THE FINITE INFLATION OF A THICK-WALLED ELASTIC TORUS

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Abstract
The finite inflation by uniform internal pressure of toroidal rubber inner tubes and tyres is an important technological problem. Kydoniefs and Spencer (5) give a perturbation solution to the inflation problem of a thick-walled perfectly elastic material which is a torus in its deformed state. Their solution is approximate in the sense that the radius of the larger circle which generates the torus is assumed to be small in comparison to the overall radius of the torus. The work of these authors is extended to the general homogeneous isotropic incompressible hyperelastic material. As well a similar approximate solution is given to the inflation problem of a perfectly elastic material which is a torus in its undeformed state. The solutions of both problems are approximated in the first instance by the solution for the uniform inflation of a circular cylindrical tube under uniform internal pressure. These approximations may well provide an adequate solution for practical purposes. Numerical results for these first approximations are given for the Mooney material.

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