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Non-monotonic dependence of the friction coefficient on heterogeneous stiffness.

Giacco F, Ciamarra MP, Saggese L, de Arcangelis L, Lippiello E - Sci Rep (2014)

Bottom Line: The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters.This occurs because elastic constants control the geometrical features of the rupture fronts during the stick-slip dynamics, leading to four different ordering regimes characterized by different orientations of the rupture fronts with respect to the external shear direction.We rationalize these results by means of an energetic balance argument.

View Article: PubMed Central - PubMed

Affiliation: 1] CNR-SPIN, Dep. of Physics, University of Naples "Federico II", Naples, Italy [2] Dep. of Mathematics and Physics, Second University of Naples and CNISM, Caserta, Italy.

ABSTRACT
The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters. Indeed, experiments on sheared elastic bodies have shown that the static friction coefficient depends on loading conditions, the real area of contact along the interfaces and the confining pressure. Here we show, by means of numerical simulations of a 2D Burridge-Knopoff model with a simple local friction law, that the macroscopic friction coefficient depends non-monotonically on the bulk elasticity of the system. This occurs because elastic constants control the geometrical features of the rupture fronts during the stick-slip dynamics, leading to four different ordering regimes characterized by different orientations of the rupture fronts with respect to the external shear direction. We rationalize these results by means of an energetic balance argument.

No MeSH data available.


Related in: MedlinePlus

The 2D Burridge-Knopoff model.(a) Schematic representation of the model: An elastic layer of red particles connected by yellow springs is in contact with a bottom-flat substrate (gray). The system is driven by an external spring mechanism along the x-direction at constant velocity Vd and each particle is confined by a constant pressure σn. (b) Time dependence of the shear stress σx(t) during the stick-slip dynamics for two systems with different values of ϕ. Filled black squares and open red circles indicate the values of the shear stress that, divided by σn, are used to estimate the macroscopic friction coefficient . The horizontal dash-dotted (blue) line indicates the value of the stress corresponding to the Amontons-Coulomb threshold.
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f1: The 2D Burridge-Knopoff model.(a) Schematic representation of the model: An elastic layer of red particles connected by yellow springs is in contact with a bottom-flat substrate (gray). The system is driven by an external spring mechanism along the x-direction at constant velocity Vd and each particle is confined by a constant pressure σn. (b) Time dependence of the shear stress σx(t) during the stick-slip dynamics for two systems with different values of ϕ. Filled black squares and open red circles indicate the values of the shear stress that, divided by σn, are used to estimate the macroscopic friction coefficient . The horizontal dash-dotted (blue) line indicates the value of the stress corresponding to the Amontons-Coulomb threshold.

Mentions: In this study we show that the elasticity of the contact surface influences the features of the fracture fronts leading to a non-monotonic behaviour of the friction coefficient. These results are obtained via numerical simulations of a 2D (xy) spring-block model (Fig. 1a), and are supported by analytical arguments. Our model, fully described in the method section, is a simple variation of the Burridge–Knopoff1516 (BK) model that is commonly used in seismology to describe a seismic fault under tectonic drive, and that reproduces many statistical features of earthquake occurrence17181920. The model is represented by a series of blocks, interconnected by springs of elastic constant kb and interacting with the substrate with a frictional force characterized by a uniform friction coefficient μs, initially arranged on a two dimensional square lattice of size Lx × Ly.


Non-monotonic dependence of the friction coefficient on heterogeneous stiffness.

Giacco F, Ciamarra MP, Saggese L, de Arcangelis L, Lippiello E - Sci Rep (2014)

The 2D Burridge-Knopoff model.(a) Schematic representation of the model: An elastic layer of red particles connected by yellow springs is in contact with a bottom-flat substrate (gray). The system is driven by an external spring mechanism along the x-direction at constant velocity Vd and each particle is confined by a constant pressure σn. (b) Time dependence of the shear stress σx(t) during the stick-slip dynamics for two systems with different values of ϕ. Filled black squares and open red circles indicate the values of the shear stress that, divided by σn, are used to estimate the macroscopic friction coefficient . The horizontal dash-dotted (blue) line indicates the value of the stress corresponding to the Amontons-Coulomb threshold.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4209463&req=5

f1: The 2D Burridge-Knopoff model.(a) Schematic representation of the model: An elastic layer of red particles connected by yellow springs is in contact with a bottom-flat substrate (gray). The system is driven by an external spring mechanism along the x-direction at constant velocity Vd and each particle is confined by a constant pressure σn. (b) Time dependence of the shear stress σx(t) during the stick-slip dynamics for two systems with different values of ϕ. Filled black squares and open red circles indicate the values of the shear stress that, divided by σn, are used to estimate the macroscopic friction coefficient . The horizontal dash-dotted (blue) line indicates the value of the stress corresponding to the Amontons-Coulomb threshold.
Mentions: In this study we show that the elasticity of the contact surface influences the features of the fracture fronts leading to a non-monotonic behaviour of the friction coefficient. These results are obtained via numerical simulations of a 2D (xy) spring-block model (Fig. 1a), and are supported by analytical arguments. Our model, fully described in the method section, is a simple variation of the Burridge–Knopoff1516 (BK) model that is commonly used in seismology to describe a seismic fault under tectonic drive, and that reproduces many statistical features of earthquake occurrence17181920. The model is represented by a series of blocks, interconnected by springs of elastic constant kb and interacting with the substrate with a frictional force characterized by a uniform friction coefficient μs, initially arranged on a two dimensional square lattice of size Lx × Ly.

Bottom Line: The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters.This occurs because elastic constants control the geometrical features of the rupture fronts during the stick-slip dynamics, leading to four different ordering regimes characterized by different orientations of the rupture fronts with respect to the external shear direction.We rationalize these results by means of an energetic balance argument.

View Article: PubMed Central - PubMed

Affiliation: 1] CNR-SPIN, Dep. of Physics, University of Naples "Federico II", Naples, Italy [2] Dep. of Mathematics and Physics, Second University of Naples and CNISM, Caserta, Italy.

ABSTRACT
The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters. Indeed, experiments on sheared elastic bodies have shown that the static friction coefficient depends on loading conditions, the real area of contact along the interfaces and the confining pressure. Here we show, by means of numerical simulations of a 2D Burridge-Knopoff model with a simple local friction law, that the macroscopic friction coefficient depends non-monotonically on the bulk elasticity of the system. This occurs because elastic constants control the geometrical features of the rupture fronts during the stick-slip dynamics, leading to four different ordering regimes characterized by different orientations of the rupture fronts with respect to the external shear direction. We rationalize these results by means of an energetic balance argument.

No MeSH data available.


Related in: MedlinePlus