Size-dependent plasticity in contact/friction: from discrete dislocation dynamics inside an asperity to statistical summation over asperities

The roughness of natural surfaces emerges in the form of surface asperities at length scales of micrometers or smaller, where plasticity is known to be size dependent: smaller is harder. However, existing contact/friction models, such as Greenwood-Williamson (GW) statistical model and its extended models, Persson's contact model for fractal surfaces, FEM models, either ignore plasticity or, at best, adopt size-independent plasticity. Therefore, there is a need to incorporate size-dependent plasticity into contact/friction models. The overall objective of this work is to gain a better understanding of contact/friction at micron/sub-micron length scales with an emphasis on the potential role of size-dependent plasticity.