Journal of the Mechanics and Physics of Solids 54 (2006) 2652–2674 Unloading an elastic–plastic contact of rough surfaces Y. Kadin, Y. Kligerman, I. Etsion à Department of Mechanical Engineering, Technion, Haifa 32000, Israel Received 28 November 2005; received in revised form 11 April 2006; accepted 20 April 2006 Abstract A statistical model for the unloading of elastic–plastic contact of rough surfaces is presented for a single load–unload cycle. The hystereses of load-separation and load real contact area behavior are analyzed for a wide range of surface roughness and loading conditions. The residual topography of the unloaded rough surfaces is also analyzed and the new distribution functions of asperity heights and summit radii of curvature along with a corresponding GW residual plasticity index are presented. A new modified plasticity index (MPI) is suggested which considers the energy dissipation due to unrecovered plastic deformations. This MPI varies from zero for purely elastic contacts to unity for purely plastic contacts and hence, can better define the level of plasticity of contacting rough surfaces compared to the original GW plasticity index. r 2006 Elsevier Ltd. All rights reserved. Keywords: Contact mechanics; Elastic–plastic material; Rough surface unloading 1. Introduction Unloading of contacting rough surfaces is common for most tribological pairs found in various operating machines (Williams, 2005). It can be of great concern in modern MEMS systems especially in microswitches (Majumder et al., 2001) and in head-disk interaction in magnetic storage systems to name a few. ARTICLE IN PRESS www.elsevier.com/locate/jmps 0022-5096/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmps.2006.04.013 à Corresponding author. Tel.: +972 4 829 2096; fax: +972 4 829 5711. E-mail address: etsion@tx.technion.ac.il (I. Etsion).