  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.
