Models

Torque M and load force N expressions

Mooney-Rivlin

$M=\pi \Psi a^4\left(C_{10}+C_{01}\right)$

$N=-\pi {\Psi }^2{a}^4\left(\frac{1}{2}{C}_{10}+C_{01}\right)$

Yeoh

$M=4\pi \Psi a^4\left(\frac{1}{4}{C}_{10}+\frac{1}{3}{\Psi }^2{a}^2{C}_{20}+\frac{3}{8}{\Psi }^4{a}^4{C}_{30}\right)$

$N=-2\pi {\Psi }^2{a}^4\left(\frac{1}{4}{C}_{10}+\frac{1}{3}{\Psi }^2{a}^2{C}_{20}+\frac{3}{8}{\Psi }^4{a}^4{C}_{30}\right)$

Fung

$M=\frac{2\pi C}{{\Psi }^3\beta }\left(1-{\exp }^{\beta {\Psi }^2{a}^2}+{\exp }^{\beta {\Psi }^2{a}^2}\beta {\Psi }^2{a}^2\right)$

$N=-\frac{\pi C}{{\Psi }^2\beta }\left(1-{\exp }^{\beta {\Psi }^2{a}^2}+{\exp }^{\beta {\Psi }^2{a}^2}\beta {\Psi }^2{a}^2\right)$

Gent-Thomas

$M=\frac{\pi }{{\Psi }^3}\left(6K_2\ln \left(3\right)+a^4{K}_1{\Psi }^4+2K_2{a}^2{\Psi }^2-6K_2\ln \left(a^2{\Psi }^2+3\right)\right)$

$N=-\frac{\pi }{2{\Psi }^2}\left(12K_2\ln \left(3\right)+a^4{K}_1{\Psi }^4+4K_2{a}^2{\Psi }^2-12K_2\ln \left({\Psi }^2{a}^2+3\right)\right)$