= Centred antiplane plastic fan
A centred fan consists of straight <characteristic curves> emanating from one point. <Stress> and antiplane <velocity> are constant on each ray and depend on the polar angle $\phi$. The radial tangent condition is $(\cos\phi,\sin\phi)\parallel(-f_b,f_a)$, so $f_a\cos\phi+f_b\sin\phi=0$. A boundary ray carrying a traction-free crack-face <stress> $b=0$ has slope $\tan\phi_b=-f_a/f_b$, interpreted as vertical when $f_b=0$. For the elliptic yield condition $a^2/A^2+b^2/B^2=1$, a forward fan has $a=-A^2\sin\phi/H$, $b=B^2\cos\phi/H$, $H=(A^2\sin^2\phi+B^2\cos^2\phi)^{1/2}$. The boundary rays are vertical; the adjacent rear regions have constant <stresses> $(\mp A,0)$. <Velocity> is a function of angle whose magnitude requires further loading data.
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