Wrinkling of cylindrical membranes with non-uniform thickness

• Wrinkling of an inflated cylindrical membrane with non-uniform thickness is studied.
• Effects of boundary condition and thickness variations on wrinkling are delineated.
• Order of continuity of displacement field for wrinkled membrane is pointed out.
• A relation between stretch induced softening/stiffening and wrinkling is uncovered.

Thin membranes are prone to wrinkling under various loading, geometric and boundary conditions, affecting their functionality. We consider a hyperelastic cylindrical membrane with non-uniform thickness pressurized by internal gas or fluid. When pre-stretched and inflated, the wrinkles are generated in a certain portion of the membrane depending on the loading medium and boundary conditions. The wrinkling is determined through a criterion based on kinematic conditions obtained from non-negativity of Cauchy principal stresses. The equilibrium solution of a wrinkled membrane is obtained by a specified combination of standard and relaxed strain energy function. The governing equations are discretized by a finite difference approach and a Newton–Raphson method is used to obtain the solution. An interesting relationship between stretch induced softening/stiffening with the wrinkling phenomenon has been discovered. The effects of pre-stretch, inflating medium, thickness variations and boundary conditions on the wrinkling patterns are clearly delineated.