How far does a fold go?

Abstract

We assess the spatial spread of a fold within a narrow elastic strip theoretically and computationally in the small deflection regime. We consider a hierarchy of folding-response ansatz, suitable for stretch-free deformation. The role of Poisson’s coupling between the two curvatures, and that of surface twist, is brought out. Here we show that there exists a critical Poisson’s ratio separating the regime of monotonically decaying fold profiles from that of decaying oscillatory folds. A spatially separable solution results in length-wise localised folds, the length scale of which is in excellent agreement with that obtained from simulations. The persistence length shows significant sensitivity to the Poisson’s ratio of the material. We also establish a mathematical analogy of the folding problem, with one of elastic structures on foundations, the restoring force being proportional to local deflection as well as shear in the foundation.