Models

Torsional couple M expressions

Mooney-Rivlin

$M=\pi \Psi a^4\left(C_{10}+\frac{1}{\lambda }{C}_{01}\right)$

Yeoh

$\begin{array}{l}M=4\pi \Psi a^4\left(\frac{3}{8}{\Psi }^4{a}^4\lambda C_{30}+\frac{1}{6}\lambda \left(2{\Psi }^2{C}_{20}+6{\Psi }^2\left(\frac{2}{\lambda }+{\lambda }^2-3\right)C_{30}\right)a^2\right)\\ +4\pi \Psi a^4\left(\frac{1}{4}\lambda \left(C_{10}+2\left(\frac{2}{\lambda }+{\lambda }^2-3\right)C_{20}+3{\left(\frac{2}{\lambda }+{\lambda }^2-3\right)}^2{C}_{30}\right)\right)\end{array}$

Fung

$M=\frac{2\pi C}{{\Psi }^3\beta }{\exp }^{-3\beta }\left({\exp }^{\beta (2+{\lambda }^3)/\lambda }-{\exp }^{\beta \left({\Psi }^2{a}^2\lambda +{\lambda }^3\right)/\lambda }+{\Psi }^2{a}^2\beta {\exp }^{\beta \left({\Psi }^2{a}^2\lambda +2+{\lambda }^3\right)/\lambda }\right)$

Gent-Thomas

$\begin{array}{l}M=\frac{\pi }{{\Psi }^3\lambda }\left(2K_2\ln \left(1+2{\lambda }^3\right)+4K_2{\lambda }^3\ln \left(1+2{\lambda }^3\right)+\lambda K_1{a}^4{\Psi }^4+2\lambda K_2{\Psi }^2{a}^2\right)\\ -\frac{\pi }{{\Psi }^3\lambda }\left(2K_2\ln \left({\Psi }^2{a}^2\lambda +1+2{\lambda }^3\right)+4K_2{\lambda }^3\ln \left(a^2{\Psi }^2\lambda +1+2{\lambda }^3\right)\right)\end{array}$