= Neo-Hookean tube pressure under twist and inflation
{title2=$p=\mu\log\frac{b_0a}{a_0b}+\frac{\mu}2\left(\frac{b_0^2}{b^2}-\frac{a_0^2}{a^2}\right)+\frac{\mu\alpha^2}2(b_0^2-a_0^2)$}
Here $b^2=b_0^2+a^2-a_0^2$. Substitute the <neo-Hookean solid> energy into the <twist and inflation of an incompressible tube> work identity. Differentiating with respect to $a$ gives the integrand $\mu\rho[\rho^{-2}-\rho^2/(\rho^2+c)^2+\alpha^2]$, with $c=a^2-a_0^2$. Integrating between the two reference radii proves the displayed pressure when the outer surface is traction free.
Back to article page
