Radial stretching of a thin hollow membrane: biaxial tension, tension field and buckling domains

The radial stretching of a hollow thin membrane without compressive strength is considered within the framework of the small strain tension field theory. For each type of the uniform boundary conditions, the loading plane is partitioned into the domains of biaxial tension, tension field and buckling. The extent of these domains critically depends on the value of the Poisson’s coefficient and on the aspect ratio of the membrane. The stress and displacement fields are determined at an arbitrary stage of loading, when the outer biaxially stressed (taut) annulus surrounds the inner (tension field) portion of the membrane, characterized by continuously distributed infinitesimal wrinkles. The growth of the tension field as the loading increases is analyzed. It is shown that, depending on the Poisson’s coefficient and the aspect ratio of the membrane, the tension field may or may not spread throughout the whole membrane. For the fixed outer boundary, and the applied tension or a negative displacement at the inner boundary, and for a particular combination of the material and geometric parameters, the tension field instantly spreads to a specific depth within the membrane, dependent on the Poisson’s ratio and the outer radius of the membrane, remaining constant during further increase of the loading.