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Creep test data
If creep test data are specified, ABAQUS will calculate the terms in the Prony series automatically. The normalized shear and bulk compliances are defined as
where and
is the shear compliance,
is the total shear strain,
is the
is the constant
.
is the constant shear stress in a shear creep test;
is the total volumetric strain, and
,
volumetric compliance,
pressure in a volumetric creep test. At time
The creep data are converted to relaxation data through the convolution integrals
ABAQUS then uses the normalized shear modulus modulus parameters.
Using the shear and volumetric test data consecutively
and normalized bulk
in a nonlinear least-squares fit to determine the Prony series
The shear test data and volumetric test data can be used consecutively to define the normalized shear and bulk compliances as functions of time. A separate least-squares fit is performed on each data set; and the two derived sets of Prony series parameters, into one set of parameters,
Input File Usage:
.
and
, are merged
Use the following three options. The first option is required. Only one of the second and third options is required.
*VISCOELASTIC, TIME=CREEP TEST DATA *SHEAR TEST DATA
*VOLUMETRIC TEST DATA
ABAQUS/CAE UsProperty module: material editor: Mechanical
ElasticityViscoelastic: Domain: Time and Time:
age: Creep test data
In addition, select one or both of the following: Test Data
Test Data
Using the combined test data
Shear Test Data
Volumetric Test Data
Alternatively, the combined test data can be used to specify the
normalized shear and bulk compliances simultaneously as functions of time. A single least-squares fit is performed on the combined set of test data to determine one set of Prony series parameters,
Input File Usage:
ABAQUS/CAE UsProperty module: material editor: Mechanical
ElasticityViscoelastic: Domain: Time, Time:
age: Creep test data, and Test DataCombined Test Data
Relaxation test data
As with creep test data, ABAQUS will calculate the Prony series parameters automatically from relaxation test data.
Using the shear and volumetric test data consecutively
.
Use both of the following options: *VISCOELASTIC, TIME=CREEP TEST DATA *COMBINED TEST DATA
Again, the shear test data and volumetric test data can be used
consecutively to define the relaxation moduli as functions of time. A separate nonlinear least-squares fit is performed on each data set; and the two derived sets of Prony series parameters, are merged into one set of parameters,
Input File Usage:
.
and
,
Use the following three options. The first option is required. Only one of the second and third options is required.
*VISCOELASTIC, TIME=RELAXATION TEST DATA *SHEAR TEST DATA
*VOLUMETRIC TEST DATA
ABAQUS/CAE UsProperty module: material editor: Mechanical
ElasticityViscoelastic: Domain: Time and Time:
age: Relaxation test data
In addition, select one or both of the following: Test Data
Test Data
Using the combined test data
Shear Test Data
Volumetric Test Data
Alternatively, the combined test data can be used to specify the relaxation moduli simultaneously as functions of time. A single least-squares fit is performed on the combined set of test data to determine one set of Prony series parameters,
Input File Usage:
*VISCOELASTIC, TIME=RELAXATION TEST DATA *COMBINED TEST DATA
Use both of the following options:
.
ABAQUS/CAE UsProperty module: material editor: Mechanical
ElasticityViscoelastic: Domain: Time, Time:
age: Relaxation test data, and Test DataCombined Test
Data
Frequency-dependent test data
The Prony series terms can also be calibrated using frequency-dependent test data. In this case ABAQUS uses analytical expressions that relate the Prony series relaxation functions to the storage and loss moduli. The expressions for the shear moduli, obtained by converting the Prony series terms from the time domain to the frequency domain by making use of Fourier transforms, can be written as follows:
where
is the storage modulus,
is the loss modulus,
is the
angular frequency, and N is the number of terms in the Prony series. These expressions are used in a nonlinear least-squares fit to determine the Prony series parameters from the storage and loss moduli cyclic test data obtained at M frequencies by minimizing the error function
:
where
and
are the test data and
and
, respectively, are the
instantaneous and long-term shear moduli. The expressions for the bulk moduli,
and
, are written analogously.
The frequency domain data are defined in tabular form by giving the real and imaginary parts of and —where is the circular frequency—as functions of frequency in cycles per time.
is the Fourier transform