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
AN - SCOPUS:84878153653
SN - 1364-503X
VL - 371
JO - Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences
IS - 1993
M1 - 20120431
ER -