Existence and uniqueness of azimuthal shear solutions in compressible isotropic nonlinear elasticity

Joseph E. Paullet, Debra Polignone Warne, Paul G. Warne

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The authors consider the two-point boundary-value problem resulting from the equations of nonlinear elastostatics for azimuthal shear of a Blatz-Ko tube. Previous work on this problem by Simmonds and Warne includes a numerical study of these equations and indicates that smooth radial deformation solutions (no kinks) should exist regardless of the aspect ratio of the tube, provided that the dimensionless applied torque τ is small enough (τ <≈ 0.72). The numerics of Simmonds and Warne also indicated that the existence of smooth solutions for τ >≈ 0.72 depends on the geometry of the tube, and that for τ = √3, no smooth solution exists. Motivated by this numerical work, the authors prove via a topological shooting argument the existence and uniqueness of smooth solutions to this problem for τ ≤ τcr = √3/44/3 ≈ 0.69, and the nonexistence of smooth solutions for τ = √3.

Original languageEnglish (US)
Pages (from-to)53-69
Number of pages17
JournalMathematics and Mechanics of Solids
Volume3
Issue number1
DOIs
StatePublished - Jan 1 1998

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Nonlinear Elasticity
Smooth Solution
Boundary value problems
Aspect ratio
Elasticity
Tube
Existence and Uniqueness
Torque
Geometry
Elastostatics
Shooting
Kink
Two-point Boundary Value Problem
Dimensionless
Aspect Ratio
Nonexistence
Numerical Study

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Materials Science(all)
  • Mechanics of Materials

Cite this

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Existence and uniqueness of azimuthal shear solutions in compressible isotropic nonlinear elasticity. / Paullet, Joseph E.; Warne, Debra Polignone; Warne, Paul G.

In: Mathematics and Mechanics of Solids, Vol. 3, No. 1, 01.01.1998, p. 53-69.

Research output: Contribution to journalArticle

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