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A model for multiple repeated loading and unloading of an elastic-plastic sphere and a rigid flat is presented to cover a wide range of loading conditions far beyond the elastic limit. The sphere material is modeled as elastic linear isotropic hardening and follows the von Mises yield criterion. It is shown that although most of the plastic deformation occurs during the first loading, secondary plastic flow may evolve during the first unloading. The occurrence of this secondary plastic flow depends on the level of first loading and is strongly affected by the Poisson's ratio and material hardening. The region of secondary plastic flow may propagate during the very first loading-unloading cycles, reaching a steady state after which the following loading-unloading cycles become fully elastic.

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Approach between two deformable microbodies in the presence of adhesion is sometimes accompanied by discontinuous change of the surface profile at the narrow region near their summits (jump-in phenomenon). Previous studies of adhesive spherical contact showed that neck formation during jump-in always involves onset of local plastic yield near the edge of the contact zone. The current paper reveals that pure elastic jump-in is also feasible. The solution is based on a Lennard-Jones potential in combination with the von Mises yield criterion. The theoretical strength rather than the engineering yield strength of the material is used and the sufficient condition for jump-in induced onset of plastic yield under this extreme strength is discussed.