The objective of this study was to formulate discrete and continuous s
patial models to describe the elastic-perfectly plastic deformation of
two rough surfaces in contact. The two surfaces in contact are assume
d to exhibit fractal behavior and are modeled as an effective fractal
surface compressed into a smooth rigid substrate. The rough self-affin
e fractal structure of the effective surface is approximated by a rand
om Canter set representation embedded in two dimensions. Both of the p
roposed models admit analytical solutions whether the plastic deformat
ion is volume conserving or not. Presented results illustrate the effe
cts that volume conservation and initial surface structure have on the
elastic-perfectly plastic deformation process. The results from the c
ontinuous model are compared with the results obtained from the discre
te model, and existing experimental load displacement data for the def
ormation of a bead-blasted steel surface.