Discussion on the rheological factors influencing the complexity of fractal folds

Guiting Hou, Weihao Yao, and Xuelei Yi

Most natural folds are complex fractal folds. The fractal dimension of a fold can indicate its complexity and its ability (or degree) to fill a space. The folding and its associated fractal dimensions are affected by many factors; e.g. thickness, viscosity, multiple layers, layer parallel shortening, strain softening, initial perturbation, other instabilities, preferred wavelength, non-linear material and layer anisotropy, even the bond between layer and matrix, and many other unknown factors in which the thickness and viscosity of the layer are important. Assuming only two factors (viscosity and thickness) control the complexity of folds in the buckling of a single layer, a formula is derived in this paper to represent the relation between fractal dimension (D) and rheology properties including the layer thickness (h) and viscosity (µ). Information about rheology can potentially be gained from analyzing the fractal geometry of folds. The rheological formula of fractal folds shows that the fractal dimension of folds is affected by the coupling of thickness (h) and viscosity (µ) of a single layer. In conclusion, a thicker layer with higher viscosity may more easily develop more complex folds with higher fractal dimensions, filling more space than a thin layer with lower viscosity. A higher contrast of viscosities or thickness between two layers can yield a larger difference (D1-D2) between two fractal folds. This paper gives a theorical explanation for Ramberg’s experiment.