Diffusion Calculations - Revision history

Nairnj at 17:24, 29 March 2026

2026-03-29T17:24:19Z

← Older revision		Revision as of 17:24, 29 March 2026
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	[[NairnMPM]] can do diffusion calculations coupled with stresses and strains through concentration-induced expansion.		[[NairnMPM]] can do diffusion calculations<ref name="transport"/> coupled with stresses and strains through concentration-induced expansion.
	__TOC__		__TOC__
	== Diffusion Modeling ==		== Diffusion Modeling ==

Nairnj: /* Diffusion Boundary Conditions */

2026-03-29T17:23:56Z

Diffusion Boundary Conditions

← Older revision		Revision as of 17:23, 29 March 2026
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	* You can set initial particle concentration when [[MPM Input Files#Creating the Material Points\|creating material points]]. Note, however, that initial concentrations different than the <math>\bar{c}_0</math> will cause strains to immediately evolve toward the changed state. The net effect will be an instantaneous "impact" that might cause undesirable dynamic effects. Using a [[PropertyRamp Custom Task]] is preferred method to set initial concentrations.		* You can set initial particle concentration when [[MPM Input Files#Creating the Material Points\|creating material points]]. Note, however, that initial concentrations different than the <math>\bar{c}_0</math> will cause strains to immediately evolve toward the changed state. The net effect will be an instantaneous "impact" that might cause undesirable dynamic effects. Using a [[PropertyRamp Custom Task]] is preferred method to set initial concentrations.
	* [[Rigid Material\|Rigid particles]] can provide moving concentration boundary conditions.		* [[Rigid Material\|Rigid particles]] can provide moving concentration boundary conditions.

			== References ==

			<references>

			<ref name="transport">J. A. Nairn, "Coupling Transport Equations to Mechanics in the Material Point Method Using an Approximate Full Capacity Matrix Inverse," ''Computer Methods in Applied Mechanics and Engineering'', '''420''', 116757 (2024). ([https://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/TransportPaper.pdf See PDF])</ref>

			</references>

Nairnj: /* Diffusion Modeling */

2024-05-01T20:41:02Z

Diffusion Modeling

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	Because <math>\bar{c}</math> is dimensionless, it can be defined using any consistent units for <math>c</math> and <math>c_{ref}</math>. When modeling composite materials, <math>c_{ref}</math> is a material property. Thermodynamic equilibrium in composites is when all phases reach the same chemical potential. The goal of diffusion modeling therefore is to pick <math>c_{ref}</math> for each material such that all materials have the same <math>\mu^{(ref)}</math>.		Because <math>\bar{c}</math> is dimensionless, it can be defined using any consistent units for <math>c</math> and <math>c_{ref}</math>. When modeling composite materials, <math>c_{ref}</math> is a material property. Thermodynamic equilibrium in composites is when all phases reach the same chemical potential. The goal of diffusion modeling therefore is to pick <math>c_{ref}</math> for each material such that all materials have the same <math>\mu^{(ref)}</math>.

	Once <math>c=c_{ref}</math> is picked for each material, all internal calculations are done using <math>\bar{c}</math>. Furthermore, concentration boundary conditions are expected to be in terms of dimensionless <math>\bar{c}</math> instead of terms raw concentration.		Once <math>c=c_{ref}</math> is picked for each material, all internal calculations are done using <math>\bar{c}</math>. Furthermore, concentration boundary conditions are expected to be in terms of dimensionless <math>\bar{c}</math> instead of in terms raw concentration.

	=== Reference and Saturation Concentration ===		=== Reference and Saturation Concentration ===

Nairnj: /* Activating Diffusion */

2023-08-23T23:26:24Z

Activating Diffusion

← Older revision		Revision as of 23:26, 23 August 2023
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	Note that diffusion models fluid transport through materials by transport methods nearly identical to those used to model [[Poroelasticity Calculations\|poroelasticity]]. Because they share same methods, a simulation can activate diffusion (with above commands) or poroelasticity (with comparable [[Poroelasticity Calculations\|Poroelasticity commands]]), but cannot activate them both. Any simulation, however, can combine diffusion or poroelasticity with [[Thermal Calculations\|thermal calculations and conduction]]. Note that when choosing [[MPM Input Files#Archiving Results\|archiving options]], the terms "concentration" and "porepressure" are synonyms or either can be used and the archiving will store concentration terms for diffusion calculations or pore pressure terms for [[Poroelasticity Calculations\|poroelasticity calculations]].		Note that diffusion models fluid transport through materials by transport methods nearly identical to those used to model [[Poroelasticity Calculations\|poroelasticity]]. Because they share same methods, a simulation can activate diffusion (with above commands) or poroelasticity (with comparable [[Poroelasticity Calculations\|Poroelasticity commands]]), but cannot activate them both. Any simulation, however, can combine diffusion or poroelasticity with [[Thermal Calculations\|thermal calculations and conduction]]. Note that when choosing [[MPM Input Files#Archiving Results\|archiving options]], the terms "concentration" and "porepressure" are synonyms or either can be used and the archiving will store concentration terms for diffusion calculations or pore pressure terms for [[Poroelasticity Calculations\|poroelasticity calculations]].

			Note that diffusion calculations are often improved by using [[PeriodicXPIC Custom Task#Using FMPM(k) For Transport Properties\|FMPM(k) methods]].

	== Diffusion Material Properties ==		== Diffusion Material Properties ==

Nairnj: /* Activating Diffusion */

2023-06-22T20:28:28Z

Activating Diffusion

← Older revision		Revision as of 20:28, 22 June 2023
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	* <tt>(YesOrNo)</tt> must be "Yes" or "No" to activate or not activate diffusion calculations. It can also be "solvent" to indicate diffusion of a liquid into another material. In <tt>XML</tt> input files, the presence of a <tt><Diffusion></tt> command activates diffusion (it can add a style='1' attribute).		* <tt>(YesOrNo)</tt> must be "Yes" or "No" to activate or not activate diffusion calculations. It can also be "solvent" to indicate diffusion of a liquid into another material. In <tt>XML</tt> input files, the presence of a <tt><Diffusion></tt> command activates diffusion (it can add a style='1' attribute).
	* <tt>(conc0)</tt> is used to set a concentration potential for the stress-free concentration potential or to enter <math>\bar{c}_0</math>. The default <tt>(conc0)</tt> is 0. All material points will be initialized to <math>\bar{c}</math> of <tt>(conc0)</tt> unless explicitly set to a different potential. Note that for historic reasons, <tt>XML</tt> input files sets <math>\bar{c}_0</math> with a "reference" attribute. The use of that name should not be confused with <math>c_{ref}</math> for each material, which is set with the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].		* <tt>(conc0)</tt> is used to set a concentration potential for the stress-free concentration potential or to enter <math>\bar{c}_0</math>. The default <tt>(conc0)</tt> is 0. All material points will be initialized to <math>\bar{c}</math> of <tt>(conc0)</tt> unless explicitly set to a different potential. Note that for historic reasons, <tt>XML</tt> input files sets <math>\bar{c}_0</math> with a "reference" attribute. The use of that name should not be confused with <math>c_{ref}</math> for each material, which is set with the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].
	* <tt>(nolimit)</tt> is used to select the diffusion model. If entered as "limit", the calculations interpret <math>c_{ref}</math> in each material to be defining a saturation constant and to limit <math>\bar{c}</math> to the interval [0,1]. To change to a model where <math>c_{ref}</math> has another meaning and <math>\bar{c}</math> can be any non-negative value, enter the text "nolimit" (or "1"). In <tt>XML</tt> input files, the "nolimit" attribute must be an ~~integer~~ and any ~~value~~ greater than zero ~~changes to allow any non-negative <math>\bar{c}</math>~~. The default (when omitted) is the "limit" ~~approach~~. The code output will ~~list~~ "0 <= c/csat <= 1" for "limit" mode and "c/csat >= 0" for "nolimit" mode.		* <tt>(nolimit)</tt> is used to select the diffusion model. If entered as "limit" (or "0"), the calculations interpret <math>c_{ref}</math> in each material to be defining a saturation constant and to limit <math>\bar{c}</math> to the interval [0,1]. To change to a model where <math>c_{ref}</math> has another meaning and <math>\bar{c}</math> can be any non-negative value, enter the text "nolimit" (or "1"). In <tt>XML</tt> input files, the "nolimit" attribute must be an "0" for "limit" mode or and any integer greater than zero for "nolimit" mode. The default (when omitted) is the "limit" mode. The code output will say "0 <= c/csat <= 1" for "limit" mode and "c/csat >= 0" for "nolimit" mode.

	By default, diffusion uses update methods analogous to FLIP methods used in mechanics. This update, however, sometimes results in concentration oscillations on particles within one cell. Diffusion simulations with oscillations can be improved by using [[PeriodicXPIC Custom Task#Using FMPM(k) For Transport Properties\|periodic FMPM(k)]] for diffusion updates.		By default, diffusion uses update methods analogous to FLIP methods used in mechanics. This update, however, sometimes results in concentration oscillations on particles within one cell. Diffusion simulations with oscillations can be improved by using [[PeriodicXPIC Custom Task#Using FMPM(k) For Transport Properties\|periodic FMPM(k)]] for diffusion updates.

Nairnj: /* Activating Diffusion */

2023-06-22T20:25:22Z

Activating Diffusion

← Older revision		Revision as of 20:25, 22 June 2023
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	* <tt>(YesOrNo)</tt> must be "Yes" or "No" to activate or not activate diffusion calculations. It can also be "solvent" to indicate diffusion of a liquid into another material. In <tt>XML</tt> input files, the presence of a <tt><Diffusion></tt> command activates diffusion (it can add a style='1' attribute).		* <tt>(YesOrNo)</tt> must be "Yes" or "No" to activate or not activate diffusion calculations. It can also be "solvent" to indicate diffusion of a liquid into another material. In <tt>XML</tt> input files, the presence of a <tt><Diffusion></tt> command activates diffusion (it can add a style='1' attribute).
	* <tt>(conc0)</tt> is used to set a concentration potential for the stress-free concentration potential or to enter <math>\bar{c}_0</math>. The default <tt>(conc0)</tt> is 0. All material points will be initialized to <math>\bar{c}</math> of <tt>(conc0)</tt> unless explicitly set to a different potential. Note that for historic reasons, <tt>XML</tt> input files sets <math>\bar{c}_0</math> with a "reference" attribute. The use of that name should not be confused with <math>c_{ref}</math> for each material, which is set with the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].		* <tt>(conc0)</tt> is used to set a concentration potential for the stress-free concentration potential or to enter <math>\bar{c}_0</math>. The default <tt>(conc0)</tt> is 0. All material points will be initialized to <math>\bar{c}</math> of <tt>(conc0)</tt> unless explicitly set to a different potential. Note that for historic reasons, <tt>XML</tt> input files sets <math>\bar{c}_0</math> with a "reference" attribute. The use of that name should not be confused with <math>c_{ref}</math> for each material, which is set with the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].
	* <tt>(nolimit)</tt> is used to select the diffusion model. If entered as "limit" ~~(or "0")~~, the calculations interpret <math>c_{ref}</math> in each material to be defining a saturation constant and to limit <math>\bar{c}</math> to the interval [0,1]. To change to a model where <math>c_{ref}</math> has another meaning and <math>\bar{c}</math> can be any non-negative value, enter the text "nolimit" (or "1"). In <tt>XML</tt> input files, the "nolimit" attribute must be an integer and any value greater than zero changes on allow any non-negative <math>\bar{c}</math>. The default ~~setting has varied with code versions, which means parameter should be set~~ (~~or double check output file to verify correct calculation mode~~). ~~Old versions that did not have the option always used the~~ "limit" mode.		* <tt>(nolimit)</tt> is used to select the diffusion model. If entered as "limit", the calculations interpret <math>c_{ref}</math> in each material to be defining a saturation constant and to limit <math>\bar{c}</math> to the interval [0,1]. To change to a model where <math>c_{ref}</math> has another meaning and <math>\bar{c}</math> can be any non-negative value, enter the text "nolimit" (or "1"). In <tt>XML</tt> input files, the "nolimit" attribute must be an integer and any value greater than zero changes to allow any non-negative <math>\bar{c}</math>. The default (when omitted) is the "limit" approach. The code output will list "0 <= c/csat <= 1" for "limit" mode and "c/csat >= 0" for "nolimit" mode.

	By default, diffusion uses update methods analogous to FLIP methods used in mechanics. This update, however, sometimes results in concentration oscillations on particles within one cell. Diffusion simulations with oscillations can be improved by using [[PeriodicXPIC Custom Task#Using FMPM(k) For Transport Properties\|periodic FMPM(k)]] for diffusion updates.		By default, diffusion uses update methods analogous to FLIP methods used in mechanics. This update, however, sometimes results in concentration oscillations on particles within one cell. Diffusion simulations with oscillations can be improved by using [[PeriodicXPIC Custom Task#Using FMPM(k) For Transport Properties\|periodic FMPM(k)]] for diffusion updates.

Nairnj: /* Activating Diffusion */

2023-06-22T20:13:46Z

Activating Diffusion

← Older revision		Revision as of 20:13, 22 June 2023
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	* <tt>(YesOrNo)</tt> must be "Yes" or "No" to activate or not activate diffusion calculations. It can also be "solvent" to indicate diffusion of a liquid into another material. In <tt>XML</tt> input files, the presence of a <tt><Diffusion></tt> command activates diffusion (it can add a style='1' attribute).		* <tt>(YesOrNo)</tt> must be "Yes" or "No" to activate or not activate diffusion calculations. It can also be "solvent" to indicate diffusion of a liquid into another material. In <tt>XML</tt> input files, the presence of a <tt><Diffusion></tt> command activates diffusion (it can add a style='1' attribute).
	* <tt>(conc0)</tt> is used to set a concentration potential for the stress-free concentration potential or to enter <math>\bar{c}_0</math>. The default <tt>(conc0)</tt> is 0. All material points will be initialized to <math>\bar{c}</math> of <tt>(conc0)</tt> unless explicitly set to a different potential. Note that for historic reasons, <tt>XML</tt> input files sets <math>\bar{c}_0</math> with a "reference" attribute. The use of that name should not be confused with <math>c_{ref}</math> for each material, which is set with the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].		* <tt>(conc0)</tt> is used to set a concentration potential for the stress-free concentration potential or to enter <math>\bar{c}_0</math>. The default <tt>(conc0)</tt> is 0. All material points will be initialized to <math>\bar{c}</math> of <tt>(conc0)</tt> unless explicitly set to a different potential. Note that for historic reasons, <tt>XML</tt> input files sets <math>\bar{c}_0</math> with a "reference" attribute. The use of that name should not be confused with <math>c_{ref}</math> for each material, which is set with the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].
	* <tt>(nolimit)</tt> is used to select the diffusion model. ~~The default~~ (~~when this option is omitted~~) ~~is to~~ interpret <math>c_{ref}</math> in each material to be defining a saturation constant and to limit <math>\bar{c}</math> to the interval [0,1]. To change to a model where <math>c_{ref}</math> has another meaning and <math>\bar{c}</math> can be any non-negative value, enter the text "nolimit" or ~~any number greater than~~ 1. In <tt>XML</tt> input files, the "nolimit" attribute must be an integer and any value greater than zero changes on allow any non-negative <math>\bar{c}</math>.		* <tt>(nolimit)</tt> is used to select the diffusion model. If entered as "limit" (or "0"), the calculations interpret <math>c_{ref}</math> in each material to be defining a saturation constant and to limit <math>\bar{c}</math> to the interval [0,1]. To change to a model where <math>c_{ref}</math> has another meaning and <math>\bar{c}</math> can be any non-negative value, enter the text "nolimit" (or "1"). In <tt>XML</tt> input files, the "nolimit" attribute must be an integer and any value greater than zero changes on allow any non-negative <math>\bar{c}</math>. The default setting has varied with code versions, which means parameter should be set (or double check output file to verify correct calculation mode). Old versions that did not have the option always used the "limit" mode.

	By default, diffusion uses update methods analogous to FLIP methods used in mechanics. This update, however, sometimes results in concentration oscillations on particles within one cell. Diffusion simulations with oscillations can be improved by using [[PeriodicXPIC Custom Task#Using FMPM(k) For Transport Properties\|periodic FMPM(k)]] for diffusion updates.		By default, diffusion uses update methods analogous to FLIP methods used in mechanics. This update, however, sometimes results in concentration oscillations on particles within one cell. Diffusion simulations with oscillations can be improved by using [[PeriodicXPIC Custom Task#Using FMPM(k) For Transport Properties\|periodic FMPM(k)]] for diffusion updates.

Nairnj: /* Diffusion Modeling */

2023-06-12T18:21:31Z

Diffusion Modeling

← Older revision		Revision as of 18:21, 12 June 2023
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	Because <math>\bar{c}</math> is dimensionless, it can be defined using any consistent units for <math>c</math> and <math>c_{ref}</math>. When modeling composite materials, <math>c_{ref}</math> is a material property. Thermodynamic equilibrium in composites is when all phases reach the same chemical potential. The goal of diffusion modeling therefore is to pick <math>c_{ref}</math> for each material such that all materials have the same <math>\mu^{(ref)}</math>.		Because <math>\bar{c}</math> is dimensionless, it can be defined using any consistent units for <math>c</math> and <math>c_{ref}</math>. When modeling composite materials, <math>c_{ref}</math> is a material property. Thermodynamic equilibrium in composites is when all phases reach the same chemical potential. The goal of diffusion modeling therefore is to pick <math>c_{ref}</math> for each material such that all materials have the same <math>\mu^{(ref)}</math>.

	~~One~~ <math>c=c_{ref}</math> is picked for each material, all internal calculations are done using <math>\bar{c}</math>. Furthermore, concentration boundary conditions are expected to be in terms of dimensionless <math>\bar{c}</math> instead of terms raw concentration.		Once <math>c=c_{ref}</math> is picked for each material, all internal calculations are done using <math>\bar{c}</math>. Furthermore, concentration boundary conditions are expected to be in terms of dimensionless <math>\bar{c}</math> instead of terms raw concentration.

	=== Reference and Saturation Concentration ===		=== Reference and Saturation Concentration ===

Nairnj: /* Reference and Saturation Concentration */

2023-05-04T22:49:54Z

Reference and Saturation Concentration

← Older revision		Revision as of 22:49, 4 May 2023
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	The initial implementation of diffusion in [[NairnMPM]] was to model diffusion of solvents into solids including expansion due to solvent (''e.g.'', swelling of wood due to moisture content). Most results for such solvent effects are based on mass fraction solvent content and expansion coefficients are measured as swelling strain per weight fracture solvent. As a result, [[NairnMPM]] assumes <math>c</math> and <math>c_{ref}</math> are both mass fraction solvent and the reference state is set to the saturation limit for solvent content or <math>c_{sat}</math> (which is specified for each material type in [[Common Material Properties#Basic Properties\|basic material properties]]). By this model, concentration can never exceed saturation concentration meaning that the <math>\bar{c}</math> is restricted to the interval [0,1] and equilibrium conditions correspond to all particles being at the same <math>\bar{c}</math> (''i.e.'', at the same fracture of their saturation concentration).		The initial implementation of diffusion in [[NairnMPM]] was to model diffusion of solvents into solids including expansion due to solvent (''e.g.'', swelling of wood due to moisture content). Most results for such solvent effects are based on mass fraction solvent content and expansion coefficients are measured as swelling strain per weight fracture solvent. As a result, [[NairnMPM]] assumes <math>c</math> and <math>c_{ref}</math> are both mass fraction solvent and the reference state is set to the saturation limit for solvent content or <math>c_{sat}</math> (which is specified for each material type in [[Common Material Properties#Basic Properties\|basic material properties]]). By this model, concentration can never exceed saturation concentration meaning that the <math>\bar{c}</math> is restricted to the interval [0,1] and equilibrium conditions correspond to all particles being at the same <math>\bar{c}</math> (''i.e.'', at the same fracture of their saturation concentration).

	The saturation model is the default method for diffusion calculations but it can be changed by redefining <math>c_{ref}</math> with any other units. For example, one could model concentration in moles per unit volume (molar concentration). This model still uses <math>\bar{c}</math> but that potential can now exceed 1 or can have any non-negative value. For this approach to work in composites, <math>c_{ref}</math> can be any state but each material must ~~pick~~ <math>c_{ref}</math> such that all materials have the same chemical potential at their reference concentrations. Note that despite this change in meaning of <math>c_{ref}</math>, it is still entered using the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].		The saturation model is the default method for diffusion calculations but it can be changed by redefining <math>c_{ref}</math> with any other units. For example, one could model concentration in moles per unit volume (molar concentration). This model still uses <math>\bar{c}</math> but that potential can now exceed 1 or can have any non-negative value. For this approach to work in composites, <math>c_{ref}</math> can be any state but each material must define <math>c_{ref}</math> such that all materials have the same chemical potential at their reference concentrations. Note that despite this change in meaning of <math>c_{ref}</math>, it is still entered using the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].

	=== Stress-Free Concentration ===		=== Stress-Free Concentration ===

Nairnj: /* Reference and Saturation Concentration */

2023-05-04T22:47:24Z

Reference and Saturation Concentration

← Older revision		Revision as of 22:47, 4 May 2023
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	=== Reference and Saturation Concentration ===		=== Reference and Saturation Concentration ===

	The initial implementation of diffusion in [[NairnMPM]] was to model diffusion of solvents into solids including expansion due to solvent (''e.g.'', swelling of wood due to moisture ~~constant~~). Most results for such solvent effects are based on mass fraction solvent content and expansion coefficients are measured as swelling strain per weight fracture solvent. As a result, [[NairnMPM]] assumes <math>c</math> and <math>c_{ref}</math> are both mass fraction solvent and the reference state is set to the saturation limit for solvent content or <math>c_{sat}</math> (which is specified for each material type in [[Common Material Properties#Basic Properties\|basic material properties]]). By this model, concentration can never exceed saturation concentration meaning that the <math>\bar{c}</math> is restricted to the interval [0,1] and equilibrium conditions correspond to all particles being at the same <math>\bar{c}</math> (''i.e.'', at the same fracture of their saturation concentration).		The initial implementation of diffusion in [[NairnMPM]] was to model diffusion of solvents into solids including expansion due to solvent (''e.g.'', swelling of wood due to moisture content). Most results for such solvent effects are based on mass fraction solvent content and expansion coefficients are measured as swelling strain per weight fracture solvent. As a result, [[NairnMPM]] assumes <math>c</math> and <math>c_{ref}</math> are both mass fraction solvent and the reference state is set to the saturation limit for solvent content or <math>c_{sat}</math> (which is specified for each material type in [[Common Material Properties#Basic Properties\|basic material properties]]). By this model, concentration can never exceed saturation concentration meaning that the <math>\bar{c}</math> is restricted to the interval [0,1] and equilibrium conditions correspond to all particles being at the same <math>\bar{c}</math> (''i.e.'', at the same fracture of their saturation concentration).

	The saturation model is the default method for diffusion calculations but it can be changed by redefining <math>c_{ref}</math> with any other units. For example, one could model concentration in moles per unit volume (molar concentration). This model still uses <math>\bar{c}</math> but that potential can now exceed 1 or can have any non-negative value. For this approach to work in composites, <math>c_{ref}</math> can be any state but each material must pick <math>c_{ref}</math> such that all materials have the same chemical potential at their reference concentrations. Note that despite this change in meaning of <math>c_{ref}</math>, it is still entered using the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].		The saturation model is the default method for diffusion calculations but it can be changed by redefining <math>c_{ref}</math> with any other units. For example, one could model concentration in moles per unit volume (molar concentration). This model still uses <math>\bar{c}</math> but that potential can now exceed 1 or can have any non-negative value. For this approach to work in composites, <math>c_{ref}</math> can be any state but each material must pick <math>c_{ref}</math> such that all materials have the same chemical potential at their reference concentrations. Note that despite this change in meaning of <math>c_{ref}</math>, it is still entered using the <tt>csat</tt> [[Common Material Properties#Basic Properties\|material property]].