Finite-element modelling of single-layer folding in elasto-viscous materials: the effect of initial perturbation geometry

Abstract

The influence of periodic, isolated bell-shaped and random initial perturbations on single-layer fold amplification was numerically modelled for a wide range of elasto-viscous material properties. The results from this finite-element modelling (FEM) are markedly different from previous finite-difference (FLAC) models, but similar to analogue scale-models. For periodic perturbations, only the introduced waveform is amplified into folds, even for an initial wavelength much shorter or longer than the fastest growing ‘dominant’ wavelength. Hinge and inflection points remain fixed to the same material points and there is no hinge migration to allow development of the dominant wavelength. Enhanced elastic behaviour increases the growth rate of shorter wavelength components and hence modifies the final fold shape, but hinge or inflection points still remain fixed. For initial isolated bell-shaped perturbations, a slow serial sideways propagation of folding along the layer leads to the eventual development of an internally periodic fold packet of near constant amplitude at high values of shortening (>50%). Increased elastic or non-linear power law viscous behaviour promotes localization about the initial isolated perturbation. Even for random initial irregularities, the final high-amplitude fold shape is only quasi-periodic and still shows the influence of the initial perturbation geometry. The maximum amplitude of these initial irregularities also influences the final fold shape, especially when the growth rate of the folds is low. For the same viscosity contrast, smaller initial amplitude promotes growth of long wavelength components producing final shapes similar to those developed in higher viscosity ratio experiments. Increased elastic behaviour promotes shorter wavelengths, faster growth rates and greater wavelength selectivity, resulting in more regular periodic forms that are less influenced by initial perturbation amplitude. However, in all cases investigated, the initial perturbation geometry still exerts an influence on the finite fold shape and the irregular, only quasi-periodic form of many natural folds reflects this initial irregularity control.