*HYPERELASTIC

Products Abaqus/Standard Abaqus/Explicit Abaqus/CAE

Type Model data

LevelModel

Abaqus/CAE Property module

Optional, mutually exclusive parameters

ARRUDA-BOYCE

Include this parameter to use the Arruda-Boyce model, also known as the eight-chain model.

HENCKY

This parameter applies only to Abaqus/Standard analyses.

Include this parameter to use the Hencky model.

MARLOW

Include this parameter to use the Marlow model.

MOONEY-RIVLIN

Include this parameter to use the Mooney-Rivlin model. This method is equivalent to using the POLYNOMIAL parameter with N=1.

NEO HOOKE

Include this parameter to use the neo-Hookean model. This method is equivalent to using the REDUCED POLYNOMIAL parameter with N=1.

OGDEN

Include this parameter to use the Ogden strain energy potential.

POLYNOMIAL

Include this parameter to use the polynomial strain energy potential. This method is the default method of defining the strain energy potential.

REDUCED POLYNOMIAL

Include this parameter to use the reduced polynomial strain energy potential. This method is equivalent to using the POLYNOMIAL parameter with $C_{i j} = 0$ for $j \neq 0$ .

USER

This parameter applies only to Abaqus/Standard analyses.

Include this parameter if the derivatives of the strain energy potential with respect to the strain invariants are defined in user subroutine UHYPER or if the derivatives of the strain energy potential with respect to the principal stretches are defined in user subroutine UHYPER_STRETCH.

VALANIS-LANDEL

This parameter applies only to Abaqus/Standard analyses.

Include this parameter to use the Valanis-Landel model.

VAN DER WAALS

Include this parameter to use the Van der Waals model, also known as the Kilian model.

YEOH

Include this parameter to use the Yeoh model. This method is equivalent to using the REDUCED POLYNOMIAL parameter with N=3.

Required parameters if the USER parameter is included

FORMULATION

This parameter applies only to Abaqus/Standard analyses.

Set FORMULATION=INVARIANT (default) to indicate that the hyperelastic energy potential is formulated in terms of invariants and is defined in user subroutine UHYPER.

Set FORMULATION=STRETCH to indicate that the hyperelastic energy potential is formulated in terms of the principal stretches and is defined in user subroutine UHYPER_STRETCH.

TYPE

This parameter applies only to Abaqus/Standard analyses.

Set TYPE=INCOMPRESSIBLE to indicate that the hyperelastic material defined by UHYPER or by UHYPER_STRETCH is incompressible.

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

Optional parameters

BETA

This parameter can be used only when both the VAN DER WAALS and TEST DATA INPUT parameters are used; it defines the value of $β$ while the other coefficients of the Van der Waals model are fitted from the test data given by the user. If this parameter is omitted, $β$ will be determined from a nonlinear, least-squares fit of the test data. Allowable values of BETA are $0 \leq β \leq 1$ . It is recommended to set $β$ = 0 if only one type of test data is available.

MODULI

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

Set MODULI=INSTANTANEOUS to indicate that the hyperelastic material constants define the instantaneous behavior. This is the only option available if you define the hyperelastic material in user subroutine UHYPER or user subroutine UHYPER_STRETCH.

Set MODULI=LONG TERM to indicate that the hyperelastic material constants define the long-term behavior. This option is not available when you define the hyperelastic material in user subroutine UHYPER or user subroutine UHYPER_STRETCH. It is the default for all other hyperelastic models.

N

This parameter can be used only with the OGDEN, POLYNOMIAL, and REDUCED POLYNOMIAL parameters. Include this parameter to define the order of the strain energy potential. The default is N=1.

If the TEST DATA INPUT parameter is used, the parameter N can take only the values 1 or 2 for the POLYNOMIAL form and up to 6 for the OGDEN and REDUCED POLYNOMIAL forms.

If the TEST DATA INPUT parameter is omitted, the maximum value of N is 6 for either form.

POISSON

Set this parameter equal to the Poisson's ratio, $ν$ , to account for compressibility. This parameter cannot be used if the material coefficients are specified directly or if volumetric behavior is defined by entering nonzero values for $D_{i}$ on the data line or by specifying the VOLUMETRIC TEST DATA option. In addition, this parameter cannot be used for the Marlow model or for the Valanis-Landel model if the nominal lateral strains are specified on the UNIAXIAL TEST DATA, BIAXIAL TEST DATA, or PLANAR TEST DATA option.

PROPERTIES

This parameter applies only to Abaqus/Standard analyses.

This parameter can be used only if the USER parameter is specified. Set this parameter equal to the number of property values needed as data in user subroutine UHYPER or in user subroutine UHYPER_STRETCH. The default value is 0.

TEST DATA INPUT

Include this parameter if the material constants are to be computed by Abaqus from data taken from simple tests on a material specimen.

If this parameter is omitted, the material constants must be given directly on the data lines. This parameter cannot be used with the Hencky model. It is not relevant for the Marlow model or the Valanis-Landel model; you must specify the test data for these models.

To define the material behavior by giving test data

Alternative options for specifying test data rather than specifying relevant material constants on the data lines of the HYPERELASTIC option are applicable to all hyperelastic material models except the user-defined model. No data lines are used with the HYPERELASTIC option when the MARLOW, VALANIS-LANDEL, or TEST DATA INPUT parameter is specified. In this case the test data are specified with the BIAXIAL TEST DATA, PLANAR TEST DATA, UNIAXIAL TEST DATA, and VOLUMETRIC TEST DATA options.

Data lines to define the material constants for the ARRUDA-BOYCE model

First line

$μ$ .
$λ_{m}$ .
$D$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

Data lines to define the material constants for the HENCKY model

First line

Young's modulus, $E$ . (Units of FL⁻².)
Poisson's ratio, $ν$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

Data lines to define the material constants for the MOONEY-RIVLIN model

First line

$C_{10}$ .
$C_{01}$ .
$D_{1}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

Data lines to define the material constants for the NEO HOOKE model

First line

$C_{10}$ .
$D_{1}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

Data lines to define the material constants for the OGDEN strain energy potential

First line if N=1

$μ_{1}$ .
$α_{1}$ .
$D_{1}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

First line if N=2

$μ_{1}$ .
$α_{1}$ .
$μ_{2}$ .
$α_{2}$ .
$D_{1}$ .
$D_{2}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

First line if N=3

$μ_{1}$ .
$α_{1}$ .
$μ_{2}$ .
$α_{2}$ .
$μ_{3}$ .
$α_{3}$ .
$D_{1}$ .
$D_{2}$ .

Second line if N=3

$D_{3}$ .
Temperature.

Repeat this pair of data lines as often as necessary to define the material constants as a function of temperature.

Data lines for higher values of N (up to 6)

The data lines for higher values of N follow the same pattern. First, give the $μ_{i}$ and $α_{i}$ for i from 1 to N. Then, give the N coefficients $D_{i}$ . Finally, give the temperature. Exactly eight data values should be given on each line.

Data lines to define the material constants for the POLYNOMIAL strain energy potential

First line if N=1

$C_{10}$ .
$C_{01}$ .
$D_{1}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

First line if N=2

$C_{10}$ .
$C_{01}$ .
$C_{20}$ .
$C_{11}$ .
$C_{02}$ .
$D_{1}$ .
$D_{2}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

First line if N=3

$C_{10}$ .
$C_{01}$ .
$C_{20}$ .
$C_{11}$ .
$C_{02}$ .
$C_{30}$ .
$C_{21}$ .
$C_{12}$ .

Second line if N=3

$C_{03}$ .
$D_{1}$ .
$D_{2}$ .
$D_{3}$ .
Temperature.

Repeat this pair of data lines as often as necessary to define the material constants as a function of temperature.

Data lines for higher values of N (up to 6)

The data lines for higher values of N follow the same pattern. For each value of $(i + j)$ from 1 to N, give the $C_{i j}$ , with i decreasing from $(i + j)$ to zero and j increasing from zero to $(i + j)$ . Then, give the N coefficients $D_{i}$ . Finally, give the temperature. Exactly eight data values should be given on each line.

Data lines to define the material constants for the REDUCED POLYNOMIAL strain energy potential

First line if N=1

$C_{10}$ .
$D_{1}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

First line if N=2

$C_{10}$ .
$C_{20}$ .
$D_{1}$ .
$D_{2}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

First line if N=3

$C_{10}$ .
$C_{20}$ .
$C_{30}$ .
$D_{1}$ .
$D_{2}$ .
$D_{3}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

Data lines for higher values of N (up to 6)

The data lines for the higher values of N follow the same pattern. First, give the $C_{i 0}$ for $i$ from $1$ to $N$ . Then, give the N coefficients $D_{i}$ . Finally, give the temperature. Exactly eight data values should be given on each line.

Data lines to define the material properties for the USER 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 or HYSTERESIS 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.

Data lines to define the material constants for the VAN DER WAALS model

First line

$μ$ .
$λ_{m}$ .
$a$ .
$β$ .
$D$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.

Data lines to define the material constants for the YEOH model

First line

$C_{10}$ .
$C_{20}$ .
$C_{30}$ .
$D_{1}$ .
$D_{2}$ .
$D_{3}$ .
Temperature.

Repeat this data line as often as necessary to define the material constants as a function of temperature.