of vertical concentration (or moisture) [[Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bConc</tt> values monotonically increasing \|\| none \|\| none
	\|-		\|-
	\| [[Transversely Isotropic Material#Material Properties\|TI Properties]] \|\| Enter thermal expansion, solvent expansion, and poroelasticity properties as usual for transversely isotropic materials. \|\| varies \|\| varies		\| [[Transversely Isotropic Material#Material Properties\|TI Properties]] \|\| Enter thermal expansion, solvent expansion, and poroelasticity properties as usual for transversely isotropic materials. \|\| varies \|\| varies

Nairnj: /* Material Properties */

2024-04-18T03:11:06Z

Material Properties

← Older revision		Revision as of 03:11, 18 April 2024
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	\|-		\|-
	\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times (must be positive) \|\| none \|\| 0.0625		\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times (must be positive) \|\| none \|\| 0.0625
			\|-
			\| bTemp<br>bTValue \|\| Enter <tt>(bTemp,bTValue)</tt> pairs for piecewise interpolation of vertical temperature [[Isotropic Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bTemp</tt> values monotonically increasing \|\| (degrees,none) \|\| none
			\|-
			\| bConc<br>bCValue \|\| Enter <tt>(bConc,bCValue)</tt> pairs for piecewise interpolation of vertical concentration (or moisture) [[Isotropic Viscoelastic Material#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bConc</tt> values monotonically increasing \|\| none \|\| none
	\|-		\|-
	\| [[Transversely Isotropic Material#Material Properties\|TI Properties]] \|\| Enter thermal expansion, solvent expansion, and poroelasticity properties as usual for transversely isotropic materials. \|\| varies \|\| varies		\| [[Transversely Isotropic Material#Material Properties\|TI Properties]] \|\| Enter thermal expansion, solvent expansion, and poroelasticity properties as usual for transversely isotropic materials. \|\| varies \|\| varies

Nairnj: /* Effective Time Implementation */

2024-04-18T03:09:29Z

Effective Time Implementation

← Older revision		Revision as of 03:09, 18 April 2024
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	== Effective Time Implementation ==		== Effective Time Implementation ==

	This material handles ~~variations in~~ temperature and solvent concentration by the same methods used for [[Viscoelastic Material#Effective Time Implementation\|isotropic viscoelastic materials]].		This material handles effect of temperature and solvent concentration on relaxation times by the same methods used for [[Viscoelastic Material#Effective Time Implementation\|isotropic viscoelastic materials]].

			== Elastic Mechanical Properties ==

			This material handles effect of temperature and solvent concentration on elastic properties by the same methods used for [[Viscoelastic Material#Elastic Mechanical Properties\|isotropic viscoelastic materials]].

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

Nairnj: /* Fibrous Materials */

2024-03-19T23:50:12Z

Fibrous Materials

← Older revision		Revision as of 23:50, 19 March 2024
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	Finally, any other material properties (such as thermal expansion coefficients) should be set to the special cases for an isotropic material.		Finally, any other material properties (such as thermal expansion coefficients) should be set to the special cases for an isotropic material.

	~~=== Fibrous Materials ===~~

	A potential use for a transversely isotropic viscoelastic material is to model fiber-reinforced composites including wood (although transversely isotropic is not a great model for wood because it cannot represent low transverse shear modulus compared to radial and tangential transverse tensile moduli). If the axial direction is the fiber direction, one might expect that time dependence will be much weaker in the axial direction than in the transverse direction. This behavior could be approximated by setting <math>n</math> and <math>\ell</math> independent of time. Because an elastic material has <math>n=E_A+4K_T\nu_A^2</math> and <math>\ell = 2K_t\nu_A</math>, this approximation implies <math>E_A</math>, <math>K_T</math>, and <math>\nu_A</math> are all independent of time. The final result is that only <math>G_T(t)</math> and <math>G_A(t)</math> are time dependent. This model is one approximation, but would have zero creep in the axial direction and therefore no use in modeling that response (unless experiments also show zero creep).

	A second option might be to let <math>K_T(t)</math> depend on time while <math>E_A</math> and <math>\nu_A</math> remain independent of time. This approach does not work and results in non-physical response to axial loading. The problem appears that it predicts that <math>n(t)</math> decreases in time. For isotropic materials, <math>n(t)</math> increases in time and it also likely increases for fibrous materials as well. In brief, to model viscoelastic properties of fibrous material that might include effects in the axial direction, the modeling will need to input all five time-dependent properties allowed by this material. Those properties should be based on experimental observations.

	== Effective Time Implementation ==		== Effective Time Implementation ==

Nairnj: /* Material Properties */

2024-03-19T23:49:16Z

Material Properties

← Older revision		Revision as of 23:49, 19 March 2024
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	\| Tref \|\| Reference temperature to shift relaxation times using the WLF equation. If <tt>Tref</tt><0, then no shifting is done and relaxation times will be independent of temperature. \|\| K \|\| -1		\| Tref \|\| Reference temperature to shift relaxation times using the WLF equation. If <tt>Tref</tt><0, then no shifting is done and relaxation times will be independent of temperature. \|\| K \|\| -1
	\|-		\|-
	\| C1 \|\| Coefficient in WLF equation used when <tt>Tref</tt>≥0 to shift relaxation times \|\| none \|\| 17.44		\| C1 \|\| Coefficient in WLF equation used when <tt>Tref</tt>≥0 to shift relaxation times. If the entered value is negative, the thermal shift switches to Arrhenious activation energy with ''ΔH<sub>a</sub> = -RC<sub>1</sub>'', \|\| none \|\| 17.44
	\|-		\|-
	\| C2 \|\| Coefficient in WLF equation used when <tt>Tref</tt>≥0 to shift relaxation times \|\| none \|\| 51.6		\| C2 \|\| Coefficient in WLF equation used when <tt>Tref</tt>≥0 to shift relaxation times (not used if ''C<sub>1</sub>'' is negative). \|\| none \|\| 51.6
	\|-		\|-
	\| mref \|\| Reference concentration to shift relaxation times using the WLF-style equation. If <tt>mref</tt><0, then no shifting is done and relaxation times will be independent of concentration. \|\| K \|\| -1		\| mref \|\| Reference concentration to shift relaxation times using the WLF-style equation. If <tt>mref</tt><0, then no shifting is done and relaxation times will be independent of concentration. \|\| K \|\| -1

Nairnj: /* Material Properties */

2024-03-19T20:19:25Z

Material Properties

← Older revision		Revision as of 20:19, 19 March 2024
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	Other elastic properties are given by		Other elastic properties are given by


	<math>\nu_A(0) = {\ell(0)\over 2K_T(0)}		<math>\nu_A(0) = {\ell(0)\over 2K_T(0)}
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	E_A(0) = n(0) - 4K_T(0)\nu_A^2 = n(0) - \frac{\ell(0)^2}{K_T(0)}		E_A(0) = n(0) - 4K_T(0)\nu_A^2 = n(0) - \frac{\ell(0)^2}{K_T(0)}
	</math>		</math>


	<math>\frac{1}{E_T(0)} = \frac{1}{4K_T(0)} +\frac{1}{4G_T(0)} + {\nu_A(0)^2\over E_A(0)}		<math>\frac{1}{E_T(0)} = \frac{1}{4K_T(0)} +\frac{1}{4G_T(0)} + {\nu_A(0)^2\over E_A(0)}

Nairnj: /* Material Properties */

2024-03-19T20:19:02Z

Material Properties

← Older revision		Revision as of 20:19, 19 March 2024
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	\|}		\|}

	The material properties need to define the time dependence 5 properties. The process for each one is to enter the long-term value first (GT0, GA0, KT0, en0, ell0) and then to follow each one by ntaus (only needed in <tt>XML</tt> files) and by one Pk and tauk value for each term in the series. ~~The elastic~~ values ~~for each property are calculated from the value~~ at time = zero. Other elastic properties are ~~then found from~~		The material properties need to define the time dependence 5 properties. The process for each one is to enter the long-term value first (GT0, GA0, KT0, en0, ell0) and then to follow each one by ntaus (only needed in <tt>XML</tt> files) and by one Pk and tauk value for each term in the series. Elastic value, or the property values at time zero, are sums of all Pk terms for that property. For example:


			<math>G_T(0) = G_{T0} + \sum_{k=1}^{N_{GT}} G_{Tk}
			</math>

			Other elastic properties are given by

	<math>\nu_A(0) = {\ell(0)\over 2K_T(0)}		<math>\nu_A(0) = {\ell(0)\over 2K_T(0)}
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	\qquad {\rm and} \qquad		\qquad {\rm and} \qquad
	\nu_T(0) = \frac{E_T(0)}{2G_T(0)}-1		\nu_T(0) = \frac{E_T(0)}{2G_T(0)}-1
	~~</math>~~

	~~The above initial values, or the properties at time zero, are sums of all Pk terms for that property. For example~~

	~~     ~~
	~~<math>G_T(0) = G_{T0} + \sum_{k=1}^{N_{GT}} G_{Tk}~~
	</math>		</math>

Nairnj: /* Material Properties */

2024-03-19T20:17:08Z

Material Properties

← Older revision		Revision as of 20:17, 19 March 2024
Line 116:		Line 116:
	\|}		\|}

	The material properties need to define the time dependence 5 properties ~~(when fibrous is 0)~~. The process for each one is to enter the long-term value first (GT0, GA0, KT0, en0, ell0) and then to follow each one by ntaus (only needed in <tt>XML</tt> files) and by one Pk and tauk value for each term in the series.		The material properties need to define the time dependence 5 properties. The process for each one is to enter the long-term value first (GT0, GA0, KT0, en0, ell0) and then to follow each one by ntaus (only needed in <tt>XML</tt> files) and by one Pk and tauk value for each term in the series. The elastic values for each property are calculated from the value at time = zero. Other elastic properties are then found from

	~~When fibrous is 1, you instead enter time-independent~~ values for ~~EA and nuA~~. ~~When fibrous is 0, their initial values calculated~~ from:


	<math>\nu_A(0) = {\ell(0)\over 2K_T(0)}		<math>\nu_A(0) = {\ell(0)\over 2K_T(0)}
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	E_A(0) = n(0) - 4K_T(0)\nu_A^2 = n(0) - \frac{\ell(0)^2}{K_T(0)}		E_A(0) = n(0) - 4K_T(0)\nu_A^2 = n(0) - \frac{\ell(0)^2}{K_T(0)}
	</math>		</math>

	~~The remaining, initial transverse properties are:~~


	<math>\frac{1}{E_T(0)} = \frac{1}{4K_T(0)} +\frac{1}{4G_T(0)} + {\nu_A(0)^2\over E_A(0)}		<math>\frac{1}{E_T(0)} = \frac{1}{4K_T(0)} +\frac{1}{4G_T(0)} + {\nu_A(0)^2\over E_A(0)}

Nairnj: /* Material Properties */

2024-03-19T20:14:53Z

Material Properties

← Older revision		Revision as of 20:14, 19 March 2024
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	\|}		\|}

	The material properties need to define the time dependence ~~of 3 properties (when fibrous is 1) or~~ 5 properties (when fibrous is 0). The process for each one is to enter the long-term value first (GT0, GA0, KT0, en0, ell0) and then to follow each one by ntaus (only needed in <tt>XML</tt> files) and by one Pk and tauk value for each term in the series.		The material properties need to define the time dependence 5 properties (when fibrous is 0). The process for each one is to enter the long-term value first (GT0, GA0, KT0, en0, ell0) and then to follow each one by ntaus (only needed in <tt>XML</tt> files) and by one Pk and tauk value for each term in the series.

	When fibrous is 1, you instead enter time-independent values for EA and nuA. When fibrous is 0, their initial values calculated from:		When fibrous is 1, you instead enter time-independent values for EA and nuA. When fibrous is 0, their initial values calculated from: