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A note on the pure torsion of a circular cylinder for a compressible nonlinearly elastic material with nonconvex strain-energy

✍ Scribed by Cornelius O. Horgan; Debra A. Polignone

Publisher: Springer Netherlands
Year: 1995
Tongue: English
Weight: 431 KB
Volume: 37
Category: Article
ISSN: 0374-3535
DOI: 10.1007/bf00040944

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✦ Synopsis

The large deformation torsion problem for an elastic circular cylinder subject to prescribed twisting moments at its ends is examined for a particular homogeneous isotropic compressible material, namely the Blatz-Ko material. For this material, the displacement equations of equilibrium in three-dimensional elastostatics can lose ellipticity at sufficiently large deformations. For the torsion problem, it is shown that this occurs when the prescribed torque reaches a critical value. For values of the twisting moment greater than this critical value, there is an axial core of the cylinder on which ellipticity holds, surrounded by an annular region where loss of ellipticity has occurred. The physical implications in terms of localized shear bands are briefly discussed.

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This note concerns the problem of quasi-static pure bending of a beam in the context of the complete theory of linear elastic materials with voids presented in [1]. It is shown here that the solution in the context of the complete theory of [1] is coincident with the pure bending solution of classic