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


Reference:

Dodwell, T. J., Peletier, M. A., Budd, C. J. and Hunt, G. W., 2012. Self-similar voiding solutions of a single layered model of folding rocks. SIAM Journal on Applied Mathematics, 72 (1), pp. 444-463.

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    Official URL:

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

    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.

    Details

    Item Type Articles
    CreatorsDodwell, T. J., Peletier, M. A., Budd, C. J. and Hunt, G. W.
    DOI10.1137/110822499
    DepartmentsFaculty of Engineering & Design > Mechanical Engineering
    Faculty of Science > Mathematical Sciences
    Research CentresBath Institute for Complex Systems (BICS)
    Publisher StatementBudd_SIAM_J_Appl_Math_2012_72_1_444.pdf: © 2012 Society for Industrial and Applied Mathematics
    RefereedYes
    StatusPublished
    ID Code32438

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