Ogden’s model for hyperelastic foams

This model is very similar to the incompressible material model:

w = £ a jei( if+if+ifo – 3+£ «I (yi _ f),

‘ =1 1 1 ’

where the initial shear modulus has the form:

and module Ko:

N (1 ^ jo = 53 3 + A) .

Ogden’s models are mainly used for modelling foams of deformations above 700 %.

Arruda-Boyce equation

This equation has the form:

+ D I 2


where U is the potential energy of strains per unit volume, A,,, and

D temperature-dependent material parameters,

І1 = h1 + k2 + h2, (8.28)


J total volume coefficient,

Jel elasticity volume coefficient and k physical elongation.

The initial shear modulus [io in relation to ^ is expressed by the equation:

Most often, the coefficient k„, takes the value 7, for which ko = 1.0125, and the initial value of the module ko is