= Triangular equilibrium construction for inextensible-fibre plane strain
Write the <Cauchy stress tensor> in the local fibre frame as $\sigma=s\,e\otimes e+h(e\otimes n+n\otimes e)+t\,n\otimes n$. The compatible geometry has $\nabla\theta=\kappa e$, $\nabla\cdot e=0$ and $\nabla\cdot n=-\kappa$. With zero <body force>, <force balance> becomes $e\cdot\nabla s=2\kappa h-n\cdot\nabla h$ and $n\cdot\nabla t-\kappa t=-e\cdot\nabla h-\kappa s$. For specified <shear stress> $h$, the first equation determines $s$ along fibres, then the second determines $t$ along transverse curves. Pressure and fibre tension supply these two normal constraint reactions. This is a local stress construction; boundary tractions must be chosen consistently with its integration data.
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