Large Elastic Deformation Theories and Unstable Deformations of Rubber Structures: Thick Tubes

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Abstract
A variety of quantitative theories for the large elastic deformations of rubbers have been proposed. Most useful for applications in engineering, for example, because they most readily lead to the presentation of computed results in dimensionless form, are those which involve one elastic constant only (such as Young's modulus) in addition to Poisson's ratio (0.5 for incompressible rubbers). Two such theories (referred to as the Neo‐Hookean and the Varga, Dickie‐Smith elasticities) are considered here and applied to the analysis of large deformations of thick cylindrical rubber tubes. Predictions are compared to experimental results. The deformations considered are basically divided into two types: 1) longitudinal extension under constant inside pressure in which the tube is longitudinally extended by applying a variable longitudinal force while a constant pressure is maintained inside; 2) inflation under constant longitudinal force in which the tube is inflated by applying a variable pressure while a constant longitudinal force is exerted. Simple extension is a special case of type 1 when the constant pressure is zero and simple inflation is a special case of type 2 when the constant longitudinal force is zero.

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