When you push up your sleeves, wrinkles form, which eventually evolve into ridges (pictured). As familiar as you may be with this phenomenon, have you ever thought about its underlying mechanism? It involves the complex nonlinear mechanical behaviour of large deformations and surface instabilities, which in turn give rise to a sophisticated morphological evolution. And now, Yifan Yang and co-workers have revealed a hitherto unknown post-buckling behaviour that involves multiple bifurcation transitions (Phys. Rev. Lett. https://doi.org/10.1103/PhysRevLett.120.215503; 2018).

Credit: Bombaert Patrick/Alamy Stock Photo

The process is slightly simpler when examined in a planar geometry: think of compressing a sheet of paper on a table from both ends. Under lateral compression, the paper bends to form one single fold in a localized region, thereby buckling out of the plane. For sleeves, however, the curved surface of the human arm makes the process even more intricate.

To meet this challenge, Yang et al. established a model of a soft shell sliding on a rigid cylinder. They traced the entire evolution of the surface patterns and identified different phase regions by capturing successive bifurcations. Under compression, the shell initially buckled into periodic axisymmetric wrinkles at a critical threshold. It then underwent a wrinkle-to-ridge transition upon further axial compression, whereby one single ridge grew at the expense of the intermediate wrinkles. On further compression, a third bifurcation occurred when the amplitude of the ridge reached its limit, and the symmetry was broken with the ridge sagging into a recumbent fold, thus releasing strain energy in its vicinity.

In contrast to buckling in a planar geometry, the effect of the curvature turns out to be crucial for driving the multiple successive bifurcations in the morphological evolution of soft shells, especially for the primary supercritical unbuckled-to-wrinkled transition. The wrinkle and ridge patterns can coexist and be flexibly alternated through compressing and uncompressing.

Another important factor that determines the instability mode selection is the imperfection experienced by the shell. In the study by Yang et al., direct support from the core eliminated the imperfection sensitivity of the shell and led to stable axisymmetric patterns, whereas a gap between the core and the shell induced the appearance of unstable diamond-like patterns.

Understanding the nonlinear morphological transitions of soft matter holds potential for multifunctional surface fabrication, and hence widespread applications. Roll up your sleeves, there is more work to do in this area.