Contact behaviour of simulated rough spheres generated with spherical harmonics

Abstract: 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.