Chevron folding patterns and heteroclinic orbits
Physica D: Nonlinear Phenomena
Reason for embargo
We present a model of multilayer folding in which layers with bending stiffness EI are separated by a very stiff elastic medium of elasticity k2 and subject to a horizontal load P. By using a dynamical systems analysis of the resulting fourth order equation, we show that as the end shortening per unit length E is increased, then if k2 is large there is a smooth transition from small amplitude sinusoidal solutions at moderate values of P to larger amplitude chevron folds, with straight limbs separated by regions of high curvature when P is large. The chevron solutions take the form of near heteroclinic connections in the phase-plane. By means of this analysis, values for P and the slope of the limbs are calculated in terms of E and k2.
We would like to acknowledge the support of the FP7 Marie-Curie ITN FIRST, the Pacific Institute for Mathematics Sciences (PIMS) and the NSERC Discovery Grant for the funding of the research described in this paper
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.
Available online 11 May 2016