Serial parallel folding with friction: a primitive model using cubic B-splines

An earlier nonlinear model for two-layer parallel folding with bedding plane slip is extended to embrace serial buckling behaviour. Approximating the folds using two cubic B-splines, a quasi-energy formulation admits both synchronous and serial-type buckling under conditions of both controlled load and controlled end-shortening. In the early stages of evolution, non-periodic saddle points, corresponding to localized folds, are found to provide the preferred solution. However, as the end-shortening increases, the saddle points converge with unstable maxima representing synchronous folding, until only periodic solutions exist. This shift from localized to two-hump periodic behaviour is seen as a primitive exposition of the more general theme of serial or sequential fold formation.