## 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 minimised 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≠1. The model shows good agreement when compared with experiments on layers of paper.

Original language | English |
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Pages (from-to) | 1011-1028 |

Number of pages | 18 |

Journal | Mathematical Geosciences |

Volume | 46 |

Issue number | 8 |

Early online date | 7 Oct 2014 |

DOIs | |

Publication status | Published - 28 Nov 2014 |

## Keywords

- Delamination
- Energy methods
- Folding
- Saddle reef formation