Finite elastic non-symmetrical inflation and eversion of circular cylindrical rubber tubes

Abstract

For large elastic deformations of perfectly elastic rubber–like materials, the non–symmetrical inflation and eversion of circular cylindrical rubber tubes is examined for a family of strain–energy functions, which includes the neo–Hookean and Varga materials as special cases. It is shown that the formal mathematical difficulties of deducing exact analytical solutions are less severe for the eversion problem than for the inflation problem. New solutions are ‘determined’ for both inflation and eversion, and that for inflation is applied to the problem of the lateral compression of a hollow rubber tube. This is an important practical problem for which there are at present no theoretical formulae based on the proper theory of finite elasticity. The load–deflection relations obtained are found to have the same overall qualitative features as the limited experimental curves and that arising from the ‘shape factor’ model, which is the standard engineering approximation.