On the nucleation and growth of kink and shear bands

G.W. Hunt, T.J. Dodwell, J. Hammond

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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.
LanguageEnglish
Article number20120431
JournalPhilosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences
Volume371
Issue number1993
Early online date20 May 2013
DOIs
StatusPublished - Jun 2013

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kink bands
Shear Bands
Shear bands
Kink
Nucleation
Tail
Critical Load
nucleation
shear
Nonlinear equations
Granular Media
Stiffness
Boundary conditions
Shortage
retaining
falling
Dipole
nonlinear equations
stiffness
Nonlinear Equations

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

In: Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences, Vol. 371, No. 1993, 20120431, 06.2013.

Research output: Contribution to journalArticle

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