Folder: A numerical tool to simulate the development of structures in layered media

• We present a tool for modelling and visualizing deformation in layer media.
• Folder is capable of modelling large system with linear and non-linear materials.
• We discuss and quantify errors related with numerical modelling in layered media.
• We present examples of Folder application.
• We provide novel analytical solutions of growth rates for folding and necking in confined medium.

We present Folder, a numerical toolbox for modelling deformation in layered media subject to layer parallel shortening or extension in two dimensions. The toolbox includes a range of features that ensure maximum flexibility to configure model geometry, define material parameters, specify numerical parameters, and choose the plotting options. Folder builds on an efficient finite element method model and implements state of the art iterative and time integration schemes. We describe the basic Folder features and present several case studies of single and multilayer stacks subject to layer parallel shortening and extension. Folder additionally comprises an application that illustrates various analytical solutions of growth rates calculated for the cases of layer parallel shortening and extension of a single layer with interfaces perturbed with a single sinusoidal waveform. We further derive two novel analytical expressions for the growth rate in the cases of layer parallel shortening and extension of a linear viscous layer embedded in a linear viscous medium of a finite thickness. These solutions help understand mechanical instabilities in layered rocks and provide a unique opportunity for benchmarking of numerical codes. We demonstrate how Folder can be used for benchmarking of numerical codes. We test the accuracy of single-layer folding simulations using various 1) spatial and temporal resolutions, 2) iterative algorithms for non-linear materials, and 3) time integration schemes. The accuracy of the numerical results is quantified by: 1) comparing them to analytical solutions, if available, or 2) running convergence tests. As a result, we provide a map of the most optimal choice of grid size, time step, and number of iterations to keep the results of the numerical simulations below a given error for a given time integration scheme. Folder is an open source MATLAB application and comes with a user-friendly graphical interface. Folder is suitable for both educational and research purposes.

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