Non-uniform inflation of a cylindrical elastic membrane and direct determination of the strain energy function

Abstract

The existence of non-uniform inflation solutions in a closed end, initially cylindrical elastic membrane is proved by introducing plausible general constitutive assumptions. The deformation eventually reaches a steady progressive pattern under a constant internal pressure. Such deformations will actually occur because they require less work than the corresponding uniform deformations of the same membrane enclosing same amounts of ideal gas. The strain energy at each particle can be expressed algebraically in terms of the extension ratios and other measurable quantities. This suggests a simple and accurate method for directly determining the strain energy function over a wide range of strain.