### Abstract

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.

Language | English |
---|---|

Pages | 444-463 |

Number of pages | 20 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 72 |

Issue number | 1 |

Early online date | 21 Feb 2012 |

DOIs | |

Status | Published - 2012 |

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

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 72, no. 1, pp. 444-463. DOI: 10.1137/110822499

}

TY - JOUR

T1 - Self-similar voiding solutions of a single layered model of folding rocks

AU - Dodwell,T. J.

AU - Peletier,M. A.

AU - Budd,Chris J.

AU - Hunt,G. W.

PY - 2012

Y1 - 2012

N2 - In this paper we derive an obstacle problem with a free boundary to describe theformation of voids at areas of intense geological folding. An elastic layer is forced by overburdenpressure against a V-shaped rigid obstacle. Energy minimization leads to representation as a nonlinearfourth-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 thephysical significance of this differential equation. Finally, we show that this equation scales to a singleparametric group, revealing a scaling law connecting the size of the void with the pressure/stiffnessratio. This paper is seen as the first step toward a full multilayered model with the possibility ofvoiding.

AB - In this paper we derive an obstacle problem with a free boundary to describe theformation of voids at areas of intense geological folding. An elastic layer is forced by overburdenpressure against a V-shaped rigid obstacle. Energy minimization leads to representation as a nonlinearfourth-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 thephysical significance of this differential equation. Finally, we show that this equation scales to a singleparametric group, revealing a scaling law connecting the size of the void with the pressure/stiffnessratio. This paper is seen as the first step toward a full multilayered model with the possibility ofvoiding.

UR - http://www.scopus.com/inward/record.url?scp=84859905931&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1137/110822499

U2 - 10.1137/110822499

DO - 10.1137/110822499

M3 - Article

VL - 72

SP - 444

EP - 463

JO - SIAM Journal on Applied Mathematics

T2 - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -