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To the right is the experiments conducted by Willis on folding towards the end of the 19th century. Left is a photograph of buckle folds developed at the contact of Untala granite(left) and overlying supracrustal sequence (right). Note that the contact is gently folded but a felsic vein in the amphibolites to the right has buckled nearly as a single layer fold with extremely uniform thickness and very regular periodicity. Buckling of this layer must have proceeded fast and Wi was close to Wd.

Buckle folds:

single layer situation where a more competent layer is surrounded by an incompetent material. The former is free to form buckle folds that have a parallel character, while the former will show another shape. Biot (1957)  --correspondence principle between elastic and viscoelastic materials (Newtonian viscosity), looks at stress-strain relationships in buckled layer. Ramberg (1959) -- approaches problem as one of fluid dynamics - particular function which satisfies both the biharmonic equation of a stream function and boundary conditions around a buckled layer. Both develop idea of dominant wavelength. Only valid for small % of strain, but then have inheritance principle; wd = 2 t ^3 ( 1 / 62 ) where wd is dominant wavelength, t is layer thickness, and 1 and 2 are the viscosities of the dominant layer and surrounding medium respectively. note that deviatoric stress plays no direct role. viscosity contrast, if < 5 get pure shortening. too high deviatoric stress get brittle failure, too low pure shortening. see this with ptygmatic folds in some outcrops; average wad/t ratio of 27 are folds with ratio around 5-7; possibly due to non-Newtonian viscosity. extrados and intrados of a beam - features that would indicate buckling.