Theoretical analysis of inflated tube wrinkling behavior under pure bending

Inflatable tubes, owing to their lightweight and foldable characteristics, have important applications in soft robots and space expandable structures. The application of a bending load to the inflated tube might induce local instability on its compressed side, leading to the formation of wrinkles that could potentially compromise the structural strength. Therefore, it is necessary to have a comprehensive understanding of the wrinkling behavior exhibited by inflated tubes under bending load. Initially, a theoretical solution is developed for the critical wrinkling behavior of inflated tubes under pure bending, drawing upon the principle of minimum potential energy. According to the energy expression of the system, the critical wrinkling behavior of inflated tubes depends on dimensionless geometrical and internal pressure parameters. The critical wrinkling load and wrinkle pattern of the system are influenced by the thickness-radius ratio and the ratio of internal air pressure to Young's modulus. Subsequently, the theoretical solutions are validated through several finite element analysis examples and a systematic investigation is conducted into the influence of dimensionless geometrical and internal pressure parameters. Finally, the evolution of morphology in post-buckling is investigated through numerical results. The findings suggest that during post-buckling, the wrinkles may undergo a secondary bifurcation and evolve into a non-axisymmetric diamond-like pattern. These results hold significant implications for understanding the bending instability and failure mechanisms of inflated tubes.