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Keywords
(6)
Differential Equation
Energy Minimization
Free Boundary
Obstacle Problem
Ordinary Differential Equation
Scaling Law
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Selfsimilar voiding solutions of a single layered model of folding rocks
Selfsimilar voiding solutions of a single layered model of folding rocks,10.1137/110822499,Timothy Dodwell,Mark Peletier,Christopher Budd,Giles Hunt
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Selfsimilar voiding solutions of a single layered model of folding rocks
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Timothy Dodwell
,
Mark Peletier
,
Christopher Budd
,
Giles Hunt
In this paper we derive an
obstacle problem
with a
free boundary
to describe the formation of voids at areas of intense geological folding. An elastic layer is forced by overburden pressure against a Vshaped rigid obstacle.
Energy minimization
leads to representation as a nonlinear fourthorder ordinary differential equation, for which we prove their exists a unique solution. Drawing parallels with the KuhnTucker theory, virtual work, and ideas of duality, we highlight the physical significance of this differential equation. Finally we show this equation scales to a single parametric group, revealing a
scaling law
connecting the size of the void with the pressure/stiffness ratio. This paper is seen as the first step towards a full multilayered model with the possibility of voiding.
Published in 2012.
DOI:
10.1137/110822499
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References
(14)
Level set methods for the displacement of layered materials
(
Citations: 4
)
J. A. Boon
,
C. J. Budd
,
G. W. Hunt
Journal:
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
, vol. 463, no. 2082, pp. 14471466, 2007
A nonlinear model for parallel folding with friction
(
Citations: 6
)
C. J. Budd
,
R. Edmunds
,
G. W. Hunt
Journal:
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
, vol. 459, no. 2036, pp. 20972119, 2003
Theory of differential equations
(
Citations: 80
)
A. R. Forsyth
Parallel folding in multilayered structures
(
Citations: 6
)
R. Edmunds
,
G. W. Hunt
,
M. Ahmer Wadee
Journal:
Journal of The Mechanics and Physics of Solids  J MECH PHYS SOLIDS
, vol. 54, no. 2, pp. 384400, 2006
On the smoothness of convex envelopes
(
Citations: 28
)
A. Griewank
,
P. J. Rabier
Published in 1990.