Self-similar voiding solutions of a single layered model of folding rocks

T. J. Dodwell, M. A. Peletier, Chris J. Budd, G. W. Hunt

Research output: Contribution to journalArticle

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Abstract

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 V-shaped rigid obstacle. Energy minimization leads to representation as a nonlinear
fourth-order ordinary differential equation, for which we prove there exists a unique solution.
Drawing parallels with the Kuhn–Tucker theory, virtual work, and ideas of duality, we highlight the
physical significance of this differential equation. Finally, we show that 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 toward a full multilayered model with the possibility of
voiding.
LanguageEnglish
Pages444-463
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume72
Issue number1
Early online date21 Feb 2012
DOIs
StatusPublished - 2012

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Self-similar Solutions
Voids
Folding
Rocks
Obstacle Problem
Energy Minimization
Scaling laws
Scaling Laws
Free Boundary
Ordinary differential equations
Unique Solution
Fourth Order
Stiffness
Duality
Ordinary differential equation
Differential equations
Differential equation
Model
Drawing

Cite this

Self-similar voiding solutions of a single layered model of folding rocks. / Dodwell, T. J.; Peletier, M. A.; Budd, Chris J.; Hunt, G. W.

In: SIAM Journal on Applied Mathematics, Vol. 72, No. 1, 2012, p. 444-463.

Research output: Contribution to journalArticle

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