Pressure-Driven Wrinkling of Soft Inner-Lined Tubes
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We consider the wrinkling of the inextensible elastic lining of an inner-lined tube under an imposed pressure difference. We derive a simple equation modeling the elastic properties of the lining, the pressure, and the soft-substrate forces. Numerical continuation is used to construct a bifurcation diagram as a function of the imposed pressure difference for in-plane deformations, in excellent agreement with a weakly nonlinear theory we develop. Our approach explains how the wavelength and amplitude of the wrinkles are selected as a function of the parameters in cylindrical wrinkling systems and shows the emergence of localized folds and mixed-mode states through secondary bifurcations from wrinkled states. The system under study is a starting point for understanding the wrinkling of arterial endothelium under blood-pressure changes, which has been shown to play a key anti-defouling role in the circulatory system.