Multi-layered folding with voids

by T. J. Dodwell, G. W. Hunt, M. A. Peletier, and C. J. Budd

Philosophical Transactions AVolume 370(1965):1740-1758

April 28, 2012

©2012 by The Royal Society

Folding patterns in thin bedded shales and sandstones in Cornwall (UK): (a) parallel folding at Bude and (b) chevron folding at Millook Haven.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

(a) Kink banding in compressed layers of a paper.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

A compression test with a weaker, but stiffening, foundation (foam).

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

A compression test with low initial overburden pressure.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

Sharp-angle, straight-limb folds give rise to smaller void spaces than rounded folds.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

Single elastic layer, of infinite length, being forced into a corner by the action of pressure q.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

Finite-length beam under pressure loading q and axial compression P.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

(a) ℓ against q/B.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

(a) ℓ against P/B.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

The main graph shows values of P for given Δ for two types of solutions of the Euler–Lagrange equation (2.5), for fixed pressure q=1, angle of limb fx=k=1 and length of beam L. (a,b) The

smaller plots show the profile of the layer at the positions indicated...

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

The formation of higher order accommodation structures in the hinge regions of a multi-layered buckle.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

Multi-layered set-up.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

(a) Boundary functions determined via front propagation.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

(a) An example of solution profiles for fixed angle k=0.75, h=0.02, load P=1 and overburden pressure q=100.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

Relationship between void size and k, for increasing values of q/B. q/B=1,10,100, P/B=1, h=0.1 and N=20.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society

Construction of an m-periodic package as straight limbs connected by circular arcs.

T. J. Dodwell et al. Phil. Trans. R. Soc. A 2012;370:1740-1758

©2012 by The Royal Society