Elastic Instabilities of Inflated Rubber Shells

Using a simple constitutive law for elastic behavior that includes the feature of a maximum allowable strain, equations are derived for inflation pressure as a function of the amount of inflation for three rubber shells: a thin-walled spherical balloon, a small spherical cavity in a large rubber block, and a thin-walled cylindrical tube. The results are compared with those obtained using the neo-Hookean constitutive law. Uniform expansion is generally predicted to become unstable at a modest degree of inflation but the new relations give a second stable inflation state, in accord with experience.