Nonlinear antiplane deformation of an elastic body (Q2760756)

The antiplane elastic deformation of a homogeneous isotropic prestretched cylindrical body is studied in a nonlinear formulation in actual-state variables under incompressibility conditions, the absence of volume forces, and under constant lateral loading along the generatrix. The boundary-value problem of axial displacement is obtained in Cartesian and complex variables and sufficient ellipticity conditions for this problem are indicated in terms of the elastic potential. The similarity to a plane vortex-free gas flow is established. The problem is solved for Mooney and Rivlin -- Sonders materials simulating strong elastic deformations of rubberlike materials. Axisymmetric solutions are considered.