ECCOMAS 2024

Concurrent Multiscale Modelling of Boundary Lubrication, Enabled by Machine Learning

  • Holey, Hannes (Karlsruhe Institute of Technology)
  • Gumbsch, Peter (Karlsruhe Institute of Technology)
  • Pastewka, Lars (University of Freiburg)

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Friction and lubrication are inherent multiscale problems, particularly when the gap between contacting bodies is on the order of molecular interaction length scales. These conditions occur predominantly in the so-called boundary lubrication regime under high normal loads, low sliding speeds or with low viscosity lubricants. Continuum descriptions of the interfacial flow problem can be augmented with atomistic simulations to account for various nonlinear effects such as fluid-wall slip [1]. However, modelling lubrication across scales beyond purely sequential approaches has so far remained elusive. In this talk, I will present a reformulation of the classical lubrication equations that allows straightforward concurrent coupling between continuum and molecular models [2]. Instead of using fixed-form constitutive expressions that are parametrized a priori using atomistic methods, we build surrogate models for the interfacial shear stress and normal pressure on-the-fly. Concurrent coupling is achieved by an active learning scheme based on Gaussian process regression [3], which allows for a data-efficient interpolation of the microscopic stresses obtained from molecular dynamics simulations in a high-dimensional parameter space. Furthermore, the Gaussian process posterior variance provides a transparent path to uncertainty quantification in lubrication. We validate the proposed method for simple fluids and highlight its application potential for more realistic systems. REFERENCES [1] A. Codrignani, S. Peeters, H. Holey, F. Stief, D. Savio, L. Pastewka, G. Moras, K. Falk, and M. Moseler. Toward a Continuum Description of Lubrication in Highly Pressurized Nanometer-Wide Constrictions: The Importance of Accurate Slip Laws, Science Advances 9(48): eadi2649, 2023. [2] H. Holey, A. Codrignani, P. Gumbsch, and L. Pastewka, Height-Averaged Navier–Stokes Solver for Hydrodynamic Lubrication, Tribology Lettters 70:36, 2022. [3] C. E. Rasmussen and C. K. I. Williams. Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning. Cambridge, MA: MIT Press, 2006.