The finite deformation of internally pressurized hollow cylinders and spheres for a class of compressible elastic materials.

*(English)*Zbl 0603.73038The finite elastic deformation of hollow circular cylinders and spheres under applied uniform internal pressure is studied and conditions for the initiation of a localized shear bifurcation are obtained. The location of this bifurcation relative to the pressure maximum is investigated. It is shown that when the ratio of the outer undeformed radius to the inner undeformed radius is larger then a critical value, the shear bifurcation occurs before the pressure maximum is attained, while when this ratio is smaller then the critical value, the converse is true. The analysis is carried out for a particular compressible elastic foam rubber material (the Blatz-Ko material). The results are obtained in closed analytic form.