Defining a general hyperelastic material for Nastran analyses

In Nastran, you can use the MATHP bulk data entry to specify material properties for use in a fully nonlinear hyperelastic analysis. In Pre/Post, you use the Hyperelastic-general option in the Manage Materials dialog box to define a MATHP bulk data entry. You can use a Hyperelastic-general material to model a Mooney-Rivlin or Neo-Hookean material.

Generalized strain energy function

With a MATHP material, the generalized Mooney-Rivlin strain energy function may be expressed as follows:

Equation 9-1.

and 2D1 = K and 2(A10 + A01) = G at small strains.

where:

	first distortional strain invariant
	second distortional strain invariant
Aij	material constants related to shear deformation (distortion)
Di	material constants related to volumetric deformation
T	current temperature
T0	initial temperature
K	bulk modulus
G	shear modulus

The model reduces to a Mooney-Rivlin material Na = 1 and to a Neo-Hookean material if Na = 1 and A01 = 0.0.

Specifying the basic properties for the material

In the Hyperelastic Material dialog box, you use the:

• Mass Density option to define the mass density of the material in its original configuration. This option corresponds to the RHO field on the MATHP bulk data entry.

• Strain Energy Polynomial Order options to define the order of the distortional and volumetric strain energy polynomial functions. These options corresponds to the NA and ND fields on the MATHP bulk data entry.

• Structural Damping Coefficient option to specify the coefficient of structural damping. This option corresponds to the GE field on the MATHP bulk data entry.

• Temperature (TREF) option on the Thermal page to specify a reference temperature value. Nastran uses this value to calculate a temperature-dependent thermal expansion coefficient. This option corresponds to the TREF field on the MATHP bulk data entry.

Defining the material constants

In the Hyperelastic Material dialog box, you use:

• The Distortional Deformation options to specify the distortional (shear) deformation constants. These options correspond to the Aij fields on the MATHP bulk data entry.

• The Volumetric Deformation options to specify the volumetric deformation constants. These options correspond to the Di fields on the MATHP bulk data entry.

You obtain the values to enter for the Distortional Deformation and Volumetric Deformation options from a least squares fitting of experimental data. You can either curve fit your own experimental data or use Nastran’s curve-fitting algorithm to determine the material constants. In the Distortional Deformation and Volumetric Deformation options:

• If you select Constants from the Definition list, you can enter your own values for the material constants.

• If you select Tables from the Definition list, you can select a field that contains a set of experimental data for Nastran to use to obtain the constants.

To calculate the constants for distortional deformation, you can use one or more of the following types of deformation data:

• Simple tension-compression data (TAB1 field in the MATHP bulk data entry).

• Equibiaxial tension data (TAB2 field in the MATHP bulk data entry).

• Simple shear data (TAB3 field in the MATHP bulk data entry).

• Pure shear data (TAB4 field in the MATHP bulk data entry).

For volumetric deformation, you can use pure volumetric compression data to calculate the constants (TABD field in the MATHP bulk data entry).

Note:

Conventional Mooney-Rivlin and Neo-Hookean materials are fully incompressible. However, you cannot use a Hyperelastic-general material to define full incompressibility. You can simulate full incompressibility by specifying a large enough value in the D1 field in the Volumetric Deformation options. However, specifying a D1 value greater than 103 is not recommended.

Checking the f06 file for an updated MATHP bulk data entry

If use the Tables option to specify a set of experimental data, when you solve your model, Nastran’s curve-fitting algorithm computes the material constants from that data and prints an updated MATHP entry with those constants in the f06 file. You can examine this updated entry and see whether Nastran’s curve-fitting algorithm fit your experimental data to a Mooney-Rivlin or Neo-Hookean material.

The following example shows an excerpt from an f06 file:

 *** SYSTEM INFORMATION MESSAGE 6410 (IFP8)     BEGIN PROCESSING OF MATHP ENTRY ID =    1     DISTORTIONAL PARAMETER FITTING.     SQUARE ROOT OF SUM OF THE ERRORS SQUARED =    0.24080E+02     UPDATED MATHP ENTRY               1    2.165421E+00    1.784055E-02    1.500000E+03    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00                               1               1    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00    0.000000E+00

In this example, NA=1 and A01=1, which means that the supplied experimental data fit to a Mooney-Rivlin material.

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