*ANISOTROPIC HYPERELASTIC

Products Abaqus/Standard Abaqus/Explicit Abaqus/CAE

Type Model data

LevelModel

Abaqus/CAE Property module

Required parameters

DEFINITION

Set DEFINITION=FUNG-ANISOTROPIC to use the generalized Fung anisotropic strain energy potential.

Set DEFINITION=FUNG-ORTHOTROPIC to use the generalized Fung orthotropic strain energy potential.

Set DEFINITION=HOLZAPFEL-GASSER-OGDEN to use the Holzapfel-Gasser-Ogden strain energy potential.

Set DEFINITION=HOLZAPFEL-OGDEN to use the Holzapfel-Ogden strain energy potential.

Set DEFINITION=KALISKE-SCHMIDT to use the Kaliske-Schmidt strain energy potential.

Set DEFINITION=USER if the strain energy potential and its derivatives are defined in a user subroutine (user subroutines UANISOHYPER_INV and UANISOHYPER_STRAIN in Abaqus/Standard or VUANISOHYPER_INV and VUANISOHYPER_STRAIN in Abaqus/Explicit).

Required parameters if DEFINITION=USER is specified

FORMULATION

Set FORMULATION=STRAIN to indicate that the anisotropic hyperelastic energy potential is formulated in terms of the components of the Green strain tensor and is defined by either UANISOHYPER_STRAIN in Abaqus/Standard or VUANISOHYPER_STRAIN in Abaqus/Explicit.

Set FORMULATION=INVARIANT to indicate that the anisotropic hyperelastic energy potential is formulated in terms of pseudo-invariants and is defined by either UANISOHYPER_INV in Abaqus/Standard or VUANISOHYPER_INV in Abaqus/Explicit.

TYPE

This parameter applies only to Abaqus/Standard analyses.

Set TYPE=INCOMPRESSIBLE to indicate that the anisotropic hyperelastic material defined by UANISOHYPER_INV or UANISOHYPER_STRAIN is incompressible.

Set TYPE=COMPRESSIBLE to indicate that the hyperelastic material defined by UANISOHYPER_INV or UANISOHYPER_STRAIN is compressible.

Optional parameters

DEPENDENCIES

Set this parameter equal to the number of field variable dependencies included in the definition of the anisotropic hyperelastic material properties. If this parameter is omitted, it is assumed that the material properties are constant or depend only on temperature. See Specifying Field Variable Dependence for more information.

LINEARIZATION STRETCH

This parameter applies only if DEFINITION=HOLZAPFEL-OGDEN.

Set LINEARIZATION STRETCH= $λ_{f L}$ to indicate that the second and third exponential terms in the Holzapfel-Ogden strain energy potential are linearized/approximated by polynomial functions when fiber stretches reach $λ_{f L}$ . The value of $λ_{f L}$ should be greater than or equal to 1.

If this parameter is omitted, the exponential terms in the strain energy potential are not linearized.

LOCAL DIRECTIONS

This parameter can be used only in combination with invariant-based strain energy potentials, such as DEFINITION=HOLZAPFEL-GASSER-OGDEN; DEFINITION=HOLZAPFEL-OGDEN; DEFINITION=KALISKE-SCHMIDT; and DEFINITION=USER, FORMULATION=INVARIANT.

Set this parameter equal to the number of preferred local directions (or fiber directions) in the material. The default is LOCAL DIRECTIONS=0.

When LOCAL DIRECTIONS=N, the definitions of the N local direction vectors in the reference configuration are specified using the ORIENTATION, LOCAL DIRECTIONS=M option, with M ≥ N. If M > N, the first N directions are used.

If the Holzapfel-Gasser-Ogden, Holzapfel-Ogden, or Kaliske-Schmidt strain energy potential is used, you must specify at least one local direction.

MODULI

This parameter is applicable only when the ANISOTROPIC HYPERELASTIC option is used in conjunction with the VISCOELASTIC option.

Set MODULI=INSTANTANEOUS to indicate that the anisotropic hyperelastic material constants define the instantaneous behavior. This parameter value is not available for frequency domain viscoelasticity in an Abaqus/Standard analysis. This is the only option available if the anisotropic hyperelastic potential is defined in a user subroutine.

Set MODULI=LONG TERM to indicate that the hyperelastic material constants define the long-term behavior. This option is not available when a user subroutine is used to define the anisotropic hyperelastic potential. It is the default for all other anisotropic hyperelastic models.

PROPERTIES

This parameter applies only if DEFINITION=USER is specified.

Set this parameter equal to the number of property values needed as data in user subroutines UANISOHYPER_INV and UANISOHYPER_STRAIN in Abaqus/Standard or VUANISOHYPER_INV and VUANISOHYPER_STRAIN in Abaqus/Explicit. The default value is 0.

Data lines to define the material constants for the FUNG-ANISOTROPIC model

First line

$b_{1111}$ .
$b_{1122}$ .
$b_{2222}$ .
$b_{1133}$ .
$b_{2233}$ .
$b_{3333}$ .
$b_{1112}$ .
$b_{2212}$ .

Second line

$b_{3312}$ .
$b_{1212}$ .
$b_{1113}$ .
$b_{2213}$ .
$b_{3313}$ .
$b_{1213}$ .
$b_{1313}$ .
$b_{1123}$ .

Third line

$b_{2223}$ .
$b_{3323}$ .
$b_{1223}$ .
$b_{1323}$ .
$b_{2323}$ .
$c$ . (Units of FL⁻².)
$D$ . (Units of F⁻¹L².)
Temperature.

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

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

Repeat this set of data lines as often as necessary to define the material constants as a function of temperature and other predefined field variables.

Data lines to define the material constants for the FUNG-ORTHOTROPIC model

First line

$b_{1111}$ .
$b_{1122}$ .
$b_{2222}$ .
$b_{1133}$ .
$b_{2233}$ .
$b_{3333}$ .
$b_{1212}$ .
$b_{1313}$ .

Second line

$b_{2323}$ .
$c$ . (Units of FL⁻².)
$D$ . (Units of F⁻¹L².)
Temperature.
First field variable.
Etc., up to four field variables per line.

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 material constants as a function of temperature and other predefined field variables.

Data lines to define the material constants for the HOLZAPFEL-GASSER-OGDEN model

First line

$C_{10}$ . (Units of FL⁻².)
$D$ . (Units of F⁻¹L².)
$k_{1}$ . (Units of FL⁻².)
$k_{2}$ .
Fiber dispersion parameter $κ$ ( $0 \leq κ \leq 1 / 3$ ).
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 material constants as a function of temperature and other predefined field variables.

Data lines to define the material constants for the HOLZAPFEL-OGDEN model

First line

$a$ . (Units of FL⁻².)
$b$ .
$a_{f}$ . (Units of FL⁻².)
$b_{f}$ .
$a_{s}$ . (Units of FL⁻².)
$b_{s}$ .
$a_{f s}$ . (Units of FL⁻².)
$b_{f s}$ .

Second line

$D$ . (Units of F⁻¹L².)
Temperature.
First field variable.
Etc., up to six field variables.

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

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

Repeat this set of data lines as often as necessary to define the material constants as a function of temperature and other predefined field variables.

Data lines to define the material constants for the KALISKE-SCHMIDT model

First line

$a_{1}$ . (Units of FL⁻².)
$a_{2}$ . (Units of FL⁻².)
$a_{3}$ . (Units of FL⁻².)
$b_{1}$ . (Units of FL⁻².)
$b_{2}$ . (Units of FL⁻².)
$b_{3}$ . (Units of FL⁻².)
$c_{2}$ . (Units of FL⁻².)
$c_{3}$ . (Units of FL⁻².)

Second line

$c_{4}$ . (Units of FL⁻².)
$c_{5}$ . (Units of FL⁻².)
$c_{6}$ . (Units of FL⁻².)
$d_{2}$ . (Units of FL⁻².)
$d_{3}$ . (Units of FL⁻².)
$d_{4}$ . (Units of FL⁻².)
$d_{5}$ . (Units of FL⁻².)
$d_{6}$ . (Units of FL⁻².)

Third line

$e_{2}$ . (Units of FL⁻².)
$e_{3}$ . (Units of FL⁻².)
$e_{4}$ . (Units of FL⁻².)
$e_{5}$ . (Units of FL⁻².)
$e_{6}$ . (Units of FL⁻².)
$f_{2}$ . (Units of FL⁻².)
$f_{3}$ . (Units of FL⁻².)
$f_{4}$ . (Units of FL⁻².)

Fourth line

$f_{5}$ . (Units of FL⁻².)
$f_{6}$ . (Units of FL⁻².)
$g_{2}$ . (Units of FL⁻².)
$g_{3}$ . (Units of FL⁻².)
$g_{4}$ . (Units of FL⁻².)
$g_{5}$ . (Units of FL⁻².)
$g_{6}$ . (Units of FL⁻².)
$D$ . (Units of F⁻¹L².)

Fifth line (leave blank if no temperature or field variables are specified)

Temperature.
First field variable.
Etc., up to seven field variables per line.

Repeat this set of data lines as often as necessary to define the material constants as a function of temperature and other predefined field variables.

Data lines to define the material properties for the USER anisotropic hyperelasticity model

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

Give the material properties, eight per line. If this option is used in conjunction with the VISCOELASTIC option, the material properties must define the instantaneous behavior. If this option is used in conjunction with the MULLINS EFFECT option, the material properties must define the primary response.

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