Rubber Cylinders under Hydrostatic Pressure with Variable Poisson's Ratio

Abstract

Abstract Elastomers are increasingly used in specialized engineering applications where their complex shape often requires a detailed stress analysis. Specialized programmes have to be used for incompressible materials such as elastomers, since the standard computer finite element packages are unable to give accurate solutions for rubbers with Poisson's ratio close to 0.5. The present paper uses an established finite difference method to examine the deflected shape of rubbers under hydrostatic pressure. A particular case of a rubber cylinder subjected to hydrostatic pressure is examined, where a natural tendency is to assume that the rubber cylinder will reduce slightly in volume, evenly all the way round. However, by performing a detailed finite difference analysis, it was found that the final shape, under pressure, was dependent on the value of Poisson's ratio, and height to diameter ratio of the rubber cylinder. An interesting result is that the end of the cylinder, and the circumferential surface will change shape from a concave to a convex surface by changing the value of ν for certain cylindrical shapes of rubber.