Defining frequency 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 Frequency.

Click the arrow to the right of the Frequency field, and select the option of your choice for determining viscoelastic material parameters:

• Select Formula to define the frequency dependence by the power law formulae.

• Select Tabular to define the frequency response in tabular form. You must provide the real and imaginary parts of $\omega g^{*}$ and $\omega k^{*}$—where $\omega$ is the circular frequency—as functions of frequency in cycles per time.

• Select Prony if you want Abaqus to calculate the frequency dependence from a time domain Prony series description of the dimensionless shear and bulk relaxation moduli.

• 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.

If you selected Creep test data or Relaxation test data from the Frequency 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 of the data points in the least-squares fit.

If you selected Tabular from the Frequency option list, you can specify two additional options:

Type

This parameter specifies whether you are defining continuum material properties or effective thickness-direction gasket properties.

Select Isotropic if you are defining continuum material properties. This choice is appropriate when the viscoelasic material model is used for any continuum, structural, or special-purpose elements whose material response is modeled using continuum material properties.

Select Traction if you are defining effective thickness-direction gasket properties. This option is supported only for gasket elements whose behavior is modeled directly using a gasket behavior model.

Preload

This parameter specifies the nature of preload used for defining frequency domain viscoelastic material properties or effective thickness-direction gasket properties.

Select Uniaxial to specify that the material properties correspond to a uniaxial test.

Select Volumetric to specify that the material properties correspond to a volumetric test. This setting cannot be used to define effective thickness-direction gasket properties.

Select Uniaxial and Volumetric to specify that the material properties correspond to both types of tests. This setting cannot be used to define effective thickness-direction gasket properties.

Select None if you choose not to specify a preload parameter.

If you selected Formula from the list of Frequency options, enter the following data in the Data table:

g1*real

Real part of $g_1^{*}$.

g1*imag

Imaginary part of $g_1^{*}$.

a

Value of a.

k1*real

Real part of $k_1^{*}$.

k1*imag

Imaginary part of $k_1^{*}$. If the material is incompressible, this value is ignored.

b

Value of b. If the material is incompressible, this value is ignored.

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 Tabular from the list of Frequency options, enter the data relevant to your Type and Preload selections (not all of the following parameters will apply):

Omega g* real

Real part of $\omega g^{*}$. $\left(\omega \mathrm{\Re }\left(g^{*}\right)=G_{\mathrm{\ell }}/G_{\mathrm{\infty }}\right)$

Omega g* imag

Imaginary part of $\omega g^{*}$. $(\omega \mathrm{\Im }(g*)=1-G_s/G_{\mathrm{\infty }})$

Omega k* real

Real part of $\omega k^{*}$. $\left(\omega \mathrm{\Re }\left(k^{*}\right)={\mathrm{K}}_{\mathrm{\ell }}/{\mathrm{K}}_{\mathrm{\infty }}\right)$ If the material is incompressible, this value is ignored.

Omega k* imag

Imaginary part of $\omega k^{*}$. $\left(\omega \mathrm{\Im }\left(k^{*}\right)=1-{\mathrm{K}}_s/{\mathrm{K}}_{\mathrm{\infty }}\right)$ If the material is incompressible, this value is ignored.

Frequency

Frequency, f, in cycles per time.

Loss Modulus

Uniaxial or bulk loss modulus.

Storage Modulus

Uniaxial or bulk storage modulus.

Uniaxial Strain

Uniaxial nominal strain (defines the level of uniaxial preload).

Volume Ratio

Volume ratio, J (current volume/original volume; defines the level of volumetric preload).

Normalized Loss Modulus

Real part of $\omega k^{*}$. $\left(\omega \mathrm{\Re }\left(k^{*}\right)={\mathrm{K}}_{\mathrm{\ell }}/{\mathrm{K}}_{\mathrm{\infty }}\right)$ for thickness-direction gasket behavior with no preload.

Normalized Shear Modulus

Imaginary part of $\omega k^{*}$. $\left(\omega \mathrm{\Im }\left(k^{*}\right)=1-{\mathrm{K}}_s/{\mathrm{K}}_{\mathrm{\infty }}\right)$ for thickness-direction gasket behavior with no preload.

You may need to expand the dialog box to see all the columns. For detailed information on how to enter data, see Entering tabular data.

If you selected Prony from the list of Frequency options, enter the following data in the Data table:

g_i Prony

${\overline{g}}_i^P$, the modulus ratio in the first term in the Prony series expansion of the shear relaxation modulus.

k_i Prony

${\overline{k}}_i^P$, the modulus ratio in the first term in the Prony series expansion of the bulk relaxation modulus.

tau_i Prony

${\tau }_i$, the relaxation time for the first term in the Prony series expansion.

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, use the Test Data menu to specify test data from which to define viscoelastic behavior. See the following sections for details:

• Specifying shear test data”

• Specifying volumetric test data”

• Specifying combined test data”

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).