Periodic void formation in chevron folds

TL;DR

This paper presents an energy-based model explaining the periodic formation of voids in chevron folds, aligning well with experimental observations and revealing conditions for different periodicities.

Contribution

It introduces a novel energy minimization framework modeling void formation in chevron folds, incorporating nonlinear free boundary problems and validating with experiments.

Findings

Minimum-energy solutions can have different periodicities, including m=1.

Model predictions agree well with experimental results.

Void formation patterns depend on energy contributions and boundary constraints.

Abstract

An energy-based model is developed to describe the periodic formation of voids/saddle reefs in hinge zones of chevron folds. Such patterns have been observed in a series of experiments on layers of paper, as well as in the field. A simplified hinge region in a stack of elastic layers, with straight limbs connected by convex segments, is constructed so that a void forms every m layers and repeats periodically. Energy contributions include strain energy of bending, and work done both against a confining overburden pressure and an axial compressive load. The resulting total potential energy functional for the system is minimized subject to the constraint of non-interpenetration of layers, leading to representation as a nonlinear second-order free boundary problem. Numerical solutions demonstrate that there can exist a minimum-energy m-periodic solution with m equal to 1. Good agreement is found with experiments on layers of paper.