Hyperfoam Options

You can create a hyperfoam material model to describe a cellular solid whose porosity permits very large volumetric changes.

In the elastomeric foam (hyperfoam) material model the elastic behavior of the foams is based on the strain energy function.

U = \sum_{i = 1}^{N} \frac{{2 μ}_{i}}{α_{i}^{2}} [{\hat{λ}}_{1}^{α_{i}} + {\hat{λ}}_{2}^{α_{i}} + {\hat{λ}}_{3}^{α_{i}} - 3 + \frac{1}{β_{i}} ({(J^{e l})}^{- α_{i} β_{i}} - 1)],

where $N$ is a material parameter; $μ_{i}$ , $α_{i}$ , and $β_{i}$ are temperature-dependent material parameters;

{\hat{λ}}_{i} = {(J^{t h})}^{- \frac{1}{3}} λ_{i} \to {\hat{λ}}_{1} {\hat{λ}}_{2} {\hat{λ}}_{3} = J^{e l};

and $λ_{i}$ are the principal stretches. The elastic volume ratio, $J^{e l}$ , relates the total volume ratio (current volume/reference volume), $J$ , and the thermal volume ratio, $J^{t h}$ :

J^{e l} = \frac{J}{J^{t h}} .

$J^{t h}$ is given by

J^{t h} = {(1 + ε^{t h})}^{3},

where $ε^{t h}$ is the linear thermal expansion strain that is obtained from the temperature and the isotropic thermal expansion coefficient.

The coefficients $μ_{i}$ are related to the initial shear modulus, $μ_{0}$ , by:

μ_{0} = \sum_{i = 1}^{N} μ_{i},

where the initial bulk modulus, $Κ_{0}$ , follows from

Κ_{0} = \sum_{i = 1}^{N} {2 μ}_{i} (\frac{1}{3} + β_{i}) .

For each term in the energy function, the coefficient $β_{i}$ determines the degree of compressibility. $β_{i}$ is related to the Poisson's ratio, $ν_{i}$ , by the expressions

β_{i} = (\frac{ν_{i}}{{1 - 2 ν}_{i}}), ν_{i} = (\frac{β_{i}}{{1 + 2 β}_{i}}) .

Thus, if $β_{i}$ is the same for all terms, we have a single effective Poisson's ratio, $ν$ . This Poisson's ratio is valid for finite values of the logarithmic principal strains $ε_{1}, ε_{2}, ε_{3}$ ; in uniaxial tension $ε_{2} = ε_{3} = - ν ε_{1}$ .


Input Data	Description
Strain energy potential order	Numeric order, $N$ .
mu1	$μ_{1}$
alpha1	$α_{1}$
nu1	$ν_{1}$
Use temperature-dependent data	Specify material parameters that depend on temperature. A Temperature field appears in the data table.
Moduli time scale	Select Instantaneous or Long Term for the application of viscoelastic effects.