A numerical model for calculation of the restitution coefficient of elastic-perfectly plastic and adhesive bodies with rough surfaces

An in-house contact mechanics model is used to simulate contact of rough spheres having elastic-perfectly plastic contact with adhesion. The model uses a Boundary Element Method (BEM) and employs Fast Fourier Transforms (FFT) for numerical efficiency. We have validated our model for smooth surfaces with the Hertz contact behaviour in elastic regime, JKR adhesive model in the adhesive regime and Thornton and Ning's analytical model in elasto-plastic adhesive regime. Furthermore, the effect of yield stress, interface energy and surface roughness on the Coefficient of Restitution (COR) is investigated. The results show that surface roughness dramatically affects the COR and higher roughness values lead to lower CORs in general. In addition, changes of COR based on different maximum indentation depth in the presence of surface roughness consists of 3 stages; The asperity dominant, bulk elastic dominant and bulk plastic dominant. Interestingly, it was shown that there is a critical indentation depth beyond which the effect of surface roughness will disappear and rough surfaces act like smooth ones. This critical indentation depth is proportional to the Rq value of the surface roughness. Numerical results suggest that the yield stress influences the COR and higher yields stress results in higher COR for both rough and smooth surfaces. Results also suggest that the effect of interface energy on the COR for smooth surfaces is significant at low indentations and minimum for rough surfaces.