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

3. Motivating Examples

4. Experiments

5. 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.

6. In-between States

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

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

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

10. P Δ

11. 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.

12. Swallowtail
Lagrangian formulation
Eulerian formulation
Serial folding

13. LSM applied to parallel fold

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

15. 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