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Analytical elastic-plastic solutions for the torsion of a round bar with a heterogeneous cross section

Hello,

I am trying to derive/find an analytical expression
for the torsion of a round bar made of an heterogeneous material. But I just do
not seem to find any solution available in the literature other than for a
homogeneous material, which can be find in any theory of plasticity book (e.g.
Theory of Plasticity, 3rd Ed., J. Chakarabarty, pp. 132-136).

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