An approach to folding kinematics from the analysis of folded oblique surfaces

Two-dimensional analysis of folded surfaces oblique to the mechanical layering can shed light on the kinematic mechanisms that operated during the development of folds. A new version of the program ‘FoldModeler’, developed in the Mathematica™ environment, is used to obtain the deformed configuration of an initial pattern of oblique surfaces deformed by any combination of the most common kinematic folding mechanisms: flexural flow, tangential longitudinal strain, with or without area change and heterogeneous simple shear. The layer can also undergo any form of homogeneous strain at any moment of the folding process. The outputs of the program provide complete information about the strain distribution in the folded layer that includes graphs of the angle between the oblique surfaces as a function of the inclination of the layering through the fold. These graphs can be very useful to discriminate between the mechanisms that operate in the development of natural folds, and they have been obtained and discussed for the most common combinations of strain patterns. The program is applied to obtain theoretical folds that give a good fit of some natural examples of folded oblique surfaces.