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.