ABAQUS/CAE User's Manual


12.10.3 Defining mass diffusion

You can use the Edit Material dialog box to define the following aspects of mass diffusion:

Defining diffusivity

Diffusivity defines the diffusion, or movement, of one material through another. The governing equations for mass diffusion are an extension of Fick's equations: they allow for nonuniform solubility of the diffusing substance in the base material and for mass diffusion driven by gradients of temperature and pressure. See the following sections for more information:

To define diffusivity:

  1. From the menu bar in the Edit Material dialog box, select OtherMass Diffusion Diffusivity.

    (For information on displaying the Edit Material dialog box, see “Creating or editing a material,” Section 12.6.1.)

  2. Click the arrow to the right of the Type field, and specify the directional dependence of the diffusivity.

  3. Select a Law option to specify how you want to define diffusivity behavior:

    • Select General to choose general mass diffusion behavior.

    • Select Fick to choose Fick's diffusion law.

    For more information, see “Defining diffusivity” in “Diffusivity,” Section 20.5.1 of the ABAQUS Analysis User's Manual.

  4. Toggle on Use temperature-dependent data to define diffusivity data as a function of temperature.

    A column labeled Temp appears in the Data table.

  5. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables on which the diffusivity data depend.

  6. In the Data table, enter the applicable data:

    D

    Isotropic diffusivity. (Units of L2T–1.) (For isotropic diffusion).

    D11, D22, and D33

    Orthotropic diffusivity terms. (Units of L2T–1.)

    D11, D12, D22, D13, D23, D33

    Anisotropic diffusivity terms. (Units of L2T–1.)

    Concentration

    Mass concentration of the diffusing material.

    Temp

    Temperature.

    Field n

    Predefined field variables.

    You may need to expand the dialog box to see all the columns in the Data table. For detailed information on how to enter data, see “Entering tabular data,” Section 3.2.7.

  7. To describe temperature-driven diffusion, select Soret Effect from the Suboptions menu. (This option is valid only if you selected General in Step 3.) See “Defining general temperature-driven mass diffusion.” in “Defining mass diffusion,” Section 12.10.3, for detailed instructions.

  8. To describe pressure-driven mass diffusion, select Pressure Effect from the Suboptions menu. See “Defining pressure-driven mass diffusion.” in “Defining mass diffusion,” Section 12.10.3, for detailed instructions.

  9. Click OK to close the Edit Material dialog box. Alternatively, you can select another material behavior to define from the menus in the Edit Material dialog box (see “Browsing and modifying material behaviors,” Section 12.6.2, for more information).

Defining general temperature-driven mass diffusion.

The Soret effect factor, , governs temperature-driven mass diffusion. You can define the Soret effect factor as a function of concentration, temperature, and/or field variables. See “Diffusivity,” Section 20.5.1 of the ABAQUS Analysis User's Manual, for more information.

Note:  You can specify the Soret effect factor only if you select general mass diffusion behavior in the diffusivity definition. (If you select Fick's diffusion law, the Soret effect factor is calculated automatically.) For more information, see “Fick's law” in “Mass diffusion analysis,” Section 6.8.1 of the ABAQUS Analysis User's Manual.

To define the Soret effect factor:

  1. From the Suboptions menu in the Edit Material dialog box, select Soret Effect.

    A Suboption Editor appears.

  2. Toggle on Use temperature-dependent data to define the Soret effect factor as a function of temperature.

    A column labeled Temp appears in the Data table.

  3. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables included in the definition of the Soret effect factor.

  4. Enter the following data in the Data table:

    kappa_s

    Soret effect factor, . (Units of F1/2L–1.)

    Concentration

    Mass concentration of the diffusing material.

    Temp

    Temperature.

    Field n

    Predefined field variables.

  5. Click OK to return to the Edit Material dialog box.

Defining pressure-driven mass diffusion.

The pressure stress factor, , governs mass diffusion driven by the gradient of the equivalent pressure stress. You can define the pressure stress factor as a function of concentration, temperature, and/or field variables. See “Diffusivity,” Section 20.5.1 of the ABAQUS Analysis User's Manual, for more information.

To define the pressure stress factor:

  1. From the Suboptions menu in the Edit Material dialog box, select Pressure Effect.

    A Suboption Editor appears.

  2. Toggle on Use temperature-dependent data to define the pressure stress factor as a function of temperature.

    A column labeled Temp appears in the Data table.

  3. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables included in the definition of the pressure stress factor.

  4. Enter the following data in the Data table:

    kappa_p

    Pressure stress factor, . (Units of LF–1/2.)

    Concentration

    Mass concentration of the diffusing material.

    Temp

    Temperature.

    Field n

    Predefined field variables.

  5. Click OK to return to the Edit Material dialog box.

Defining solubility

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

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. For more information, see the following sections:

To define solubility:

  1. From the menu bar in the Edit Material dialog box, select OtherMass Diffusion Solubility.

    (For information on displaying the Edit Material dialog box, see “Creating or editing a material,” Section 12.6.1.)

  2. Toggle on Use temperature-dependent data to define solubility as a function of temperature.

    A column labeled Temp appears in the Data table.

  3. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables on which the solubility depends.

  4. Enter the following data in the Data table:

    Solubility

    Solubility. (Units of PLF–1/2.)

    Temp

    Temperature.

    Field n

    Predefined field variables.

    For detailed information on how to enter data, see “Entering tabular data,” Section 3.2.7.

  5. Click OK to close the Edit Material dialog box. Alternatively, you can select another material behavior to define from the menus in the Edit Material dialog box (see “Browsing and modifying material behaviors,” Section 12.6.2, for more information).