Mechanics and wrinkling patterns of pressurized bent tubes

Take a drinking straw and bend it from its ends. After sufficient bending, the tube buckles forming a kink, where the curvature is localized in a very small area. This instability, known generally as the Brazier effect, is inherent to thin-walled cylindrical shells, which are particularly ubiquitous in living systems, such as rod-shaped bacteria. However, tubular biological structures are often pressurized, and the knowledge of the mechanical response upon bending in this scenario is limited. In this work, we use a computational model to study the mechanical response and the deformations as a result of bending pressurized tubes. In addition, we develop a model inspired by tension-field theory to analytically describe the mechanical behavior before and after the wrinkling transition. Furthermore, we investigate the development and evolution of wrinkle patterns beyond the instability, showing different wrinkled configurations. We discover the existence of a multiwavelength mode following the purely sinusoidal wrinkles and anticipating the kinked configuration of the tube.