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Periodic Void Formation in Chevron Folds

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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 \(m \ne 1\). The model shows good agreement when compared with experiments on layers of paper.

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Acknowledgments

The authors would like to thank both Mark Peletier and Bruce Hobbs for various discussions and inputs throughout this work, as well as Ahmer Wadee who during his time at Bath carried out Experiment 1 under the EPSRC project GR/L17177/01.

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Correspondence to T. J. Dodwell.

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Dodwell, T.J., Hunt, G.W. Periodic Void Formation in Chevron Folds. Math Geosci 46, 1011–1028 (2014). https://doi.org/10.1007/s11004-014-9562-x

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