A new numerical model for investigating the effect of surface roughness on the stick and slip of contacting surfaces with identical materials

A numerical model replicating the stick-slip contact of two elastically similar materials is presented in this paper. Based on the Coulomb's law described in the partial-slip theory of Ciavarella, the model adopts a complementary condition that facilitates the design of a novel algorithm to separate the stick and slip regions. Via the comparison between simulation results and analytical solutions, the developed model is validated and applied to study the role played by the roughness of realistic surfaces in the separation of stick and slip regions. It is found that a higher root mean square (RMS) gradient leads to smaller contacting area under constant load while the root mean square (RMS) roughness has insignificant influence if the RMS gradient is kept constant, which is in line with current literature. Under the effects of the RMS gradient, the relationship between varying skewness or kurtosis and contacting regions is irregular. Furthermore, stick regions are found to respond identically to those varying roughness factors. However, the ratio of stick regions to the total contacting region is revealed to be unaffected by the surface roughness parameters when a tangential load is applied on the contacting surfaces following a linear behaviour.