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Competition between roughness and strength for scale-dependent surfaces.

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Understanding rock strength is challenging due to scale-dependent properties. This study develops a new theory for multiscale rough surfaces, revealing how yield stress impacts contact mechanics and surface evolution.

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Area of Science:

  • Geophysics and Materials Science
  • Mechanics of Materials
  • Surface Physics

Background:

  • Rocks exhibit scale-dependent strength, making theoretical modeling difficult.
  • Natural rough surfaces evolve through asperity collisions during shear.
  • Previous work suggested a link between surface aspect ratio and shear strain at yield.

Purpose of the Study:

  • To develop a rigorous theoretical framework for scale-dependent strength in multiscale rough surfaces.
  • To investigate the yielding behavior of elastoplastic surfaces with scale-dependent yield stress.
  • To quantitatively interpret natural surfaces by analyzing their topography and strength.

Main Methods:

  • Utilized Persson's formalism for computing contact area of rough surfaces using stochastic differential equations.
  • Developed a theory for elastoplastic yielding incorporating scale-dependent yield stress.
  • Examined surfaces with power-law scaling for topography (C∼λ^{-m}) and yield stress (Y∼λ^{-n}).

Main Results:

  • Numerical solutions show bounded deviation from elastic scaling, consistent with prior heuristic arguments.
  • Plasticity erodes contacts when the topography spectral exponent 'm' is lower than 'n-3'.
  • This corresponds to a Hurst exponent lower than 1-n/2, providing quantitative differences from prior scaling arguments.

Conclusions:

  • The developed theory provides a rigorous, quantitative approach to understanding scale-dependent strength in rough surfaces.
  • The findings enable a more accurate interpretation of natural surfaces based on their multiscale roughness and yield properties.
  • This work bridges the gap between scaling arguments and a formal treatment of surface mechanics.