### Abstract

Original language | English |
---|---|

Pages (from-to) | 498-517 |

Number of pages | 21 |

Journal | Zeitschrift für Angewandte Mathematik und Physik |

Volume | 59 |

Issue number | 3 |

Early online date | 6 Aug 2007 |

DOIs | |

Publication status | Published - May 2008 |

### Fingerprint

### Keywords

- 74B20
- 74P99
- finite elasticity
- large deformations
- nonlinear elasticity
- azimuthal shear
- complementary variational principle
- triality theory

### Cite this

*Zeitschrift für Angewandte Mathematik und Physik*,

*59*(3), 498-517. https://doi.org/10.1007/s00033-007-7047-1

**Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem.** / Gao, D. Y.; Ogden, R. W.

Research output: Contribution to journal › Article

*Zeitschrift für Angewandte Mathematik und Physik*, vol. 59, no. 3, pp. 498-517. https://doi.org/10.1007/s00033-007-7047-1

}

TY - JOUR

T1 - Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem

AU - Gao, D. Y.

AU - Ogden, R. W.

PY - 2008/5

Y1 - 2008/5

N2 - The pure azimuthal shear problem for a circular cylindrical tube of nonlinearly elastic material, both isotropic and anisotropic, is examined on the basis of a complementary energy principle. For particular choices of strain-energy function, one convex and one non-convex, closed-form solutions are obtained for this mixed boundary-value problem, for which the governing differential equation can be converted into an algebraic equation. The results for the non-convex strain energy function provide an illustration of a situation in which smooth analytic solutions of a nonlinear boundary-value problem are not global minimizers of the energy in the variational statement of the problem. Both the global minimizer and the local extrema are identified and the results are illustrated for particular values of the material parameters.

AB - The pure azimuthal shear problem for a circular cylindrical tube of nonlinearly elastic material, both isotropic and anisotropic, is examined on the basis of a complementary energy principle. For particular choices of strain-energy function, one convex and one non-convex, closed-form solutions are obtained for this mixed boundary-value problem, for which the governing differential equation can be converted into an algebraic equation. The results for the non-convex strain energy function provide an illustration of a situation in which smooth analytic solutions of a nonlinear boundary-value problem are not global minimizers of the energy in the variational statement of the problem. Both the global minimizer and the local extrema are identified and the results are illustrated for particular values of the material parameters.

KW - 74B20

KW - 74P99

KW - finite elasticity

KW - large deformations

KW - nonlinear elasticity

KW - azimuthal shear

KW - complementary variational principle

KW - triality theory

U2 - 10.1007/s00033-007-7047-1

DO - 10.1007/s00033-007-7047-1

M3 - Article

VL - 59

SP - 498

EP - 517

JO - Zeitschrift für Angewandte Mathematik und Physik

JF - Zeitschrift für Angewandte Mathematik und Physik

SN - 0044-2275

IS - 3

ER -