  Normal contact behaviour between non adhesive fractal rough particles is
studied using a finite element method (FEM). A series of spherical grain
surfaces with distinguished roughness features are generated by means of
Spherical Harmonics. These surfaces are described by two roughness descriptors,
namely, relative roughness (Rr) and fractal dimension (FD). The contact
behaviour of rough spheres with a rigid flat surface is simulated using FEM to
quantify the influences of surface structure and sphere morphology by focusing
on contact stiffness and true contact area. The dependence of normal contact
stiffness (k) on applied normal force (F) is found to follow a power law over
four orders of magnitude, with both alpha and beta being highly correlated with
Rr and FD. With increasing load, the power exponent converges to that of
Hertzian contact, e.g., 1/3, independent of Rr. Regions of true contact evolve
through the formation of new microcontacts and their progressive merging,
meanwhile the area distributions of contact island induced by various forces
tend to obey similar Weibull distributions due to fractal nature in their
surfaces. Contacts with larger values of Rr are found to produce contact
contours with higher fractal dimension as calculated by a 2D box-counting
method. Our results suggest that the correlation between radial lengths in a
quasi spherical particle should be considered in studying contact behaviour.
