Abstract
Description of the transitional process from a static to a dynamic frictional regime is a fundamental problem of modern physics. Previously, we developed a model based on the well-known Frenkel-Kontorova model to describe dry macroscopic friction. Here, this model has been modified to include the effect of dissipation in derived relations between the kinematic and dynamic parameters of a transition process. The main (somewhat counterintuitive) result is a demonstration that the rupture (i.e., detachment front) velocity of the slip pulse which arises during the transition does not depend on friction. The only parameter (besides the elastic and plastic properties of the medium) controlling the rupture velocity is the shear to normal stress ratio. In contrast to the rupture velocity, the slip velocity does depend on friction. The model we have developed describes these processes over a wide range of rupture and slip velocities (up to 7 orders of magnitude) allowing, in particular, the consideration of seismic events ranging from regular earthquakes, with rupture velocities on the order of a few km/s, to slow slip events, with rupture velocities of a few km/day.
Highlights
The relative movement of two solids in contact is accompanied by friction, an essentially nonlinear dissipative process
We have proposed a novel model [37,38] in which sliding occurs in much the same way as in plasticity, i.e., due to movement of a defect we define as a “macroscopic dislocation”, which requires much less shear stress than uniform displacement of frictional surfaces
Associated with the respective slip velocity corresponds to the value of shear stress calculated based on the rupture velocity (Figure 6, top panel); the value of shear stress for the ETS event ( 0.213) is larger than the value predicted by the rupture velocity (Figure 6, bottom panel)
Summary
The relative movement of two solids in contact is accompanied by friction, an essentially nonlinear dissipative process. Laboratory friction experiments have shown that the critical shear force needed to initiate a macroscopic slip pulse between frictional surfaces is usually much less than that predicted by theory [7] Motivated by these similarities, we have proposed a novel model [37,38] in which sliding occurs in much the same way as in plasticity, i.e., due to movement of a defect we define as a “macroscopic dislocation”, which requires much less shear stress than uniform displacement of frictional surfaces. A more detailed description may be found in our previous articles [37,38]
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