A mass diffusion analysis models the transient or steady-state diffusion of one material through another, such as the diffusion of hydrogen through a metal. 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. For more information, see Mass diffusion analysis, Section 6.8.1 of the ABAQUS Analysis User's Manual.
When you configure a mass diffusion procedure, the step editor displays the Basic, Incrementation, and Other tabs. Settings you can configure with these tabbed pages include steady-state or transient response and automatic or fixed incrementation.
To configure settings on the Basic tabbed page:
In the Edit Step dialog box, display the Basic tabbed page.
(For information on displaying the Edit Step dialog box, see Creating a step, Section 14.9.2, or Editing a step, Section 14.9.3.)
In the Description field, enter a short description of what occurs during this analysis step. ABAQUS stores the text that you enter in the output database, and the text is displayed in the state block by the Visualization module.
Select a Response option:
Select Steady-state to specify that the analysis provide the steady-state solution directly. The rate of change of concentration with respect to time is omitted from the governing diffusion equation in a steady-state analysis. For more information, see Steady-state analysis” in “Mass diffusion analysis, Section 6.8.1 of the ABAQUS Analysis User's Manual.
Select Transient to perform time integration with the backward Euler method. This method is unconditionally stable for linear problems. For more information, see Transient analysis” in “Mass diffusion analysis, Section 6.8.1 of the ABAQUS Analysis User's Manual.
Note: After you have selected a Response option, a message appears informing you that ABAQUS/Standard has selected the Default load variation with time option (located on the Other tabbed page) that corresponds to your Response selection. Click Dismiss to close the message dialog box.
In the Time period field, enter a time scale for the analysis.
To configure settings on the Incrementation tabbed page:
In the Edit Step dialog box, display the Incrementation tabbed page.
(For information on displaying the Edit Step dialog box, see Creating a step, Section 14.9.2, or Editing a step, Section 14.9.3.)
Select a Type option:
Select Automatic if you want ABAQUS/Standard to determine suitable time increment sizes.
Select Fixed to specify direct user control of the incrementation. ABAQUS/Standard uses an increment size that you specify as the constant increment size throughout the step.
In the Maximum number of increments field, enter the upper limit to the number of increments in the step. The analysis stops if this maximum is exceeded before ABAQUS/Standard arrives at the complete solution for the step.
If you selected Automatic incrementation in Step 2, enter values for Increment size:
In the Initial field, enter the initial time increment. ABAQUS/Standard modifies this value as required throughout the step.
In the Minimum field, enter the minimum time increment allowed. If ABAQUS/Standard needs a smaller time increment than this value, it terminates the analysis.
In the Maximum field, enter the maximum time increment allowed.
If you selected Fixed incrementation in Step 2, enter a value for the constant time increment in the Increment size field.
If you selected Automatic incrementation in Step 2 and Transient analysis on the Basic tabbed page, do the following:
Enter a value in the End step when normalized concentration change is less than n field. The analysis will end when all nodal normalized concentrations are changing at a rate that is less than the rate that you enter.
Enter a value in the Max. allowable normalized concentration change field. ABAQUS/Standard restricts the time step to ensure that this value is not exceeded at any node (except nodes with boundary conditions) during any increment of the step.
To configure settings on the Other tabbed page:
In the Edit Step dialog box, display the Other tabbed page.
(For information on displaying the Edit Step dialog box, see Creating a step, Section 14.9.2, or Editing a step, Section 14.9.3.)
Accept the selection of the Unsymmetric matrix storage and solution scheme. This scheme is the only Matrix storage option that is valid for mass diffusion analyses. For more information on matrix storage, see Matrix storage and solution scheme in ABAQUS/Standard” in “Procedures: overview, Section 6.1.1 of the ABAQUS Analysis User's Manual.
Click the arrow to the right of the Convert severe discontinuity iterations field, and select an option for dealing with severe discontinuities during nonlinear analysis:
Select Off to force a new iteration if severe discontinuities occur during an iteration.
Select On to estimate residual forces associated with severe discontinuities and to check whether the equilibrium tolerances are satisfied. A solution may converge if the severe discontinuities (such as penetrations or tensile contact forces) are small. This option also changes some time incrementation parameters and uses different criteria to determine whether to do another iteration or to make a new attempt with a smaller increment size.
Select Propagate from previous step to use the value specified in the previous general analysis step. This value appears in parenthesis to the right of the field.
ABAQUS/Standard automatically selects the Default load variation with time option that corresponds to your Response selection on the Basic tabbed page. It is recommended that you leave the Default load variation with time selection unchanged.
Click the arrow to the right of the Extrapolation of previous state at start of each increment field, and select a method for determining the first guess to the incremental solution:
Select Linear to indicate that the process is essentially monotonic and ABAQUS/Standard should use a 100% linear extrapolation, in time, of the previous incremental solution to begin the nonlinear equation solution for the current increment.
Select Parabolic to indicate that the process should use a quadratic extrapolation, in time, of the previous two incremental solutions to begin the nonlinear equation solution for the current increment.
Select None to suppress any extrapolation.
Once you have finished configuring settings for the step, click OK to close the Edit Step dialog box.