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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 morphology of the clusters of slipping particles depends on the elastic heterogeneitiy.(a) Scatter plot of the clusters dimensions, along the directions parallel and transverse to the shear, for system having different values of ϕ. By reducing the stiffness of the system we observe regions with different cluster shapes, indicated by the letters C, LC, DP, DT. (b) Schematic representations of the geometry of the clusters corresponding to the regions reported in the scatter plot. Here we show a system of dimension Lx = 20 and Ly = 5, the same behaviour is also observed for larger systems.
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f4: The morphology of the clusters of slipping particles depends on the elastic heterogeneitiy.(a) Scatter plot of the clusters dimensions, along the directions parallel and transverse to the shear, for system having different values of ϕ. By reducing the stiffness of the system we observe regions with different cluster shapes, indicated by the letters C, LC, DP, DT. (b) Schematic representations of the geometry of the clusters corresponding to the regions reported in the scatter plot. Here we show a system of dimension Lx = 20 and Ly = 5, the same behaviour is also observed for larger systems.

Mentions: In Fig. 4a we present a parametric plot of ly/Ly vs lx/Lx for four different values of ϕ. Cluster configurations can be distinguished into four classes, determined by ϕ, whose typical shape is reported in Fig. 4b. For we have the crystalline regime (C), represented by black circles in the region with . In this case, the system behaves as a rigid body and slips involve all particles, keeping the original crystalline order. For smaller value of ϕ we have the laminar crystalline regime (LC, red squares) where and ly with values in the range [1, Ly]. In this regime, a typical slip involves the motion of one or few parallel lines. This is consistent with the ordering features observed in this regime (LC lower panel), characterized by order along the direction of the shear and disorder along the transverse direction. A further reduction of ϕ first breaks order in the shearing direction, giving rise to the disorder–parallel regime (DP, green diamonds), and then fully disorders the system, giving rise to the disorder–transverse regime (DT, blue triangles). The shape of the clusters in both these regions are asymmetric with lx/Lx > ly/Ly in the DP whereas lx/Lx < ly/Ly in the DT. This information can be directly extracted from Fig. 4a where we observe that the DP and the DT regimes respectively populate regions above and below the diagonal. We characterize the asymmetry of the cluster shape comparing their average longitudinal and transverse sizes, lx/ly. As shown in Fig. 2b, this ratio varies non–monotonically with ϕ, and has a maximum corresponding to the minimum of . This suggests that the lowest value of is obtained when slips involve the horizontal displacement of the smallest number of lines.


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 morphology of the clusters of slipping particles depends on the elastic heterogeneitiy.(a) Scatter plot of the clusters dimensions, along the directions parallel and transverse to the shear, for system having different values of ϕ. By reducing the stiffness of the system we observe regions with different cluster shapes, indicated by the letters C, LC, DP, DT. (b) Schematic representations of the geometry of the clusters corresponding to the regions reported in the scatter plot. Here we show a system of dimension Lx = 20 and Ly = 5, the same behaviour is also observed for larger systems.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: The morphology of the clusters of slipping particles depends on the elastic heterogeneitiy.(a) Scatter plot of the clusters dimensions, along the directions parallel and transverse to the shear, for system having different values of ϕ. By reducing the stiffness of the system we observe regions with different cluster shapes, indicated by the letters C, LC, DP, DT. (b) Schematic representations of the geometry of the clusters corresponding to the regions reported in the scatter plot. Here we show a system of dimension Lx = 20 and Ly = 5, the same behaviour is also observed for larger systems.
Mentions: In Fig. 4a we present a parametric plot of ly/Ly vs lx/Lx for four different values of ϕ. Cluster configurations can be distinguished into four classes, determined by ϕ, whose typical shape is reported in Fig. 4b. For we have the crystalline regime (C), represented by black circles in the region with . In this case, the system behaves as a rigid body and slips involve all particles, keeping the original crystalline order. For smaller value of ϕ we have the laminar crystalline regime (LC, red squares) where and ly with values in the range [1, Ly]. In this regime, a typical slip involves the motion of one or few parallel lines. This is consistent with the ordering features observed in this regime (LC lower panel), characterized by order along the direction of the shear and disorder along the transverse direction. A further reduction of ϕ first breaks order in the shearing direction, giving rise to the disorder–parallel regime (DP, green diamonds), and then fully disorders the system, giving rise to the disorder–transverse regime (DT, blue triangles). The shape of the clusters in both these regions are asymmetric with lx/Lx > ly/Ly in the DP whereas lx/Lx < ly/Ly in the DT. This information can be directly extracted from Fig. 4a where we observe that the DP and the DT regimes respectively populate regions above and below the diagonal. We characterize the asymmetry of the cluster shape comparing their average longitudinal and transverse sizes, lx/ly. As shown in Fig. 2b, this ratio varies non–monotonically with ϕ, and has a maximum corresponding to the minimum of . This suggests that the lowest value of is obtained when slips involve the horizontal displacement of the smallest number of lines.

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