Viscoelastic Material - Revision history

Nairnj: /* Variable Temperature */

2026-01-16T01:01:30Z

Variable Temperature

← Older revision		Revision as of 01:01, 16 January 2026
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	<math>\log a_T = \frac{\Delta H_a}{R\ln 10}\left(\frac{1}{T}-\frac{1}{T_{ref}}\right)</math>		<math>\log a_T = \frac{\Delta H_a}{R\ln 10}\left(\frac{1}{T}-\frac{1}{T_{ref}}\right)</math>

	where <math>\Delta H_a</math> is an apparent activation energy and ''R'' is the gas constant. This alternate shift factor is selected <tt>Tref</tt> and then setting ''C<sub>1</sub>'' to a negative number given by		where <math>\Delta H_a</math> is an apparent activation energy and ''R'' is the gas constant. This alternate shift factor is selected by entering <tt>Tref</tt> and then setting ''C<sub>1</sub>'' to a negative number given by


	<math>C_1 = -\frac{\Delta H_a}{R}</math>		<math>C_1 = -\frac{\Delta H_a}{R}</math>

	in units of degrees K.		in units of degrees K. The ''C<sub>2</sub>'' property is not used.

	=== Variable Solvent Concentration ===		=== Variable Solvent Concentration ===

Nairnj: /* Elastic Mechanical Properties */

2024-05-01T22:27:31Z

Elastic Mechanical Properties

← Older revision		Revision as of 22:27, 1 May 2024
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	<math>P(T,m) = b_Tb_mP(T_0,m_0)</math>		<math>P(T,m) = b_Tb_mP(T_0,m_0)</math>

	where <math>b_T</math> and <math>b_m</math> relative shifts of mechanical property <math>P(T,m)</math> as a function of temperature or moisture. The vertical shift factors are determined by entering any number of <math>(T,b_T)</math> and <math>(m,b_m)</math> pairs with monotonically increasing <math>T</math> and <math>m</math>. If simulation value is outside the entered range, it is found by linear extrapolation for first two or last two entered points. The reference temperature and moisture are arbitrary and equal to temperature where vertical shifts factors equal one. Note that vertical shifting can be used even when horizontal shifting is not used. Any ~~materials~~ that ~~enters 2 of more~~ pairs will calculate vertical ~~shifting~~.		where <math>b_T</math> and <math>b_m</math> relative shifts of mechanical property <math>P(T,m)</math> as a function of temperature or moisture. The vertical shift factors are determined by entering any number of <math>(T,b_T)</math> and <math>(m,b_m)</math> pairs with monotonically increasing <math>T</math> and <math>m</math>. If simulation value is outside the entered range, it is found by linear extrapolation for first two or last two entered points. The reference temperature and moisture are arbitrary and equal to temperature where vertical shifts factors equal one. Note that vertical shifting can be used even when horizontal shifting is not used. Any material that <math>(T,b_T)</math> or <math>(m,b_m)</math> pairs will calculate vertical shift factors.

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

Nairnj: /* Elastic Mechanical Properties */

2024-05-01T22:25:48Z

Elastic Mechanical Properties

← Older revision		Revision as of 22:25, 1 May 2024
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	<math>G(0) = G_e = G_0 + \sum_{i=1}^n G_i</math>		<math>G(0) = G_e = G_0 + \sum_{i=1}^n G_i</math>

	When simulations include a change in temperature or moisture, it is possible that both relaxations times and initial elastic properties will change. In time-temperature-superposition theory for time plots, these effects correspond to horizontal shifting (for ~~changed~~ in relaxation times) and vertical shifting (for changes in elastic properties). Vertical shifting is ~~model~~ in this material by setting all mechanical properties to		When simulations include a change in temperature or moisture, it is possible that both relaxations times and initial elastic properties will change. In time-temperature-superposition theory for time plots, these effects correspond to horizontal shifting (for changes in relaxation times) and vertical shifting (for changes in elastic properties). Vertical shifting is modeled in this material by setting all mechanical properties to


	<math>P(T,m) = b_Tb_mP(~~T_{ref}~~,~~m_{ref}~~)</math>		<math>P(T,m) = b_Tb_mP(T_0,m_0)</math>

	where <math>b_T</math> and <math>b_m</math> relative shifts of mechanical property <math>P(T,m)</math> as a function of temperature or moisture. The vertical shift factors are determined by entering any number of <math>(T,b_T)</math> and <math>(m,b_m)</math> pairs with monotonically increasing <math>T</math> and <math>m</math>. If simulation value is outside the entered range, it is found by linear extrapolation for first two or last two entered points.		where <math>b_T</math> and <math>b_m</math> relative shifts of mechanical property <math>P(T,m)</math> as a function of temperature or moisture. The vertical shift factors are determined by entering any number of <math>(T,b_T)</math> and <math>(m,b_m)</math> pairs with monotonically increasing <math>T</math> and <math>m</math>. If simulation value is outside the entered range, it is found by linear extrapolation for first two or last two entered points. The reference temperature and moisture are arbitrary and equal to temperature where vertical shifts factors equal one. Note that vertical shifting can be used even when horizontal shifting is not used. Any materials that enters 2 of more pairs will calculate vertical shifting.

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

Nairnj: /* Material Properties */

2024-04-18T03:06:38Z

Material Properties

← Older revision		Revision as of 03:06, 18 April 2024
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	\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times \|\| none \|\| 0.0625		\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times \|\| none \|\| 0.0625
	\|-		\|-
	\| bTemp<br>bTValue \|\| Enter <tt>(bTemp,bTValue)</tt> pairs for piecewise interpolation of vertical temperature 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 [[#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) 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) [[#Elastic Mechanical Properties\|shift of elastic properties]]. Enter any number of pairs with <tt>bConc</tt> values monotonically increasing \|\| none \|\| none
	\|-		\|-
	\| alpha \|\| Thermal expansion coefficient (ignored when using MGEOS law) \|\| ppm/K \|\| 40		\| alpha \|\| Thermal expansion coefficient (ignored when using MGEOS law) \|\| ppm/K \|\| 40

Nairnj: /* Material Properties */

2024-04-18T03:04:30Z

Material Properties

← Older revision		Revision as of 03:04, 18 April 2024
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	\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times \|\| none \|\| 0.0625		\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times \|\| none \|\| 0.0625
	\|-		\|-
	\| bTemp \|\| ~~Coefficient in WLF~~-~~style equation used when~~ <tt>~~mref~~</tt>~~≥0 to~~ shift ~~relaxation times~~ \|\| none \|\| 10		\| bTemp<br>bTValue \|\| Enter <tt>(bTemp,bTValue)</tt> pairs for piecewise interpolation of vertical temperature 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) shift of elastic properties. Enter any number of pairs with <tt>bConc</tt> values monotonically increasing \|\| none \|\| none
	\|-		\|-
	\| alpha \|\| Thermal expansion coefficient (ignored when using MGEOS law) \|\| ppm/K \|\| 40		\| alpha \|\| Thermal expansion coefficient (ignored when using MGEOS law) \|\| ppm/K \|\| 40

Nairnj: /* Material Properties */

2024-04-18T02:59:24Z

Material Properties

← Older revision		Revision as of 02:59, 18 April 2024
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	\|-		\|-
	\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times \|\| none \|\| 0.0625		\| Cm2 \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times \|\| none \|\| 0.0625
			\|-
			\| bTemp \|\| Coefficient in WLF-style equation used when <tt>mref</tt>≥0 to shift relaxation times \|\| none \|\| 10
	\|-		\|-
	\| alpha \|\| Thermal expansion coefficient (ignored when using MGEOS law) \|\| ppm/K \|\| 40		\| alpha \|\| Thermal expansion coefficient (ignored when using MGEOS law) \|\| ppm/K \|\| 40

Nairnj: /* Elastic Mechanical Properties */

2024-04-18T02:56:56Z

Elastic Mechanical Properties

← Older revision		Revision as of 02:56, 18 April 2024
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	<math>G() = G_e = G_0 + \sum_{i=1}^n G_i</math>		<math>G(0) = G_e = G_0 + \sum_{i=1}^n G_i</math>

			When simulations include a change in temperature or moisture, it is possible that both relaxations times and initial elastic properties will change. In time-temperature-superposition theory for time plots, these effects correspond to horizontal shifting (for changed in relaxation times) and vertical shifting (for changes in elastic properties). Vertical shifting is model in this material by setting all mechanical properties to


			<math>P(T,m) = b_Tb_mP(T_{ref},m_{ref})</math>

			where <math>b_T</math> and <math>b_m</math> relative shifts of mechanical property <math>P(T,m)</math> as a function of temperature or moisture. The vertical shift factors are determined by entering any number of <math>(T,b_T)</math> and <math>(m,b_m)</math> pairs with monotonically increasing <math>T</math> and <math>m</math>. If simulation value is outside the entered range, it is found by linear extrapolation for first two or last two entered points.

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

Nairnj: /* Elastic Mechanical Properties */

2024-04-18T02:44:51Z

Elastic Mechanical Properties

← Older revision		Revision as of 02:44, 18 April 2024
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	== Elastic Mechanical Properties ==		== Elastic Mechanical Properties ==

	The elastic properties of a viscoelastic material are the effective elastic properties at zero time.		The elastic properties of a viscoelastic material are the effective elastic properties at zero time. For example, the elastic shear modulus is


			<math>G() = G_e = G_0 + \sum_{i=1}^n G_i</math>

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

Nairnj: /* Effective Time Implementation */

2024-04-18T02:43:45Z

Effective Time Implementation

← Older revision		Revision as of 02:43, 18 April 2024
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	Simulations to include solvent effects on relaxations times must activate [[Diffusion Calculations]], and enter [[Common Material Properties\|material properties]] for saturation concentration, solvent expansion coefficient, and diffusion constants. Even constant-concentration simulations must activate diffusion calculations. To use constant concentration, set all particles to the same concentration (such that no diffusion occurs).		Simulations to include solvent effects on relaxations times must activate [[Diffusion Calculations]], and enter [[Common Material Properties\|material properties]] for saturation concentration, solvent expansion coefficient, and diffusion constants. Even constant-concentration simulations must activate diffusion calculations. To use constant concentration, set all particles to the same concentration (such that no diffusion occurs).

			== Elastic Mechanical Properties ==

			The elastic properties of a viscoelastic material are the effective elastic properties at zero time.

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

Nairnj: /* Variable Solvent Concentration */

2024-04-18T02:41:04Z

Variable Solvent Concentration

← Older revision		Revision as of 02:41, 18 April 2024
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	<math>\log a_m = \log \frac{\tau(m)}{\tau(m_{ref})} = - \frac{C_{m1}(m-m_{ref})}{C_{m2}+m-m_{ref}}</math>		<math>\log a_m = \log \frac{\tau(m)}{\tau(m_{ref})} = - \frac{C_{m1}(m-m_{ref})}{C_{m2}+m-m_{ref}}</math>

	This shift factor is implemented in simulations by entering <tt>mref</tt>, <tt>Cm1</tt>, and <tt>Cm2</tt>~~. Note that unlike the WLF equation, this equation does not include <math>m_{ref}</math> in the denominator~~.		This shift factor is implemented in simulations by entering <tt>mref</tt>, <tt>Cm1</tt>, and <tt>Cm2</tt>.

	If <math>C_{m1}</math> and <math>C_{m1}</math> are known at one <math>m_{ref}</math>, the shift relative to a new reference concentration, <math>m_{ref}'</math>, would be:		If <math>C_{m1}</math> and <math>C_{m1}</math> are known at one <math>m_{ref}</math>, the shift relative to a new reference concentration, <math>m_{ref}'</math>, would be: