Numerical estimation of the initial hinge-line irregularity required for the development of sheath folds: a pure shear model

Abstract

Non-cylindrical sheath folds often develop by the accentuation of inherent geometrical irregularities along the hinge line during progressive deformation. This paper presents an analysis of the growth of such non-cylindrical folds in pure shear as a function of a non-dimensional initial irregularity factor ζ_o (ζ_o = -log₁₀ [A_o/W_o], where A_o and W_o are the amplitude and the wavelength of a sinuous hinge line, respectively). Curvature accentuation of the hinge line produces sheath-like non-cylindrical folds in passive layers only when ζ_o ≤ 1. Folds with ζ_o > 1 remain weakly or moderately non-cylindrical even after a large finite strain (λ = 36). An increasing flattening strain (1 > k value > 0) component in the deformation reduces the degree of non-cylindricity. We extend the analysis into layered systems with viscosity contrasts (i.e. viscosity ratio, R), considering a strain-partitioning factor λ_f (the strain ratio between the fold hinge and bulk medium). Using finite element methods, it is shown that λ_f can be small even for low values of R (4-8). Consequently, strong non-cylindricity does not grow in higher-viscosity layers for ζ_o = 1. We ran experiments using three-dimensional finite element models to investigate the additional effects of mechanical bending on curvature accentuation of the hinge line. These experiments also show little accentuation of hinge curvature irrespective of R, when ζ_o > 1. However, for ζ_o ≤ 1, hinge-line curvature accentuates moderately when R < 8. It follows from our analysis that strongly non-cylindrical folds cannot develop unless the magnitude of initial hinge-line irregularity is sufficiently large (i.e. ζ_o «1). We also discuss the implications of the numerical results for pure shear models in the analysis of sheath folds in shear zones.