Hyperfoam

In the hyperfoam material model the elastic behavior of the foams is based on the strain energy function:

where $N$ is a material parameter; ${\mu }_i$ , ${\alpha }_i$ , and ${\beta }_i$ are temperature-dependent material parameters;

and ${\lambda }_i$ are the principal stretches. The elastic volume ratio, $J^{el}$ , relates the total volume ratio (current volume/reference volume), $J$ , and the thermal volume ratio, $J^{th}$ :

$J^{th}$ is given by

where ${\epsilon }^{th}$ is the linear thermal expansion strain that is obtained from the temperature and the isotropic thermal expansion coefficient.

The coefficients ${\mu }_i$ are related to the initial shear modulus, ${\mu }_0$ , by:

where the initial bulk modulus, ${{\rm K}}_0$ , follows from

For each term in the energy function, the coefficient ${\beta }_i$ determines the degree of compressibility. ${\beta }_i$ is related to the Poisson's ratio, ${\nu }_i$ , by the expressions

Thus, if ${\beta }_i$ is the same for all terms, we have a single effective Poisson's ratio, $\nu$ . This Poisson's ratio is valid for finite values of the logarithmic principal strains ${\epsilon }_1,{\epsilon }_2,{\epsilon }_3$ ; in uniaxial tension ${\epsilon }_2={\epsilon }_3=-\nu {\epsilon }_1$ .

Input Data	Description
Strain Energy Potential Order	Numeric order, $N$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
mun	Material parameter ${\mu }_n$
alphan	Material parameter ${\alpha }_n$
nun	Material parameter ${\nu }_n$
Moduli time scale	Select Instantaneous or Long Term for the application of viscoelastic effects.
Poisson's Ratio	$-1<\nu <0.5$ .