Strain gradient plasticity solution for an internally pressurized thick-walled spherical shell of an elastic-plastic material

An analytical solution is presented for an internally pressurized thick-walled spherical shell of an elastic strain-hardening plastic material. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke's law is invoked to represent the material response in the elastic region. The solution gives explicit expressions for the stress, strain and displacement components. The inner radius of the shell 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 for the maximum effective stress in the shell wall are also provided to illustrate applications of the newly derived solution. The new solution can be used to construct improved expanding cavity models in indentation mechanics that incorporate both the strain-hardening and indentation size effects. © 2003 Elsevier Ltd. All rights reserved.