Model for steady state friction

Abstract

A model for dynamic steady state friction between two rough surfaces is developed in which the transfer of momentum from the horizontal to the vertical direction by collisions between asperities on opposing surfaces leads to a friction law which is independent of the detailed mechanism of energy dissipation. For nonfractal surfaces the model applies above a lower critical velocity which increases exponentially with smoothness. At high velocities there is velocity weakening and, as the smoothness of the surfaces increases, the velocity dependence rapidly approaches the experimentally observed logarithmic dependence, in agreement with phenomenological state variable friction laws. For fractallike surfaces the model applies over the whole velocity range above V = 0, showing velocity strengthening at low velocities and velocity weakening at high velocities, implying the existence of a stick‐sliplike instability.

Dynamics of a Traveling Density Wave Model for Earthquakes

“…Both 2g and h depend in general on the normal stress s N , which in turn depends [24] on V . Using (6) corresponding Ito-Langevin equation [22] is…”

The organization of seismicity on fault networks.

“…While there is much to be said concerning the dynamics of friction at the smallest scales, limitations of space do not allow for a full discussion of recent efforts at modeling the dynamics of sliding of blocks with irregular contacts (23)(24)(25) or of the development of a fluid dynamics and deformation mechanics of granular materials (26-31).…”

“…USA 93 (1996) There are several scales of nonplanar geometric features: (i) topographic irregularities on fault surfaces and the presence of fault gouge that are the cause of friction on faults; (ii) larger-scale geometrical fluctuations of faults such as bends, stepovers, bifurcations, etc., of faults; (iii) the dendritic nature of the network of secondary faults associated with plate boundaries and a possibly tegular character of the space between elements of the network; and (iv) the influence of the curvature of the earth and the distances between triple junctions of the tectonic plates. We have no contribution to make to this discussion on the influence of this last item on the organization of earthquakes worldwide.While there is much to be said concerning the dynamics of friction at the smallest scales, limitations of space do not allow for a full discussion of recent efforts at modeling the dynamics of sliding of blocks with irregular contacts (23)(24)(25) or of the development of a fluid dynamics and deformation mechanics of granular materials (26-31).We concentrate attention on the issue of larger scale irregularities in fault geometry. The two problems of the irregularity on the small and the large scales differ by virtue of the size of the dimensions of the irregularities scaled by the size of the slip.…”

Fault rupture between dissimilar materials: Ill‐posedness, regularization, and slip‐pulse response

“…Possibly more important is what might be a scaled down version of the above, namely, the effects of roughness at various scales [e.g., Mora and Place, 1994;Lomnitz-Adler, 1991]. Also, as will be elaborated further in section 5.4, it seems plausible that the unsymmetric state of stress generated by an in-plane rupture around a fault (compressional on one side, extensional on the other one), combined with a nonlinear response, may sometimes result in a homogeneous material mimicking bimaterial response.…”