Finite Anti-Plane Shear Deformation of a Neo-Hookean Material Using Monge Method of Solution

Finite deformation of an incompressible hollow Neo-Hookean material under anti-plane shear is investigated. The problem is converted from Cartesian co-ordinate to cylindrical polar co-ordinate since the problem is better handled in cylindrical polar co-ordinate. The analysis produces an elliptic second order partial differential equation which sought for Monge Method of solution for the determination of displacement and stresses. Boundary value conditions are set up in determining the contacts of integration involved in the solution. Finally a closed solution for the displacement and stresses at any cross section of the cylinder is achieved.