Hyperfoam

A hyperfoam, or elastomeric foam, describes a cellular solid whose porosity permits very large volumetric changes.

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

U = i = 1 N 2 μ i α i 2 [ λ ^ 1 α i + λ ^ 2 α i + λ ^ 3 α i 3 + 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;

λ ^ i = ( J t h ) 1 3 λ i           λ ^ 1 λ ^ 2 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  =  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  =  i = 1 N μ i ,

where the initial bulk modulus, Κ 0 , follows from

Κ 0  =  i = 1 N 2 μ i ( 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  =  ( ν i 1 2 ν i ) , ν i  =  ( 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 .
Use temperature-dependent data Specifies material parameters that depend on temperature. A Temperature field appears in the data table.
mun Material parameter μ n
alphan Material parameter α n
nun Material parameter ν n
Moduli time scale Select Instantaneous or Long Term for the application of viscoelastic effects.
Poisson's Ratio 1 < ν < 0.5 .