Using a nonlinear isotropic/kinematic cyclic hardening model to define classical metal plasticity

Context:

You can define the kinematic hardening component by selecting Combined from the list of Hardening options in the Edit Material dialog box and entering the required data.

You can define the isotropic hardening component by selecting Cyclic Hardening from the Suboptions menu and entering data in the Suboption Editor that appears.

For more information on cyclic hardening, see Models for Metals Subjected to Cyclic Loading.

From the menu bar in the Edit Material dialog box, select MechanicalPlasticityPlastic.
(For information on displaying the Edit Material dialog box, see Creating or editing a material.)
Click the arrow to the right of the Hardening field, and select Combined.
Click the arrow to the right of the Data type field, and specify how you want to define the kinematic hardening component of the model:
- Select Half Cycle to provide stress-strain data obtained from the first half cycle of a unidirectional tension or compression experiment.
- Select Parameters to specify the kinematic hardening parameters $C_{k}$ and $γ_{k}$ directly.
- Select Stabilized to provide stress-strain data obtained from the stabilized cycle of a specimen that is subjected to symmetric strain cycles.
To specify the number of backstresses to include in the model, click the arrows to the right of the Number of backstresses field. The default number of backstresses is 1. The maximum number of backstresses allowed is 10.
If you selected Parameters from the list of Data type options, additional columns appear in the table to specify the kinematic hardening parameters for multiple backstresses.
Toggle on Use temperature-dependent data to define behavior data that depend on temperature.
A column labeled Temp appears in the Data table.
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.
If you selected Stabilized from the list of Data type options, you can choose to toggle on Use strain-range-dependent data. This option is useful if the shapes of the stress-strain curves are significantly different for different strain ranges.
In the Data table, enter the data relevant to your Data type selection (not all of the following parameters will apply):

Yield Stress

The stress at which yield is initiated.

Plastic Strain

Plastic strain.

Yield Stress At Zero Plastic Strain

Yield stress at zero plastic strain, ${σ |}_{0}$ .

Kinematic Hard Parameter C1

Kinematic hardening parameter, $C_{1}$ .

Gamma 1

Kinematic hardening parameter, $γ_{1}$ .

Kinematic Hard Parameter Ck and Gamma k

Kinematic hardening parameters $C_{k}$ and $γ_{k}$ for multiple backstresses.

Temp

Temperature.

Field n

Predefined field variables.

Strain Range

The strain range at which the stress-strain curve is obtained.

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 define the isotropic hardening component of the model, select Cyclic Hardening from the Suboptions menu, and enter the required data in the Suboption Editor that appears. See Defining the isotropic hardening component of a nonlinear isotropic/kinematic hardening model” for details.
If desired, use other options from the Suboptions menu to enter additional data. See the following sections for details:
- Defining anisotropic yield and creep”
- Specifying the annealing temperature of an elastic-plastic material”
Click OK to create the material and 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, for more information).