Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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: 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

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