Fig. 1: Sketch and behavior of the multi-scale model. (A) Slider and external loading conditions. (B) Spring-block network modeling elastodynamics. (C) Surface springs modeling friction on a block. (D) Macroscopic loading curve, i.e. the ratio FT/FN of driving shear force to total normal force. (E) Mesoscopic loading curve, i.e. the ratio τ/p of shear to normal stress on a block. (F) Microscopic friction model for the spring loading curve, i.e. the ratio fT/fN of friction to normal force for one spring. Arrow shows random distance traveled in sliding state. The behavior on larger scales emerges from the dynamics on the scale below.
Friction is ubiquitous and important. The direct energy loss to friction and the loss of equipment due to the related mechanical wear account for a significant part of the gross global product. The present understanding of friction is incomplete, and improving it could lead to important technological advances.
At PGP we are developing models of friction that couple the elastic deformation and partial breaking of the interface to the system size behaviour (1,2). We also plan to extend our competence to models at the atomic/molecular level. Molecular dynamics explicitly includes the forces between atoms and molecules and is the right tool for understanding how these forces combine, in a complicated surface geometry, to form the properties of the individual micro-contacts that make up a frictional interface.
Understanding how individual micro-contacts behave is a crucial step in understanding friction. Still, a hierarchy of models is required because, while friction is fundamentally due to forces between the atoms and molecules that are in contact at the frictional interface, atomic models alone are unable to handle the large length- and timescales that are involved in the relative motion of macroscopic samples. The hierarchical approach therefore opens the possibility to span the range from basic interactions to emergent behaviour.
1.J. Trømborg, J. Scheibert, D. S. Amundsen, K. Thøgersen, A. Malthe-Sørenssen, Transition from static to kinetic friction: Insights from a 2D model. Phys. Rev. Lett. 107, 074301 (2011).
2.D. S. Amundsen, J. Scheibert, K. Thøgersen, J. Trømborg, A. Malthe-Sørenssen, 1D model of precursors to frictional stick-slip motion allowing for robust comparison with experiments. Tribol. Lett. 45, 357 (2012).