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# Orthotropic diffusivity

For orthotropic diffusivity three values of diffusivity $( D _ { 1 1 } , D _ { 2 2 } , D _ { 3 3 } )$ are needed at each concentration, temperature, and field variable value.

Input File Usage: \*DIFFUSIVITY, TYPE=ORTHO

Abaqus/CAE Usage: Property module: material editor: Other→Mass Diffusion→Diffusivity: Type: Orthotropic

# Anisotropic diffusivity

For fully anisotropic diffusivity six values of diffusivity $( D _ { 1 1 } , D _ { 1 2 } , D _ { 2 2 } , D _ { 1 3 } , D _ { 2 3 } , D _ { 3 3 } )$ are needed at each concentration, temperature, and field variable value.

Input File Usage: \*DIFFUSIVITY, TYPE=ANISO

Abaqus/CAE Usage: Property module: material editor: Other→Mass Diffusion→Diffusivity: Type: Anisotropic

# Temperature-driven mass diffusion

The Soret effect factor, $\kappa _ { s }$ , governs temperature-driven mass diffusion. It can be defined as a function of concentration, temperature, and/or field variables in the context of the constitutive equation presented above. The Soret effect factor cannot be specified in conjunction with Fick’s law since it is calculated automatically in this case (see “Mass diffusion analysis,” Section 6.9.1).

Input File Usage: Use both of the following options to specify general temperature-driven mass diffusion:

\*DIFFUSIVITY, LAW=GENERAL

\*KAPPA, TYPE=TEMP

Use the following option to specify temperature-driven diffusion governed by Fick’s law:

\*DIFFUSIVITY, LAW=FICK

Abaqus/CAE Usage: Use the following options to specify general temperature-driven mass diffusion:

Property module: material editor: Other→Mass Diffusion→Diffusivity:

Law: General: Suboptions→Soret Effect

Use the following option to specify temperature-driven diffusion governed by Fick’s law:

Property module: material editor: Other→Mass Diffusion→Diffusivity:

Law: Fick

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# Pressure stress-driven mass diffusion

The pressure stress factor, $\kappa _ { p } { \mathrm { : } }$ , governs mass diffusion driven by the gradient of the equivalent pressure stress. It can be defined as a function of concentration, temperature, and/or field variables in the context of the constitutive equation presented above.

<table><tr><td>Input File Usage:</td><td>Use both of the following options:*DIFFUSIVITY, LAW=GENERAL*KAPPA, TYPE=PRESS</td></tr></table>

<table><tr><td>Abaqus/CAE Usage:</td><td>Property module: material editor: Other→Mass Diffusion→Diffusivity: Law: General: Suboptions→Pressure Effect</td></tr></table>

# Mass diffusion driven by both temperature and pressure stress

Specifying both $\kappa _ { s }$ and $\kappa _ { p }$ causes gradients of temperature and equivalent pressure stress to drive mass diffusion.

Input File Usage: Use all of the following options to specify general diffusion driven by gradients of temperature and pressure stress:

<table><tr><td>*DIFFUSIVITY, LAW=GENERAL</td></tr><tr><td>*KAPPA, TYPE=TEMP</td></tr><tr><td>*KAPPA, TYPE=PRESS</td></tr></table>

Use both of the following options to specify diffusion driven by the extended form of Fick’s law:

<table><tr><td>*DIFFUSIVITY, LAW=FICK</td></tr><tr><td>*KAPPA, TYPE=PRESS</td></tr></table>

Abaqus/CAE Usage: Use the following options to specify general diffusion driven by gradients of temperature and pressure stress:

Property module: material editor: Other→Mass Diffusion→Diffusivity: Law: General: Suboptions→Soret Effect and Suboptions→Pressure Effect

Use the following options to specify diffusion driven by the extended form of Fick’s law:

Property module: material editor: Other→Mass Diffusion→Diffusivity: Law: Fick: Suboptions→Pressure Effect

# Specifying the value of absolute zero

You can specify the value of absolute zero as a physical constant.

Input File Usage: \*PHYSICAL CONSTANTS, ABSOLUTE ZER $\scriptstyle \mathrm { O = } \theta ^ { Z }$

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Abaqus/CAE Usage: Any module: Model→Edit Attributes→model\_name: Absolute zero temperature

# Elements

The mass diffusion law can be used only with the two-dimensional, three-dimensional, and axisymmetric solid elements that are included in the heat transfer/mass diffusion element library.

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# 26.4.2 SOLUBILITY

Products: Abaqus/Standard Abaqus/CAE

# References

• “Mass diffusion analysis,” Section 6.9.1   
• “Material library: overview,” Section 21.1.1   
• \*SOLUBILITY   
• “Defining solubility” in “Defining mass diffusion,” Section 12.12.2 of the Abaqus/CAE User’s Guide, in the HTML version of this guide

# Overview

Solubility:

• is needed only for mass diffusion analysis;   
• is also known as Sievert’s parameter (in Sievert’s law);   
• must always accompany a diffusivity definition (see “Diffusivity,” Section 26.4.1); and   
• can be defined as a function of temperature and/or predefined field variables.

# Defining solubility

Solubility, s, is used to define the “normalized concentration,” , of the diffusing phase in a mass diffusion process:

$$
\phi = c / s,
$$

where c is the concentration. The normalized concentration is often also referred to as the “activity” of the diffusing material, and the gradients of the normalized concentration, along with gradients of temperature and pressure stress, drive the diffusion process (see “Diffusivity,” Section 26.4.1).

Input File Usage: \*SOLUBILITY

Abaqus/CAE Usage: Property module: material editor: Other→Mass Diffusion→Solubility

# Elements

The mass diffusion law can be used only with the two-dimensional, three-dimensional, and axisymmetric solid elements that are included in the heat transfer/mass diffusion element library.

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# 26.5 Electromagnetic properties

• “Electrical conductivity,” Section 26.5.1   
• “Piezoelectric behavior,” Section 26.5.2   
• “Magnetic permeability,” Section 26.5.3

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# 26.5.1 ELECTRICAL CONDUCTIVITY

Products: Abaqus/Standard Abaqus/CAE

# References

• “Material library: overview,” Section 21.1.1   
• \*ELECTRICAL CONDUCTIVITY   
• “Defining electrical conductivity,” Section 12.11.1 of the Abaqus/CAE User’s Guide, in the HTML version of this guide

# Overview

A material’s electrical conductivity:

• must be defined for “Coupled thermal-electrical analysis,” Section 6.7.3;   
• must be defined for “Fully coupled thermal-electrical-structural analysis,” Section 6.7.4;   
• must be used to define the electromagnetic response of a conductor for “Eddy current analysis,” Section 6.7.5;   
• can be linear or nonlinear (by defining it as a function of temperature);   
• can be isotropic, orthotropic, or fully anisotropic;   
• can be specified as a function of temperature and/or field variables; and   
• can be specified as a function of frequency for “Eddy current analysis,” Section 6.7.5.

# Directional dependence of electrical conductivity

Isotropic, orthotropic, or fully anisotropic electrical conductivity can be defined. For non-isotropic conductivity a local orientation for the material directions must be specified (“Orientations,” Section 2.2.5).

# Isotropic electrical conductivity

For isotropic electrical conductivity only one value of electrical conductivity is needed at each temperature and field variable value. Isotropic electrical conductivity is the default.

Input File Usage: \*ELECTRICAL CONDUCTIVITY, TYPE=ISOTROPIC

Abaqus/CAE Usage: Property module: material editor: Electrical/Magnetic→Electrical Conductivity: Type: Isotropic

# Orthotropic electrical conductivity

For orthotropic electrical conductivity three values of electrical conductivity $( \sigma _ { 1 1 } ^ { E } , \sigma _ { 2 2 } ^ { E } , \sigma _ { 3 3 } ^ { E } )$ E are needed at each temperature and field variable value.

Input File Usage: \*ELECTRICAL CONDUCTIVITY, TYPE=ORTHOTROPIC

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Abaqus/CAE Usage: Property module: material editor: Electrical/Magnetic→Electrical Conductivity: Type: Orthotropic

# Anisotropic electrical conductivity

For fully anisotropic electrical conductivity six values $( \sigma _ { 1 1 } ^ { E } , \sigma _ { 1 2 } ^ { E } , \sigma _ { 2 2 } ^ { E } , \sigma _ { 1 3 } ^ { E } , \sigma _ { 2 3 } ^ { E } , \sigma _ { 3 3 } ^ { E } )$ E are needed at each temperature and field variable value.

Input File Usage: \*ELECTRICAL CONDUCTIVITY, TYPE=ANISOTROPIC

Abaqus/CAE Usage: Property module: material editor: Electrical/Magnetic→Electrical Conductivity: Type: Anisotropic

# Frequency-dependent electrical conductivity

Electrical conductivity can be defined as a function of frequency in an eddy current analysis.

Input File Usage: \*ELECTRICAL CONDUCTIVITY, FREQUENCY

Abaqus/CAE Usage: Property module: material editor: Electrical/Magnetic→Electrical Conductivity: Toggle on Use frequency-dependent data

# Elements

Electrical conductivity is active only in coupled thermal-electrical elements, coupled thermal-electricalstructural elements, and electromagnetic elements (see “Choosing the appropriate element for an analysis type,” Section 27.1.3).