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

This paper presents a complete, original theoretical solution to describe the unloading and subsequent reloading behaviour of the normal contact between a rigid sphere and an elastic–perfectly plastic half space, whereas most existing solutions are only numerical or empirical obtained from numerical data. The analytical solutions derived have been incorporated into DEM codes by the UK and Australia DEM code developers, which have been used in the fields of chemical engineering, particle technology, processing engineering, and tribology. Follow-on work included adhesive force near the contact area which has recently been published.