*VISCOELASTIC

Required, mutually exclusive parameters

FREQUENCY

This parameter applies only to frequency domain procedures in Abaqus/Standard analyses.

Use this parameter to choose the frequency domain definition. In this case the material's long-term elasticity must be defined using the ELASTIC or the HYPERELASTIC option. If a frequency-domain viscoelastic response is specified for a time domain procedure, the viscoelastic response is ignored and the material response is based on the long-term elastic moduli.

Set FREQUENCY=CREEP TEST DATA to define the frequency domain response using a Prony series representation of the relaxation moduli, if the Prony series parameters are to be computed from shear and volumetric creep test data.

Set FREQUENCY=FORMULA to define the dissipative material parameters by the power law formulæ.

Set FREQUENCY=PRONY to define the frequency domain response using a Prony series representation of the relaxation moduli by specifying the Prony series parameters.

Set FREQUENCY=RELAXATION TEST DATA to define the frequency domain response using a Prony series representation of the relaxation moduli, if the Prony series parameters are to be computed from shear and volumetric relaxation test data.

Set FREQUENCY=TABULAR to provide tabular definition of the frequency domain response.

NONLINEAR

Include this parameter to define a nonlinear viscoelastic network within the parallel rheological framework.

TIME

This parameter applies only to time domain procedures.

Use this parameter to choose the time domain definition. In this case the material's elasticity must be defined using the ELASTIC, the HYPERELASTIC, or the HYPERFOAM option. If a time-domain viscoelastic response is specified for a frequency domain procedure, the viscoelastic response is ignored and the material response is based on the instantaneous elastic moduli.

Set TIME=CREEP TEST DATA if the Prony series parameters are to be computed by Abaqus from data taken from shear and volumetric creep tests.

Set TIME=FREQUENCY DATA if the Prony series parameters are to be computed by Abaqus from frequency-dependent cyclic test data.

Set TIME=PRONY to define a linear, isotropic, viscoelastic material by giving the parameters of the Prony series representation of the relaxation moduli.

Set TIME=RELAXATION TEST DATA if the Prony series parameters are to be computed by Abaqus from data taken from shear and volumetric relaxation tests.

Required parameters when the NONLINEAR parameter is included

LAW

Set LAW=BB POWER LAW to choose the preferred form of the Bergstrom-Boyce power law. It is recommended that you use this parameter setting rather than LAW=BERGSTROM-BOYCE.

Set LAW=BERGSTROM-BOYCE to choose a Bergstrom-Boyce law. This parameter setting is superseded by LAW=BB POWER LAW.

Set LAW=HYPERB to choose a hyperbolic-sine law.

Set LAW=POWER LAW to choose a power law. It is recommended that you use this parameter setting rather than LAW=STRAIN.

Set LAW=STRAIN to choose a strain hardening law. This parameter setting is superseded by LAW=POWER LAW.

Set LAW=USER to input the creep law using user subroutine UCREEPNETWORK or user subroutine VUCREEPNETWORK.

NETWORKID

Set this parameter equal to the network id. This number must be greater than or equal to 1 and smaller than or equal to the number of networks. The network ids must consist of consecutive integers.

SRATIO

Set this parameter equal to the stiffness ratio for the network. The sum of the ratios for the networks must be smaller than or equal to 1. If the sum is smaller than 1, an additional elastic network is defined with the value of the stiffness ratio such that the condition is satisfied.

Optional parameters

DEPENDENCIES

This parameter can be used only when the NONLINEAR parameter is included.

Set this parameter equal to the number of field variable dependencies included in the definition of the creep constants in addition to temperature. If this parameter is omitted, it is assumed that the creep constants have no dependencies or depend only on temperature. See Specifying Field Variable Dependence for more information.

PRELOAD

This parameter applies only to Abaqus/Standard analyses.

This parameter can be used only in conjunction with FREQUENCY=TABULAR to specify the nature of preload used for defining frequency-domain viscoelastic material properties or effective thickness-direction gasket properties.

Set PRELOAD=UNIAXIAL to specify that the frequency-domain viscoelastic material properties correspond to a uniaxial test.

Set PRELOAD=VOLUMETRIC to specify that the frequency-domain viscoelastic material properties correspond to a volumetric test. This setting is not meaningful when used with gasket elements to define effective thickness-direction properties.

PROPERTIES

This parameter applies only to Abaqus/Standard analyses and can be used only when LAW=USER is used.

Set this parameter equal to the number of property values needed as data in user subroutine UCREEPNETWORK or user subroutine VUCREEPNETWORK. The default is PROPERTIES=0.

TYPE

This parameter cannot be used in conjunction with the NONLINEAR parameter.

Use this parameter to define whether the VISCOELASTIC option is being used to define continuum material properties or effective thickness-direction gasket properties.

Set TYPE=ISOTROPIC (default, and only option for Abaqus/Explicit) to define continuum material properties. This choice is appropriate when the viscoelastic material model is used for any continuum, structural, or special-purpose elements whose material response is modeled using continuum material properties (examples of such special-purpose elements include modeling cohesive elements with a continuum response—see Modeling of an Adhesive Layer of Finite Thickness or gasket elements with a material response—see Defining the Gasket Behavior Using a Material Model). In Abaqus/Explicit this parameter should also be used for the definition of viscoelastic properties for cohesive elements with elastic traction-separation behavior (Modeling Viscoelastic Traction-Separation Behavior in Abaqus/Explicit).

Set TYPE=TRACTION to define effective thickness-direction gasket properties. This option is supported only for gasket elements whose behavior is modeled directly using a gasket behavior model (Defining the Gasket Behavior Using a Material Model).

Optional parameters when test data are given to define time domain viscoelasticity with TIME=CREEP TEST DATA, TIME=RELAXATION TEST DATA, or TIME=FREQUENCY DATA or when test data are given to define frequency domain viscoelasticity with FREQUENCY=CREEP TEST DATA or FREQUENCY=RELAXATION TEST DATA

ERRTOL: Set this parameter equal to the allowable average root-mean-square error of the data points in the least-squares fit. The default is 0.01 (1%).
NMAX: Set this parameter equal to 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 ERRTOL. The default and maximum value is 13.

Data line to define continuum material properties for FREQUENCY=FORMULA

First (and only) line

Real part of $g_{1}^{*}$ . $(g^{*} (ω) = g_{1}^{*} f^{- a})$
Imaginary part of $g_{1}^{*}$ .
Value of a.
Real part of $k_{1}^{*}$ . $(k^{*} (ω) = k_{1}^{*} f^{- b})$ If the material is incompressible, this value is ignored.
Imaginary part of $k_{1}^{*}$ . If the material is incompressible, this value is ignored.
Value of b. If the material is incompressible, this value is ignored.

Data lines to define continuum material properties for FREQUENCY=TABULAR without the PRELOAD parameter or for TIME=FREQUENCY DATA

First line

Real part of $ω g^{*}$ . $(ω ℜ (g^{*}) = G_{ℓ} / G_{\infty})$
Imaginary part of $ω g^{*}$ . $(ω ℑ (g *) = 1 - G_{s} / G_{\infty})$
Real part of $ω k^{*}$ . $(ω ℜ (k^{*}) = K_{ℓ} / K_{\infty})$ If the material is incompressible, this value is ignored.
Imaginary part of $ω k^{*}$ . $(ω ℑ (k^{*}) = 1 - K_{s} / K_{\infty})$ If the material is incompressible, this value is ignored.
Frequency, f, in cycles per time.

Repeat this data line as often as necessary to define the dissipative part of the material behavior.

Data lines to define continuum material properties for FREQUENCY=TABULAR, PRELOAD=UNIAXIAL

First line

Uniaxial loss modulus.
Uniaxial storage modulus.
Frequency, f, in cycles per time.
Uniaxial nominal strain (defines the level of uniaxial preload).

Repeat this data line as often as necessary to define the uniaxial loss and storage moduli as functions of frequency and preload.

Data lines to define continuum material properties for FREQUENCY=TABULAR, PRELOAD=VOLUMETRIC

First line

Bulk loss modulus.
Bulk storage modulus.
Frequency, f, in cycles per time.
Volume ratio, J (current volume/original volume; defines the level of volumetric preload).

Repeat this data line as often as necessary to define the bulk loss and storage moduli as functions of frequency and preload.

Data lines to specify continuum material properties with the Prony series parameters directly using TIME=PRONY or FREQUENCY=PRONY

First line

${\bar{g}}_{1}^{P}$ , the modulus ratio in the first term in the Prony series expansion of the shear relaxation modulus.
${\bar{k}}_{1}^{P}$ , the modulus ratio in the first term in the Prony series expansion of the bulk relaxation modulus.
$τ_{1}$ , the relaxation time for the first term in the Prony series expansion.

Repeat this data line as often as necessary to define the second, third, etc. terms in the Prony series. There is no restriction on the number of terms in the Prony series.

Data lines to define viscoelastic properties for cohesive elements with elastic traction-separation behavior using TIME=PRONY in Abaqus/Explicit

First line

${\bar{g}}_{1}^{P}$ , the modulus ratio in the first term in the Prony series expansion of the shear traction relaxation modulus.
${\bar{k}}_{1}^{P}$ , the modulus ratio in the first term in the Prony series expansion of the normal traction relaxation modulus.
$τ_{1}$ , the relaxation time for the first term in the Prony series expansion.

Repeat this data line as often as necessary to define the second, third, etc. terms in the Prony series. There is no restriction on the number of terms in the Prony series.

Data lines to define viscoelastic properties for cohesive elements with elastic traction-separation behavior using TIME=FREQUENCY DATA in Abaqus/Explicit

First line

Real part of $ω g^{*}$ . $(ω ℜ (g^{*}) = G_{ℓ} / G_{\infty})$
Imaginary part of $ω g^{*}$ . $(ω ℑ (g *) = 1 - G_{s} / G_{\infty})$
Real part of $ω k^{*}$ . $(ω ℜ (k^{*}) = K_{ℓ} / K_{\infty})$
Imaginary part of $ω k^{*}$ . $(ω ℑ (k^{*}) = 1 - K_{s} / K_{\infty})$
Frequency, f, in cycles per time.

Repeat this data line as often as necessary to define the dissipative part of the material behavior.

To specify viscoelastic behavior via test data

No data lines are used with this option when either TIME=CREEP TEST DATA or TIME=RELAXATION TEST DATA is specified. The test data are given by the SHEAR TEST DATA and the VOLUMETRIC TEST DATA options or by the COMBINED TEST DATA option.

Data lines to define effective thickness-direction gasket properties for PRELOAD=UNIAXIAL

First line

Effective thickness-direction loss modulus.
Effective thickness-direction storage modulus.
Frequency, f, in cycles per time.
Closure (defines the level of preload).

Repeat this data line as often as necessary to define the effective thickness-direction gasket loss and storage moduli as functions of frequency and preload.

Data lines to define effective thickness-direction gasket properties if PRELOAD=UNIAXIAL is not included

First line

Real part of $ω k^{*}$ . $(ω ℜ (k^{*}) = k_{ℓ} / k_{\infty})$ , where $k^{*}$ represents the complex effective thickness direction dynamic stiffness.
Imaginary part of $ω k^{*}$ . $(ω ℑ (k *) = 1 - k_{s} / k_{\infty})$ , where $k^{*}$ represents the complex effective thickness direction dynamic stiffness.
Frequency, f, in cycles per time.

Repeat this data line as often as necessary to define the normalized effective thickness-direction gasket loss and storage moduli as functions of frequency.

Data lines for LAW=BB POWER LAW

First line

$q_{0}$ . (Units of FL⁻².)
m.
C.
E, a constant used for regularizing the creep strain rate near the undeformed state. The value of E should be non-negative. If this field is left blank, the default value of 0.01 is used.
${\dot{ε}}_{0}$ . The default is 1.0. (Units of T⁻¹.)
Temperature.
First field variable.
Second field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than two)

Third field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the dependence of the creep constants on temperature and other predefined field variables.

Data lines for LAW=BERGSTROM-BOYCE

First line

Creep parameter, A.
Effective stress exponent, m.
Creep strain exponent, C.
E, a constant used for regularizing the creep strain rate near the undeformed state. The value of E should be non-negative. If this field is left blank, the default value of 0.01 is used.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)

Fifth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the dependence of the creep constants on temperature and other predefined field variables.

Data lines for LAW=HYPERB

First line

A. (Units of T⁻¹.)
B. (Units of F⁻¹L².)
n.
Temperature.
First field variable.
Second field variable.
Etc. up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)

Fifth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the dependence of the creep constants on predefined field variables.

Data lines for LAW=POWER LAW

First line

$q_{0}$ . (Units of FL⁻².)
n.
m.
a. The default is 0.0.
${\dot{ε}}_{0}$ . The default is 1.0. (Units of T⁻¹.)
Temperature.
First field variable.
Second field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than two)

Third field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the dependence of the creep constants on temperature and other predefined field variables.

Data lines for LAW=STRAIN

First line

A. (Units of F $^{- n}$ L $^{2 n}$ T $^{- 1 - m}$ .)
n.
m.
Temperature.
First field variable.
Second field variable.
Etc., up to four field variables.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than four)

Fifth field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the dependence of the creep constants on temperature and other predefined field variables.

Data lines for LAW=USER

No data lines are needed if the PROPERTIES parameter is omitted or set to 0. Otherwise, first line

Give the properties, eight per line.

Repeat this data line as often as necessary to define the material properties.