Wrinkling in surfaces

Wrinkles have been in the limelight for their theoretical importance in understanding geometric nonlinearities in elasticity and also for their practical significance in emerging engineering applications such as lithography-free micropatterning Yet, despite decades of study, a general predictive theory of confinement-induced wrinkling remains elusive. Such a theory would enable the creation of targeted yet reconfigurable wrinkle patterns and could identify the broadest possible class of wrinkle morphologies that can be obtained through geometrically incompatible confinement."

Source : Nature Physics (Aug. 2022)

The mathematics of wrinkling and crumpling are so notoriously complex that even sophisticated computer modeling techniques fail to accurately predict how a surface will fold up. The paper cited above managed to find solutions for some 'flat' scenarios.

In many 'real world' situations, however, there are too many variables (and quasi-random effects) to construct accurate models.

Further reading : A state variable for crumpled thin sheets, Communications Physics volume 1, article number: 70

From collapsed hulls of ships to discarded mathematical theorems written on a white piece of paper, many thin sheets end their life cycle as crumpled heaps. Nevertheless, the dynamics by which an initially flat sheet develops into a disordered and elaborate three-dimensional network of folds are often considered a hallmark example of disordered and complex system"