Continuum framework for multiscale contact mechanics of elastic-plastic fractal interfaces with intervening boundary film

A comprehensive mechanics theory was developed to analyze multiscale contact and friction behavior of elastic-plastic fractal surfaces coated with a boundary film. This approach accounts for the size-dependent behavior of asperity microcontacts that arise from the inherent roughness of fractal topographies. To capture the fundamental mechanisms governing interfacial friction, representative single-asperity models were formulated to describe both elastic and plastic deformation modes at the microscale. These models were then systematically extended across the entire asperity population, enabling an accurate representation of contact interactions over a broad range of length scales. In the elastic regime, frictional resistance is primarily attributed to shearing of the boundary film between opposing asperities. Conversely, in the plastic regime, asperities indent and plow through the softer counterface material, while the boundary film remains attached to the deformed surface contributing additional resistance through interfacial shear. The total frictional force is obtained by integrating the contributions from both elastic and plastic microcontacts, which are weighted according to the asperity-size distribution that characterizes the fractal contact interface. The developed theoretical framework provides a rigorous and scalable model for predicting the frictional behavior of rough contact interfaces covered by a strongly adhered boundary film and yields fundamental insight into the interplay between surface topography, prevalent deformation mode at the asperity scale, and boundary film shear resistance, which is especially relevant for the design and analysis of engineered surfaces in contact-mode mechanical systems.