# Generalized azimuthal shear deformations in compressible isotropic elastic materials

Kirkinis, E. & Tsai, H.
(2005)
Generalized azimuthal shear deformations in compressible isotropic elastic materials.
*SIAM Journal on Applied Mathematics*, *65*(3), pp. 1080-1099.

## Abstract

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

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ID Code: | 73433 |
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Item Type: | Journal Article |

Refereed: | Yes |

Keywords: | Azimuthal shear, Constitutive laws, Legendre transforms, Nonlinear elasticity, Quasilinear partial differential equations, Quasi-linear partial differential equations, Boundary conditions, Deformation, Kinematics, Partial differential equations, Phase transitions, Strain, Tensors, Elasticity |

DOI: | 10.1137/S0036139903438077 |

ISSN: | 00361399 (ISSN) |

Divisions: | Current > Schools > School of Mathematical Sciences Current > QUT Faculties and Divisions > Science & Engineering Faculty |

Deposited On: | 07 Jul 2014 22:49 |

Last Modified: | 09 Jul 2014 06:39 |

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