Expansion/contraction of a spherical elastic/plastic shell revisited

A semi-analytic solution for the elastic/plastic distribution of stress and strain in a spherical shell subject to pressure over its inner and outer radii and subsequent unloading is presented. The Bauschinger effect is taken into account. The flow theory of plasticity is adopted in conjunction with quite an arbitrary yield criterion and its associated flow rule. The yield stress is an arbitrary function of the equivalent strain. It is shown that the boundary value problem is significantly simplified if the equivalent strain is used as an independent variable instead of the radial coordinate. In particular, numerical methods are only necessary to evaluate ordinary integrals and solve simple transcendental equations. An illustrative example is provided to demonstrate the distribution of residual stresses and strains.