Numerical modelling of the effect of matrix anisotropy orientation on single layer fold development

Abstract

The influence of matrix anisotropy of variable orientation on single layer folding is investigated using finite element models. Both linear (Newtonian) and power-law viscous materials are considered. The results show that the available isotropic analytical solution, when modified to include an appropriate approximation for the anisotropic viscosity, accurately predicts growth rates at small amplitude for planar anisotropy oriented at α = 45° to the competent layer for a wide range of normal viscosity ratios between single layer and matrix ( μ c = 10, 100) and degrees of anisotropy ( δ = normal viscosity/shear viscosity = 2, 12, 25). For high normal viscosity ratio ( μ c = 100), the deviation from the analytical solution for other orientations increases with increasing degree of anisotropy but still remains relatively small (<5% for δ = 25). For low normal viscosity ratio ( μ c = 10), the differences for high δ are more significant and for α ≠ 0°, 45°, or 90° also depend on the imposed boundary conditions. However, if carefully applied, the analytical solution does provide a benchmark test for numerical codes that include oblique anisotropy. The numerical models at both small and finite amplitude show that a tight control on the boundary conditions is crucial for experiments with anisotropic materials, especially when the anisotropy is oblique to the boundaries. Analogue experiments with anisotropic materials, where boundary conditions are more difficult to control, must therefore be designed and interpreted with caution. Matrix anisotropy initially oriented obliquely with regard to the maximum shortening direction results in asymmetric buckle folds in the single layer and asymmetric chevron folds in the matrix, even if the deformation is purely coaxial. This is true for both linear and power-law materials and for a range of boundary conditions, both free and constrained. Asymmetric natural fold structures in anisotropic material do not therefore necessarily imply a component of non-coaxial flow.