Influence of geometrical incompatibility on morphological instability and evolution of growing tubular soft matter

Geometrical incompatibility regulated morphological pattern formation and transition across length scales are widely observed in growing soft matter systems, and have attracted considerable attentions due to their widespread applications. Here, the influence of geometrical incompatibility on the growth-induced pattern formation and morphological evolution on the outer surface of bilayer tubes is investigated comprehensively, through quantitative swelling experiment, numerical simulation and theoretical analysis. Both experimental and theoretical results demonstrate that not only the wrinkling pattern but also the critical growth factor can be regulated by manipulating geometric incompatibility. An increasing geometrical incompatibility parameter leads to a pattern transition from the longitudinal pattern to 2D pattern and then to circumferential pattern, and brings forward the onset of swelling-induced wrinkling instability. Notably, spontaneous instability can be observed on the outer surface when the geometrical incompatibility parameter rises to a critical value. Morphological phase diagrams on pattern selection further illustrate how geometrical incompatibility influences the growth-induced morphological instability by coupling with the thickness ratio and modulus ratio. In agreement with our experimental observations, the numerical results show that geometrical incompatibility also has a significant influence on the post-buckling evolution of the wrinkling patterns. The results not only provide a fundamental understanding of the morphological pattern formation on soft matter system, but also pave a new avenue for the fabrication of periodic patterns on curved surfaces through self-wrinkling.