The effect of axial stretch on cavitation in an elastic cylinder

The phenomenon of cavitation in an elastic cylinder subjected to a combined axial stretch λ_z and radial traction P is examined. One possible response of the cylinder to this loading, for all λ_z; and P, is a pure homogeneous deformation. However, for some materials, the homogeneous deformation becomes unstable at certain critical values of (λ_z, P), and a second deformation bifurcates from the homogeneous one; this latter deformation involves a cylindrical cavity co-axial with the elastic cylinder. We determine the values of (λ_z, P) at which this happens. The results are displayed by constructing a curve in the (λ_z, P)-plane which divides this plane into regions where the homogeneous deformation is stable and unstable.