Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Pure azimuthal shear of compressible non-linearly elastic circular tubes

Authors: Debra A. Polignone and Cornelius O. Horgan
Journal: Quart. Appl. Math. 52 (1994), 113-131
MSC: Primary 73G05; Secondary 73C50, 73K05
DOI: https://doi.org/10.1090/qam/1262323
MathSciNet review: MR1262323
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Abstract: The azimuthal (or circular) 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. The deformation may be achieved either by applying a uniformly distributed azimuthal shear traction on the outer surface together with zero radial traction (Problem 1) or by subjecting the outer surface to a prescribed angular displacement, with zero radial displacement (Problem 2). For an arbitrary compressible material, the cylinder will undergo both a radial and angular 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 pure azimuthal shear (i.e., a deformation with zero radial displacement) is possible is described. The corresponding angular 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/1262323
Article copyright: © Copyright 1994 American Mathematical Society

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