Tl. Warren et D. Krajcinovic, FRACTAL MODELS OF ELASTIC PERFECTLY PLASTIC CONTACT OF ROUGH SURFACESBASED ON THE CANTOR SET, International journal of solids and structures, 32(19), 1995, pp. 2907-2922
The objective of this study was to formulate discrete and continuous m
odels to describe the elastic-perfectly plastic deformation of two rou
gh surfaces in contact. The two surfaces in contact are assumed to exh
ibit fractal behavior and are modeled as an effective fractal surface
compressed into a smooth rigid substrate. The rough self-affine fracta
l structure of the effective surface is approximated using a Canter se
t representation. Both of the proposed models admit analytical solutio
ns for the cases when the plastic deformation is volume conserving or
not. Results are presented that illustrate the effects that volume con
servation and initial surface structure have on the elastic-perfectly
plastic deformation process. The results from the continuous model are
compared with the results obtained from the discrete model, and also
with existing experimental load displacement results for the deformati
on of a ground steel surface.