The equation for potential energy of strains according to Marlow has the form:
U = Udev(!t) + Uvol (Jel), (8.32)
where U is the potential energy of strains per volume unit, with Udev as the deformed part and Uvoi as the volume part—undeformed,
7j = k2 + k2 + k^, (8.33)
whereby
к = J-hi, (8.34)
where
J total volume coefficient,
Jel elasticity volume coefficient and ki main elongation.
Neo-Hookean equation
In this case, the equation for potential energy of strains has the form:
12 U = Cw(h – 3) + — J – 0 ,
where U is the potential energy of strains per unit volume, C10 and D1 temperature-dependent material coefficients:
І1 = 12 + 12 + ^2, (8-36)
whereby
1 = J-bki, (8.37)
where
J total volume coefficient,
Jel elasticity volume coefficient and Xi main elongation.
The initial value of the figural strains modulus and the module Ko has the form:
2
lo = 2C10, Ko = —. (8.38)
Polynomial form
This equation has the form:
U =Y, Cj(I – 3)i(I2 – 3У+ X2 – 1f (8-39)
i+j=1 i=1 D1
where
U potential energy of strains per volume unit,
N material parameter and
Cj and D1 temperature-dependent material coefficients,
I1 = I1 +12 +12, I2 = I12)+ 122)+ 132); (8-40)
whereby
Ii = J-hi, (8.41)
where
J total volume coefficient,
Jel elasticity volume coefficient and Xt physical elongation.
The initial value of the figural strains modulus and the module к has the form:
2
lo = 2(Cm + C01), Kg = —. (8.42)
D1
When normal stresses are small or moderately large, then the first part of the equation leads to sufficiently correct solutions,
N
U =J2 jh – 3)г'(І2 – 3/. (8.43)
i+j=1
