Mullins effect

Context:

For more information about the Mullins effect, including the meaning of the Mullins coefficients $r$ , $m$ , and $β$ , see Stress softening in elastomers.

From the menu bar in the Edit Material dialog box, select MechanicalDamage for ElastomersMullins Effect.
(For information on displaying the Edit Material dialog box, see Creating or editing a material.)
To define the Mullins data using material constants only, perform the following steps:
1. From the Definition field, select Constants.
2. To define material damage data that depend on temperature, toggle on Use temperature-dependent data.
  A column labeled Temp appears in the Data table.
3. To define behavior data that depend on field variables, click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables.
  Field variable columns appear in the Data table.
4. Enter damage parameters in the Data table:
  
  r
  
  Value of the $r$ coefficient in the Mullins effect model. $r$ must be greater than 1.
  
  m
  
  Value of the $m$ coefficient in the Mullins effect model. $m$ must be greater than or equal to zero, and the values of $m$ and $β$ cannot both be zero.
  
  beta
  
  Value of the $β$ coefficient in the Mullins effect model. $β$ must be greater than or equal to zero, and the values of $m$ and $β$ cannot both be zero.
  
  Temp
  
  Temperature, $θ$ .
  
  Field n
  
  Predefined field variables.
  
  If you include temperature values in your data, you can specify multiple rows of material data. 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.
To specify experimental unloading-reloading test data to calibrate the parameters for the Mullins effect, perform the following steps:
1. From the Definition field, select Test Data Input.
2. If desired, enter values for one or two of the damage parameters $r$ , $m$ , and $β$ from the Define Parameters options. For this type of Mullins effect definition, Abaqus/CAE uses test data you provide to calculate the remaining damage parameters.
  
  To provide a value for a damage parameter, toggle it on and specify its value in the appropriate field:
  
  r
  
  Value of the $r$ coefficient in the Mullins effect model. $r$ must be greater than 1.
  
  m
  
  Value of the $m$ coefficient in the Mullins effect model. $m$ must be greater than or equal to zero, and the values of $m$ and $β$ cannot both be zero.
  
  beta
  
  Value of the $β$ coefficient in the Mullins effect model. $β$ must be greater than or equal to zero, and the values of $m$ and $β$ cannot both be zero.
3. From the Add Test menu in the Edit Material dialog box, select Biaxial Test, Planar Test, or Uniaxial Test to add the selected type of unloading-reloading curve to the material model.
  You can add multiple versions of each type of test to the material model. Abaqus/CAE names each test you create according to its type and the order in which it was created, so the first two uniaxial material tests you define would be named Uniaxial Test 1 and Uniaxial Test 2.
4. In the Test data table, enter the test data for the selected test:
  
  Nominal Stress
  
  Nominal stress, $T_{U}$ .
  
  Nominal Strain
  
  Nominal strain, $ϵ_{U}$ .
  
  For detailed information on how to enter tabular data, see Entering tabular data.
5. Repeat the previous two steps to specify additional data calibration tests.
6. If you want to delete a calibration test, highlight its name in the Tests list and click Delete Test. When you delete a test, Abaqus/CAE removes the test from the list and renames the existing tests so that the test numbering remains consecutive. For example, if you create three biaxial tests and delete the first one (Biaxial Test 1), Biaxial Test 2 is renamed Biaxial Test 1, and Biaxial Test 3 is renamed Biaxial Test 2.
To define the Mullins effect by specifying the damage variable in the user subroutine UMULLINS in Abaqus/Standard and VUMULLINS in Abaqus/Explicit, perform the following steps:
1. From the Definition field, select User Defined.
2. In the Mullins Properties field, enter values to specify an array of material properties for this user-defined hyperelastic material. Abaqus/CAE uses this array to populate the variable PROPS passed to user subroutine UMULLINS and VUMULLINS.
See the following sections for more information:
Click OK to exit the material editor.