Reduced polynomial form

This equation has the form:

N N і

U = £ C00Q1 – 3У+ Y, D J – 1)Ъ; (8.44)

i=1 i=1 1

where

U potential energy of strains per volume unit,

N material parameter and

Cj and D1 temperature-dependent material coefficients,

/1 = 12 + Ц +12, (8.45)

whereby

!i = J-3ki, (8.46)

where

J total volume coefficient,

Jel elasticity volume coefficient and Xt physical elongation.

The initial value of the figural strains modulus and the module Ko has the form:

2

lo = 2C10, Ko = —. (8.47)

Van der Waals equation

The equation for potential energy of strains according to van der Waals has the form:

where

I = (1 – b)7x + № (8.49)

and

g = M (8’50)

Whereby U is the potential energy of strains per unit volume, ц—the initial shear modulus, A,,,—observed elongation, a—general interaction coefficient, в—constant coefficient and D—parameter influencing the compression. All these parameters are temperature-dependent. Moreover,

7i = 11 + k2 +12, and 72 = ![2) +122) + ^32); (8.51)

whereby

It = J 31t,

where

J total volume coefficient,

Jel elasticity volume coefficient and Xt physical elongation.

The initial value of the figural strains modulus and the module Ko has the form:

lo = l (8.53)

2

Ko = D. (854)

Yeoh equation

This equation can be written as:

U = Cw(h – 3) + C2o(71 – 3)2+ C3o(71 – 3)3

+ D Jel – ^2+ Dl – Jel – ^4+ Dl – Jel – ^ (8:55)

where

U potential energy of strains per volume unit and Dt temperature-dependent material coefficient,

Лі = J U,,

where

J total volume coefficient,

Jel elasticity volume coefficient and Xi physical elongation.

The initial value of the figural strains modulus and the module Ko:

lo = 2Ci0, (8.58)

2

jo = —. (8.59)

If data characterising stiffness of the foams, derived directly from many complex experiments (e. g. from multi-directional compression test), are known, then the most useful models are Ogden’s and van der Waals. If limited results of experi­mental research are available, the models Arruda-Boyce, van der Waals, Yeoh or reduced polynomials should be used. However, if there is only one set of experi­mental test results (such as axial compression), then the recommended model is Marlow.