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

Self-similar voiding solutions of a single layered model of folding rocks,10.1137/110822499,Timothy Dodwell,Mark Peletier,Christopher Budd,Giles Hunt

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