Marlow equation

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