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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 444-463 |
| Number of pages | 20 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 72 |
| Issue number | 1 |
| Early online date | 21 Feb 2012 |
| DOIs | |
| Publication status | Published - 2012 |