Spontaneous Wrinkling in Growing Sheets: Coupling Growth and Rigidity Gradients

Thin elastic sheets are highly susceptible to wrinkling instabilities, typically arising under external constraints. Yet, many growing biological structures, such as leaves, flower petals, and marine invertebrates, spontaneously develop intricate wrinkled patterns without external loads. I investigate the emergence of such instabilities driven by sharp spatial gradients in both growth and bending rigidity. Previous studies have shown that sharp growth gradients alone lead to global buckling, while extreme rigidity gradients suppress buckling in favor of pure wrinkling.

In this talk, I explore the rich intermediate regime where growth and rigidity gradients are comparably sharp. I demonstrate that wrinkles emerge with characteristic wavelengths that evolve through coarsening dynamics. Strikingly, when buckling and wrinkling occur concurrently, wrinkles become spatially confined to distinct regions, creating a hierarchical pattern of deformations. These findings provide insight into the morphogenesis of complex biological forms where differential growth couples naturally to varying material properties. More broadly, they suggest a design principle for shape-morphing synthetic materials. While differential swelling inevitably produces nonuniform rigidity, they are typically viewed as a nuisance. In contrast, my work shows this coupling can be utilized to expand the repertoire of accessible three-dimensional shapes. The resulting patterns are equally mechanically informative and visually striking, revealing the hidden interplay between geometry, growth, and elasticity.