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(a) Kink banding in compressed layers of paper. Deformation is forced in about 625 sheets of paper from a sample of 800. (b) Output: load versus end-displacement. (Adapted from Wadee et al. [2].):
Wadee AM, Hunt GW, Peletier MA. 2004 Kink band instability in layered structures. J. Mech. Phys. Solids 52, 1071–1091
This and the next slide are from:
G.W. Hunt, T.J. Dodwell and J. Hammond, “On the nucleation and growth of kink and shear bands”, The Royal Society Philosophical Transactions A, May 2013, DOI: 10.1098/rsta.2012.0431
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.
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