Elasto-plastic analytical solution for an internally pressurized thick-walled cylinder using a strain gradient plasticity theory

An analytical solution is presented for an internally pressurized thick-walled cylinder of an elastic strain-hardening plastic material in the plane strain state. A strain gradient plasticity theory is used to describe the plastic deformation, whereas the generalized Hooke's law is invoked to represent the elastic response. The solution gives explicit expressions for the stress components. The inner radius of the cylinder enters these expressions not only in non-dimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can,capture the size effect. The classical plasticity-based solution of the same problem is shown to be a special case of the present solution. Numerical results are provided to illustrate the application of the newly derived solution.