An analytical solution for the unloading in spherical indentation of elastic–plastic solids

This paper presents a contact modelling with emphases on the unloading and subsequent reloading during the contact between a rigid sphere and an elastic–perfectly plastic half-space. By using the superposition of Steuermann solutions of elastic contact bodies of profiles having the form Anr2n, analytical solutions of unloading or subsequent reloading for the contact force, contact displacement and contact pressure distribution are derived, all of which are expressed in terms of the contact radius. To demonstrate the present analytical solutions, curves between contact force and contact radius, contact pressure at the contact centre and contact radius, contact force and contact displacement, and contact pressure distribution are compared with those obtained using the nonlinear finite element analysis method.