Radial deflections of thin precompressed cylindrical rubber bush mountings

For an isotropic incompressible hyperelastic Varga material the plane stress (membrane) theory of thin sheets is employed to formulate the load-deflection relation for small superimposed radial deflections of a cylindrical rubber bush which is precompressed by a large uniform radial inflation. The Varga material is a prototype for rubber over a limited range of deformation and the load-deflection relation obtained provides an extreme lower bound to the practical situation. Moreover this relation complements existing results for cylindrical rubber bushes so that now at least some assessment can be made of the effect of precompression on the radial mode of deflection for bushes of finite length. Typical numerical values are given and are contrasted with corresponding values obtained from existing plane strain radial load-deflection relations for long precompressed cylindrical rubber bush mountings.