Static friction between rigid fractal surfaces

Area of Science:

• Tribology
• Materials Science
• Surface Physics

Background:

• Surface topography and atomic-scale friction significantly influence macroscopic friction.
• Fractal surface structures present complex challenges for traditional friction modeling.

Purpose of the Study:

• To investigate the combined effects of surface topography and atomic friction on macroscopic friction.
• To develop a new theoretical framework and simulation method for predicting friction on fractal surfaces.

Main Methods:

• Spheropolygon-based simulations were employed to model rigid blocks with fractal surface structures.
• Contact slope analysis and a novel signature function were utilized to determine surface profile interactions.
• Mathematical derivation established the relationship between atomic friction, surface slope, and macroscopic friction.

Main Results:

• The angle of macroscopic friction was found to be the sum of atomic friction angle and contact surface slope angle.
• Simulations validated the theoretical model using fractal Koch and Weierstrass-Mandelbrot surfaces.
• The signature function proved effective in describing frictional properties of complex fractal surfaces.

Conclusions:

• The study provides a validated theoretical and simulation approach for understanding friction on fractal surfaces.
• Interpreting macroscopic friction requires surface morphology descriptors derived from the signature function, not just surface slopes.
• This work advances the predictive capabilities for frictional behavior in systems with complex surface topographies.