Level Set Methods for Multilayer Geological Folding Dr J. Boon, Prof. C. Budd & Prof. G. Hunt

Motivating Examples

Experiments

Experiments on layers of paper (courtesy of Ahmer Wadee, Rorie Edmunds, Jonathan Boon) Before instability – like anisotropic material with nu = 0. After instability – like incompressible fluid under pressure.

In-between States

Model 1 Euler Energy Critical Load depends on length of strut.

Model 2 Strut on a linear elastic foundation – more realistic Critical load Wavelength

Model 3 Viscous foundation Biot: Dominant wavelength Valid for small deflections. Wavelength does not agree well with reality.

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 non-sinusoidal… Use level set method to model the multilayer geometry.

Swallowtail Lagrangian formulation Eulerian formulation Serial folding

LSM applied to parallel fold

Comparison of model with experiment Reformulate mechanical model in terms of the geometry

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