Axisymmetric finite anti-plane shear of compressible nonlinearly elastic circular tubes

Authors:
Debra A. Polignone and Cornelius O. Horgan

Journal:
Quart. Appl. Math. **50** (1992), 323-341

MSC:
Primary 73G05; Secondary 73C50

DOI:
https://doi.org/10.1090/qam/1162279

MathSciNet review:
MR1162279

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Abstract | References | Similar Articles | Additional Information

Abstract: The axial shear problem for a hollow circular cylinder, composed of homogeneous isotropic *compressible* nonlinearly elastic material, is described. The inner surface of the tube is bonded to a rigid cylinder while the outer surface is subjected to a uniformly distributed axial shear traction and the radial traction is zero. For an arbitrary compressible material, the cylinder will undergo both a radial and axial deformation. These axisymmetric fields are governed by a coupled pair of nonlinear ordinary differential equations, one of which is second-order and the other first-order. The class of materials for which *axisymmetric anti-plane* shear (i.e., a deformation with zero radial displacement) is possible is described. The corresponding axial displacement and stresses are determined explicitly. Specific material models are used to illustrate the results.

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DOI:
https://doi.org/10.1090/qam/1162279

Article copyright:
© Copyright 1992
American Mathematical Society