Level Set Methods for Multilayer
Geological Folding
Jonathan Boon, Chris Budd & Giles.Hunt
Motivating Examples
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Experiments
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Experiments on layers of paper (courtesy of Ahmer Wadee, Rorie
Edmunds, Jonathan Boon)
In-between States
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Model 1
• Euler strut
• Energy
• Critical Load
length of strut.
depends on
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Model 2
• Strut on a linear elastic foundation – more
realistic
• Critical load
• Wavelength
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Model 3
• Viscous foundation
• Biot: Dominant wavelength
• Valid for small deflections.
• Wavelength does not agree well with reality.
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P
Δ
Multilayer models
• Two layer model developed (Budd et al. 2003).
• Addition of friction to elastic foundation model.
• Can not accurately extend to n layer model
because outer layers become nonsinusoidal…
• Use level set method to model the multilayer
geometry.
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Swallowtail
Lagrangian formulation
Eulerian formulation
Serial folding
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LSM applied to parallel fold
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Comparison of model with
experiment
• Reformulate mechanical model in terms of the
geometry
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Conclusion
• Singularity formation in multilayers can be
predicted by the geometry.
• Nonlinear bending energy provides a
mechanism of restabilising a fold.
• Serial folds form most naturally from the
reactive end.
• Further work needed to verify results and to
check the effects of unmodelled behaviour
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