Sheath folds as a strain gauge in simple shear

We investigate initiation and evolution of sheath folds developing in multilayer sequences around slip surfaces in simple shear. The slip surface is initially circular and oriented at 135 degrees to the shearing direction. The flow perturbation around the rotating and deforming slip surface initiates the growth of deflections of the layers, which serves as precursors for the sheath structure. The influence of the perturbed flow on the fold growth decreases with strain as the structure is moved away from the slip surface. For gamma > 10, the sheath fold evolution is dominated by a passive simple shear. We describe the fold geometry using: 1) interlimb angle (alpha), 2) apical angle (beta), and 3) aspect ratio of the eye-structures in the section normal to the shearing direction at the fold base (R-yz). We show that the fold shapes developing in different interfaces can be characterized by a unique combination of the three parameters depending on strain magnitude. We present three strain gauge diagrams, which can be used to decipher strain from sheath folds based on any combination of two out of three parameters (alpha, beta, R-yz). We approximate the late evolution of the modelled sheath folds by analysing the passive deformation of cone structures in simple shear. We show that R-yz is asymptotically proportional to the square root of strain magnitude. (C) 2017 Elsevier Ltd. All rights reserved.