title: On the nucleation and growth of kink and shear bands.
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.
authors.affiliation: Centre for Nonlinear Mechanics, University of Bath, Bath BA2 7AY, UK. g.w.hunt@bath.ac.uk
authors.forename: G W
authors.initials: GW
authors.lastname: Hunt
authors.forename: T J
authors.initials: TJ
authors.lastname: Dodwell
authors.forename: J
authors.initials: J
authors.lastname: Hammond
keywords: bifurcation; granular media; layered structures; localization; structural geology