= Nominal end traction of a twisted neo-Hookean cylinder
{title2=$t=(-\mu\alpha x_2,\mu\alpha x_1,\mu\lambda+q/\lambda)$}
For axial stretch $\lambda$ and twist $\alpha$ per reference length, an incompressible <neo-Hookean solid> has current radius $a=R/\sqrt\lambda$. In local cylindrical orthonormal bases the <deformation gradient> is $A=\begin{pmatrix}\lambda^{-1/2}&0&0\\0&\lambda^{-1/2}&\alpha r\\0&0&\lambda\end{pmatrix}$. The <Cauchy stress tensor> is $\mu AA^T+qI$. Radial equilibrium gives $q'=\mu\alpha^2r$, and a traction-free curved surface gives $q=-\mu/\lambda+\mu\alpha^2(r^2-a^2)/2$. The nominal end <traction> is the displayed <vector>, measured per reference area. Its moment about the axis is $\int(x_1t_2-x_2t_1)dS_0=\mu\alpha\int r^2dS_0=\mu\pi R^4\alpha/(2\lambda)$. This calculation uses current moment arms with reference-area <tractions>.
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