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In this paper we derive an obstacle problem with a free boundary to describethe formation of voids at areas of intense geological folding. An elastic layeris forced by overburden pressure against a V-shaped rigid obstacle. Energyminimization leads to representation as a nonlinear fourth-order ordinarydifferential equation, for which we prove their exists a unique solution.Drawing parallels with the Kuhn-Tucker theory, virtual work, and ideas ofduality, we highlight the physical significance of this differential equation.Finally we show this equation scales to a single parametric group, revealing ascaling 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 thepossibility of voiding.

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