Contact behaviour of simulated rough spheres generated with spherical harmonics

TL;DR

This study uses finite element simulations to analyze how surface roughness and fractal features of spherical particles influence contact stiffness and contact area, revealing power-law behaviors and fractal contact patterns.

Contribution

It introduces a novel approach using spherical harmonics to generate rough sphere surfaces and systematically investigates their contact mechanics with FEM.

Findings

Contact stiffness follows a power law with force over four orders of magnitude.

Larger roughness leads to higher fractal dimension in contact contours.

Contact area distributions follow Weibull distributions due to surface fractality.

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.