### Abstract

Language | English |
---|---|

Article number | 20120431 |

Journal | Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences |

Volume | 371 |

Issue number | 1993 |

Early online date | 20 May 2013 |

DOIs | |

Status | Published - Jun 2013 |

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### Cite this

*Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences*,

*371*(1993), [20120431]. https://doi.org/10.1098/rsta.2012.0431

**On the nucleation and growth of kink and shear bands.** / Hunt, G.W.; Dodwell, T.J.; Hammond, J.

Research output: Contribution to journal › Article

*Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences*, vol. 371, no. 1993, 20120431. https://doi.org/10.1098/rsta.2012.0431

}

TY - JOUR

T1 - On the nucleation and growth of kink and shear bands

AU - Hunt, G.W.

AU - Dodwell, T.J.

AU - Hammond, J.

PY - 2013/6

Y1 - 2013/6

N2 - Similarities and differences between the phenomena of kink banding in compressed layered structures and shear banding in compressed granular media are explored. Simple models are introduced for both, and the focus is directed onto how they can nucleate from the perfectly flat state. A convincing scenario is found for each in which a mode develops from an initial bifurcation into a periodic state, followed by rapid localization under falling load, while retaining decaying but wavy tails. At a certain lower critical load, the tails lose their waviness, and the expected form of the kink or shear band appears. In each case, good numerical evidence is provided for the existence of this form of behaviour. A second potential instability for the layered case is also explored, linked to the appearance of a critical force dipole that overcomes bending stiffness locally at some point along the length. This mode, which should appear with non-wavy decaying tails at the lower of the two critical loads mentioned earlier, proves somewhat elusive. Evidence is found for its existence in the linearized approximation to the layered model, but the search for numerical solutions to the underlying nonlinear equation is hindered by a shortage of suitable boundary conditions.

AB - Similarities and differences between the phenomena of kink banding in compressed layered structures and shear banding in compressed granular media are explored. Simple models are introduced for both, and the focus is directed onto how they can nucleate from the perfectly flat state. A convincing scenario is found for each in which a mode develops from an initial bifurcation into a periodic state, followed by rapid localization under falling load, while retaining decaying but wavy tails. At a certain lower critical load, the tails lose their waviness, and the expected form of the kink or shear band appears. In each case, good numerical evidence is provided for the existence of this form of behaviour. A second potential instability for the layered case is also explored, linked to the appearance of a critical force dipole that overcomes bending stiffness locally at some point along the length. This mode, which should appear with non-wavy decaying tails at the lower of the two critical loads mentioned earlier, proves somewhat elusive. Evidence is found for its existence in the linearized approximation to the layered model, but the search for numerical solutions to the underlying nonlinear equation is hindered by a shortage of suitable boundary conditions.

UR - http://www.scopus.com/inward/record.url?scp=84878153653&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1098/rsta.2012.0431

U2 - 10.1098/rsta.2012.0431

DO - 10.1098/rsta.2012.0431

M3 - Article

VL - 371

JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

T2 - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

SN - 1364-503X

IS - 1993

M1 - 20120431

ER -