Defining time domain viscoelasticity

Context:

Abaqus assumes that the time domain viscoelasticity is defined by a Prony series expansion. You can specify the Prony series parameters directly for each term in the Prony series. Alternatively, Abaqus can calculate the terms in the Prony series using time-dependent creep test data, time-dependent relaxation test data, or frequency-dependent cyclic test data that you provide.

For more information on time domain viscoelasticity, see Time domain viscoelasticity.

From the menu bar in the Edit Material dialog box, select MechanicalElasticityViscoelastic.
(For information on displaying the Edit Material dialog box, see Creating or editing a material.)
Click the arrow to the right of the Domain field, and select Time.
Click the arrow to the right of the Time field, and select the option of your choice for determining viscoelastic material parameters:
- Select Prony if you want to enter the Prony series parameters for each term directly.
- Select Creep test data if you want Abaqus to calculate the parameters in the Prony series from creep test data that you provide. If you select this option, you must enter shear test data and/or volumetric test data in the Test Data Editor.
- Select Relaxation test data if you want Abaqus to calculate the Prony series parameters from relaxation test data. If you select this option, you must enter shear test data and/or volumetric test data in the Test Data Editor.
- Select Frequency data if you want Abaqus to calculate the Prony series parameters from frequency-dependent cyclic test data.
If you selected any of the test data options from the Time option list, you can specify two additional parameters related to the calibration of Prony series parameters:
- Click the arrows to the right of the Maximum number of terms in the Prony series field to specify the maximum number of terms (N) in the Prony series. Abaqus will perform the least-squares fit from $N = 1$ to $N =$ NMAX until convergence is achieved for the lowest N with respect to the error tolerance.
- In the Allowable average root-mean-square error field, enter the error tolerance for the data points in the least-squares fit.
If you selected Prony from the list of Time options, enter the Prony parameters in the Data table.

g_i Prony

Shear relaxation or shear traction relaxation modulus ratio, ${\bar{g}}_{i}^{P}$ .

k_i Prony

Bulk relaxation or normal traction relaxation modulus ratio, ${\bar{k}}_{i}^{P}$ .

tau_i Prony

Relaxation time, $τ_{i}$ .

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.
If you selected Frequency data from the list of Time options, enter the frequency-dependent test data in the Data table.

Omega g* real

Real part of $ω g^{*}$ .

Omega g* imag

Imaginary part of $ω g^{*}$ .

Omega k* real

Real part of $ω k^{*}$ .

Omega k* imag

Imaginary part of $ω k^{*}$ .

Frequency

Frequency, f, in cycles per time.

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.
If applicable, click Test Data to specify test data from which to define viscoelastic behavior. See the following sections for details:
To specify thermo-rheologically simple (TRS) temperature effects, use the Suboptions menu. For details, see Specifying thermo-rheologically simple (TRS) temperature dependence for time domain viscoelasticity.”
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).