Joule heating arises when the energy dissipated by an electrical current flowing through a conductor is converted into thermal energy. ABAQUS/Standard provides a fully coupled thermal-electrical procedure for analyzing this type of problem; the coupled thermal-electrical equations are solved simultaneously for both temperature and electrical potential at the nodes. For more information, see Coupled thermal-electrical analysis, Section 6.6.2 of the ABAQUS Analysis User's Manual.
When you configure a fully coupled thermal-electric procedure, the step editor displays the Basic, Incrementation, and Other tabs. Settings you can configure with these tabbed pages include the time period for the step, increment size, and solution technique preferences.
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 omit the internal energy term (the specific heat term) in the governing heat transfer equation. Only direct current is considered in the electrical problem, and it is assumed that the system has negligible capacitance. (Electrical transient effects are so rapid that they can be neglected.) For more information, see Steady-state analysis” in “Coupled thermal-electrical analysis, Section 6.6.2 of the ABAQUS Analysis User's Manual.
Select Transient to perform time integration with the same backward Euler method used in uncoupled heat transfer analyses. This method is unconditionally stable for linear problems. For more information, see Transient analysis” in “Coupled thermal-electrical analysis, Section 6.6.2 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 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 in Step 2, enter a value for the constant time increment in the Increment size field.
If you selected Transient analysis on the Basic tabbed page, do the following:
Toggle on End step when temperature change is less than n if you want the analysis to end when the temperature at every temperature degree of freedom changes at a rate that is less than a rate that you specify. If you toggle on this option, enter the desired temperature change rate in the field provided.
If you selected Automatic in Step 2, enter a value for the Max. allowable temperature change per increment. 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.
If you selected Automatic in Step 2 and you are performing a cavity radiation analysis, enter a value for Max. allowable emissivity change per increment, or accept the default of 0.1. If this value is exceeded, ABAQUS/Standard cuts back the increment until the maximum change in emissivity is less than the specified value. See Cavity radiation, Section 32.1.1 of the ABAQUS Analysis User's Manual, for more information.
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.)
Select the Matrix storage option of your choice:
Select Use solver default to allow ABAQUS/Standard to decide whether a symmetric or unsymmetric matrix storage and solution scheme is needed.
Select Unsymmetric to restrict ABAQUS/Standard to the unsymmetric storage and solution scheme. (This is the only matrix storage option available if you select the Full Newton solution technique.)
Select Symmetric to restrict ABAQUS/Standard to the symmetric storage and solution scheme.
Select the Solution technique of your choice:
Select Full Newton to use Newton's method as a numerical technique for solving nonlinear equilibrium equations. For more information, see Nonlinear solution methods in ABAQUS/Standard, Section 2.2.1 of the ABAQUS Theory Manual.
Select Separated to specify that linearized equations for the individual fields in the fully coupled procedure are to be decoupled and solved separately for each field. This option provides a less costly solution for an analysis that is fully coupled in the sense that the electrical and thermal solutions evolve simultaneously, but with a weak coupling between the two solutions. For more information, see Approximate implementation” in “Coupled thermal-electrical analysis, Section 6.6.2 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.