Drawing parallels: Modelling geological phenomena using constraint satisfaction

This paper gives insight into the transition between the different folding-types seen in nature. Using constraint satisfaction and optimization to study least energy solutions of an elastic, frictional model for concentric parallel folding, kink band waveshapes resulting from the same model are discovered. Simplifying the concentric parallel folding model down to a two layer formulation, and assuming the geometry of the whole layered material is governed by this, the behaviour of the central interface is represented using a number of points whose displacement is constrained. With a linear foundation, the full large-deflection energy formulation reaches a point where the whole system is locked up after only two folds, matching experimental evidence. This is overcome by adding a nonlinearity to the foundation, where the sequential destabilization and restabilization of experimental load-deflection plots is observed and the wave-profiles agree with the naturally occurring geological phenomenon. Increasing the nonlinearity in the foundation and the magnitude of the overburden pressure, the phenomenology of the concentric folding model can be altered to one that is more kink band-like in structure. Thus a “trigger” is found, relating two prevalent folding patterns which are generally considered to be at opposite ends of the spectrum of geometries.