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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).

The heterogeneous round bar shown below consists of a

hardened outer layer and a core denoted material 1 and 2, respectively. The

elastic-plastic behavior of the two materials are assumed to be governed by the

linear hardening stress-strain curve shown in figure 2(b). Material 1 and 2

have initial yield strength in shear *τ*y1 and *τ*y2 respectively where *τ*y1 > *τ*y2. The plastic hardening modulii for the

two materials are *H*1 and *H*2, where *H*1 < *H*2. Both materials

have identical elastic properties given by the shear modulus *G *and Poisson’s ratio. Assume the bar has length equal to unity. Determine an explicit

relation between the end twist *q**x* and the applied torque *Tx*.

Could anyone recommend an article or a textbook that

might give some hints on how to solve this problem. Any help in this regard

would be greatly appreciated.

Thanks and best regards,

Imme

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## Comments

## try this paper

J. Inst. Maths. Applics (1979) 24, 353-378

Elastic-Plastic Torsion of Heterogeneous Cylindrical Bars

D. CIORANESCU, J. SAINT JEAN PAULIN

AND

H. LANCHON

Following the study by Lanchon (1974) on elastic-plastic torsion of cylindrical bars

with simple or multiple connected cross sections, we give here a generalized

formulation including, in particular, the case of bars reinforced by longitudinal fibres.

and search for literature using this one as a reference

Good luck

Frank

------------------------------------------

Ruhr-University

Bochum

Germany