Mooney-Rivlin model

There are 2-, 3-, 5- and 9-parametric Mooney-Rivlin models known. Mooney-Rivlin model with two parameters:

Mooney-Rivlin model with nine parameters, where N =3:

3 _ _ 1

W — ^ Cj(h – 3)Xh – 3)J – (Jel – 1)2. (8.18)

t+j=1 –

For all forms of the Mooney-Rivlin function, the initial value of the shear modulus we define as:

І0 — 2(C10 + C01),

where

C10 and C01 are the coefficients determined in experimental studies

and module к:

2

j — – • (8.20)

By choosing the right type of function for the tested kind of foam, one can follow the characteristics of the material stiffness a = /(e), and so:

• for a curve without point of inflection (Fig. 8.14), an equation with two parameters can be used,

• for a curve with one point of inflection (Fig. 8.15), an equation with five parameters can be used, and

• for a curve with two points of inflection (Fig. 8.16), an equation with nine parameters can be used.

Fig. 8.15 Characteristics of stiffness of foam with one point of inflection

Fig. 8.16 Characteristics of stiffness of foam with two points of inflection

Ogden’s model

General Ogden’s model is a model based on coefficients of main extensions, whereby

where the initial shear modulus has the form:

N

1 ai i=1

2

Ko = —. o Di