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Torsion and Tension of an Incompressible Solid Cylinder 331
We note that with z = Z, the bar is in a plane strain state.
5.38 Torsion and Tension of an Incompressible Solid Cylinder
Consider the following equilibrium configuration for a circular cylinder
where (r, 6, z) are the spatial coordinates and (/?,©,Z)are the material coordinates for a
material point, Aj and &$ are stretches for elements which were in the radial and axial direc-
tions.
The left Cauchy-Green tensor B and its inverse can be obtained from Eq. (3.30.8) as
The scalar invariants of B are
1
Now, from the constitutive equation T = -pi + <p± B + <p^ , we obtain
