Morphological instability of geometrically incompatible bilayer tubes

Abstract

Surface morphological instability, induced by geometric incompatibility, is ubiquitous in nature and plays a pivotal role in maintaining specific biological functions in organs. In this study, we experimentally reveal that geometric incompatibility effectively regulates the morphological instability of bilayer tubes. Building upon these experimental findings, we develop a theoretical model to elucidate the underlying mechanical mechanism of the observed morphological instability. Theoretical analysis demonstrates that by manipulating geometric incompatibility, various patterns including circumferential, two-dimensional (2D), and axial patterns can be generated in bilayer tubes. Specifically, as the axial geometric incompatibility parameter increases, the instability pattern transitions from the circumferential pattern to the 2D pattern and eventually to the axial pattern. Furthermore, we conduct a series of quantitative experiments and finite element simulations to validate our theoretical model. Both the numerical simulations and experimental observations show excellent agreement with our theoretical predictions, demonstrating that linear stability analysis can be employed not only to predict wrinkles but also to determine the number of creases in tubular soft materials roughly. This study significantly advances our understanding of the morphological instability of geometrically incompatible bilayer tubular tissues and provides valuable insights for the fabrication of morphology-related multifunctional surfaces.