Localised folding in general deformations

Abstract

One control on the buckling of a layer (or layers) embedded in a weaker matrix is the reaction force exerted by the deforming matrix on the layer. If the system is linear and this force is a linear function of the layer deflection, as for linear elastic and viscous materials, the resulting buckles can be sinusoidal or periodic. However if the system is geometrically nonlinear, as in general non-coaxial deformations, or the matrix material is nonlinear, as for nonlinear elastic, non-Newtonian viscous and plastic materials, the buckling response may be localised so that individual packets of folds form; the resulting fold profile is not sinusoidal. These folds are called localised folds. Most natural folds are localised. One view is that irregularity derives solely from initial geometrical perturbations. We explore a different view where the irregular geometry results from a softening material or geometrical nonlinearity without initial perturbations. Localised folds form in a fundamentally different way than the Biot wavelength selection process; the concept of a dominant wavelength does not exist. Folds grow and collapse sequentially rather than grow simultaneously. We discuss the formation of localised folds with recent considerations of constitutive behaviour at geological strain rates for general three-dimensional deformations.