The occurrence of the limit-point instability is an intriguing phenomenon observed during stretching of hyperelastic membranes. In toy rubber balloons, this phenomenon may be experienced in the sudden reduction in the level of difficulty of blowing the balloon accompanied by its rapid inflation. The present paper brings out a link between the geometry and strain-hardening parameter of the membrane, and the occurrence of the limit-point instability. Inflation of membranes with different geometries and boundary conditions is considered, and the corresponding limit-point pressures are obtained for different strain-hardening parameter values. Interestingly, it is observed that the limit-point pressure for the different geometries is inversely proportional to a geometric parameter of the uninflated membrane. This dependence is shown analytically, which can be extended to a general membrane geometry. More surprisingly, the proportionality constant has a power-law dependence on the nondimensional material strain-hardening parameter. The constants involved in the power-law relation are universal constants for a particular membrane geometry.
A finite inflation analysis of two circumferentially bonded hyperelastic circular flat mem branes with uniform internal pressure is presented. The governing equations of equilib rium are obtained using the variational formulation. By making a suitable change in the field variables, the problem is formulated as a set of two coupled nonlinear two point boundary value problem (TPBVP) and is solved using the shooting method. Membranes o f identical and dissimilar material properties are considered in the analysis. For dissim ilar membranes, asymmetric inflation, and remarkably, deflation (after an initial phase of inflation) in one o f the membranes in certain cases, has been observed. The effect of infla tion pressure and material properties on the geometry of inflated configuration, state of stress, and the impending wrinkling condition of the membranes are also studied. This work has relevance to tunable inflated reflectors and lenses among other applications.
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