Hyperelastic Material

The subnode adds the equations for hyperelasticity at large strains. Hyperelastic materials can be suitable for modeling rubber and other polymers, biological tissue, and also for applications in acoustoelasticity. The is available in the Solid Mechanics, Layered Shell, and Membrane interfaces.

When a hyperelastic material is included in your model, all studies are geometrically nonlinear. The check box in the study settings is selected and cannot be cleared.

By adding the following subnodes to the node you can incorporate many other effects:

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Thermal Expansion (for Materials)

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	See also Hyperelastic Material Models in the Structural Mechanics Theory chapter.

The node is only available with some COMSOL products (see https://www.comsol.com/products/specifications/).

Shell Properties


	This section is only present when Hyperelastic Material is used in the Layered Shell interface. See the documentation for the Hyperelastic Material node in the Layered Shell chapter.

Hyperelastic Material

Select a hyperelastic from the list and then go to the applicable section for more information.

Compressibility

Hyperelastic materials can use a mixed formulation by adding the negative mean pressure as an extra dependent variable or a weak constraint to enforce the incompressibility condition. Depending on the hyperelastic material model, select from the list:

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	See also Nearly Incompressible Hyperelastic Materials and Incompressible Hyperelastic Materials in the Structural Mechanics Theory chapter.

Density

All hyperelastic material models have density as an input. The default ρ uses values . For enter another value or expression.

If any material in the model has a temperature dependent mass density, and is selected, the list will appear in the section. As a default, the value of Tref is obtained from a . You can also select to enter a value or expression for the reference temperature locally.


	The density is needed for dynamic analysis or when the elastic data is given in terms of wave speed. It is also used when computing mass forces for gravitational or rotating frame loads, and when computing mass properties (Computing Mass Properties).

See also

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Mass Density and Volume Reference Temperature.

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Using Common Model Input

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Default Model Inputs and Model Input in the COMSOL Multiphysics Reference Manual.

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Neo-Hookean

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St Venant–Kirchhoff

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Mooney–Rivlin, Two Parameters

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Mooney–Rivlin, Five Parameters

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Mooney–Rivlin, Nine Parameters

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From the list select a pair of elastic properties for the isotropic hyperelastic material — , , , , or . For each pair of properties, select from the applicable list to either use the value or enter a value or expression. Each of these pairs define the Lamé parameters at infinitesimal deformation as it is possible to convert from one set of properties to another, see Specification of Elastic Properties for Isotropic Materials.

If the option is selected from the list, enter the κ instead of the Lamé parameter λ to define the volumetric strain energy density. The default value for the bulk modulus is 100 times the initial shear modulus.

If the option is selected from the list, enter the E, the G, the μ, or the cs, depending on the selection made under the list.

St Venant–Kirchhoff

Mooney–Rivlin, Two Parameters

For the C10 and C01 both use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Mooney–Rivlin, Five Parameters

For the C10, C01, C20, C02, and C11 all use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Mooney–Rivlin, Nine Parameters

For the C10, C01, C20, C02, C11, C30, C03, C21, and C12 all use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Yeoh

For the c1, c2, and c3 all use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Ogden

In the table for the , enter values or expressions in each column: , and .

If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Storakers

For in the table for the , enter values or expressions in each column: , , and .

Varga

For the c1, c2, and c3 all use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Arruda–Boyce

For the default values for the μ0 and the N use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Gent

For the default values for the μ and the model parameter jm use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

van der Waals

For the default values for the μ, the λm, the α, and the β use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Blatz–Ko

For the μ and the β and φ all use values .

Gao

For the a and n use values .

Murnaghan

For the constants l, m, and n and the λ and μ use values .

Delfino

For the a and b use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Fung

For the A andc use values .

The A provides the anisotropic material properties that vary in the directions given by the list. The can be specified in either or notation. When is selected, a 6-by-6 symmetric matrix is displayed.

If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

Extended tube

For the Gc, Ge, α, and β use values . If the option is selected from the list, enter the κ. The default value for the bulk modulus is 100 times the initial shear modulus.

User Defined

If is selected from the list, enter an expression for the Ws.

You can also use a mixed formulation by adding the negative mean pressure as an extra dependent variable. In this case, select from the list either or .

If is selected, enter the Wsiso and the Wvol.

If is selected, enter the Wsiso only. An extra weak constrain is added to enforce the incompressibility condition Jel = 1.

For examples of:

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and , see Inflation of a Spherical Rubber Balloon. Application Library path .

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, see Elasto-Acoustic Effect in Rail Steel. Application Library path .

Energy Dissipation

To display this section, click the button (

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Select the check box to compute the energy dissipated by .

Discretization

If the hyperelastic material is nearly incompressible or incompressible, select the discretization for the — , , , or .


	The Discretization section is available when you use mixed formulation. To display the section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.

Quadrature Settings

Select the check box to reduce the integration points for the weak contribution of the feature. Select a method for — , , or to use in combination with the reduced integration scheme. The default stabilization technique is based on the shape function and shape order of the displacement field.

Control the hourglass stabilization scheme by using the option. Select (default) or .

When is selected, enter a stabilization shear modulus, Gstb. The value should be in the order of magnitude of the equivalent shear modulus.

When is selected, enter a stabilization bulk modulus, Kstb. The value should be in the order of magnitude of the equivalent bulk modulus.

Location in User Interface

Context Menus

Ribbon

Physics tab with selected:

Physics tab with , or selected: