Inflation and Instabilities of Hyperelastic Membranes

The applications of membranes are increasing rapidly in various fields of engineering and science. The geometric, material, force and contact non-linearities complicate their analysis, which increases the demand for computationally efficient methods and interpretation of counter-intuitive behaviours. To understand the complex behaviour of membrane structures, it is necessary to perform parametric studies of simple setups and understand their basic mechanical behaviour. The first part of the present work studies the free and constrained inflation of circular and cylindrical membranes. The membranes are assumed to be in contact with a soft substrate, modelled as a linear spring distribution. Adhesive and frictionless contact conditions are considered during inflation, while only adhesive contact conditions are considered during deflation. For a circular membrane, peeling of the membrane during deflation is studied, and a numerical formulation of the energy release rate is proposed. The pre-stretch produces a stiffening effect for the circular membranes, and a softening effect for the cylindrical membranes, in the pre-limit zone. The second part of the thesis discusses the instabilities observed for fluid containing cylindrical membranes. Limit points and bifurcation points are observed on primary equilibrium branches. The secondary branches emerge from bifurcation points, with their directions determined by eigenvectors corresponding to zero eigenvalues at the bifurcation point. Symmetry has major implications on stability analysis of the structures, and the relationship between eigenvalue analysis and symmetry is highlighted in this part of the thesis. The occurrence of critical points and the stability of equilibrium branches are determined by perturbation techniques. In the third part, wrinkling in the pressurized membranes is investigated, and robustness of the modified membrane theory and tension field theory is examined. The effect of boundary conditions, thickness variations, and inflating media on the wrinkling is investigated. It is observed that, with a relaxed strain energy formulation, the obtained equilibrium solutions are unstable due to the occurrence of pressure induced instabilities. These instabilities are not visible when axisymmetry is assumed or coarse discretizations in the wrinkling direction are used. A detailed analysis of pressure induced instabilities in the wrinkled membranes is described in the thesis. Descriptors: Membranes, Constrained inflation, Energy release rate, Adhesive contact condition, Limit point, Bifurcation point, Wrinkling, Tension field theory, Pressure induced instability.