Stick-slip dynamics of a granular layer under shear

Dmitri Volfson; Lev S. Tsimring; Igor S. Aranson

doi:10.1103/PhysRevE.69.031302

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Stick-slip dynamics of a granular layer under shear

Dmitri Volfson¹, Lev S. Tsimring¹, and Igor S. Aranson²

¹Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA
²Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA

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Phys. Rev. E 69, 031302 – Published 4 March, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.031302

Abstract

Stick-slip regime of shear granular flows is studied theoretically and numerically. Numerical experiments are carried out for a thin Couette cell using soft-particle molecular dynamics code in two dimensions. We apply order parameter theory of partially fluidized granular flows and find a good agreement with simulations and experiments by Nasuno et al.

References (13)

S. Nasuno et al., Phys. Rev. E 58, 2161 (1998).
I. Albert et al., Phys. Rev. E 64, 031307 (2001).
H. Hayakawa, Phys. Rev. E 60, 4500 (1999).
J.M. Carlson and A.A. Batista, Phys. Rev. E 53, 4153 (1996); ibid.57, 4986 (1998).
In our opinion melting should be driven by the shear stress, and sliding should occur as a result of melting.
I.S. Aranson and L.S. Tsimring, Phys. Rev. E 65, 061303 (2002).
D. Volfson, L.S. Tsimring, and I.S. Aranson, Phys. Rev. Lett. 90, 254301 (2003); Phys. Rev. E 68, 021301 (2003).
Another possibility to avoid “freezing” the system in the unstable solid regime at large shear stress is to modify the “free energy function” which gives rise to the order parameter equation (2), so the stable and unstable fixed points $ρ_{3}$ and $ρ_{2}$ merge and disappear at $δ > 0.3$ through a saddle-node bifurcation. Since in this case there is no fixed point at large $δ,$ the granular layer fluidizes and the plate slips rapidly after the control parameter $δ$ exceeds the critical bifurcation value. We ran simulations with such a modified order parameter equation without noise (data not shown) and found a qualitatively similar stick-slip behavior without noise excitation.
P.A. Thompson and G.S. Grest, Phys. Rev. Lett. 67, 1751 (1991).
E. Aharonov and D. Sparks (unpublished).
J. Schäfer, S. Dippel, and D.E. Wolf, J. Phys. I 6, 5 (1996).
D. Ertas et al., Europhys. Lett. 56, 214 (2000); L.E. Silbert et al., Phys. Rev. E 64, 051302 (2002).
P.A. Cundall and O.D.L. Strack, Geotechnique 29, 47 (1979).

[c1] S. Nasuno et al., Phys. Rev. E 58, 2161 (1998).

[c2] I. Albert et al., Phys. Rev. E 64, 031307 (2001).

[c3] H. Hayakawa, Phys. Rev. E 60, 4500 (1999).

[c4] J.M. Carlson and A.A. Batista, Phys. Rev. E 53, 4153 (1996); ibid.57, 4986 (1998).

[c5] In our opinion melting should be driven by the shear stress, and sliding should occur as a result of melting.

[c6] I.S. Aranson and L.S. Tsimring, Phys. Rev. E 65, 061303 (2002).

[c7] D. Volfson, L.S. Tsimring, and I.S. Aranson, Phys. Rev. Lett. 90, 254301 (2003); Phys. Rev. E 68, 021301 (2003).

[c8] Another possibility to avoid “freezing” the system in the unstable solid regime at large shear stress is to modify the “free energy function” which gives rise to the order parameter equation (2), so the stable and unstable fixed points $ρ_{3}$ and $ρ_{2}$ merge and disappear at $δ > 0.3$ through a saddle-node bifurcation. Since in this case there is no fixed point at large $δ,$ the granular layer fluidizes and the plate slips rapidly after the control parameter $δ$ exceeds the critical bifurcation value. We ran simulations with such a modified order parameter equation without noise (data not shown) and found a qualitatively similar stick-slip behavior without noise excitation.

[c9] P.A. Thompson and G.S. Grest, Phys. Rev. Lett. 67, 1751 (1991).

[c10] E. Aharonov and D. Sparks (unpublished).

[c11] J. Schäfer, S. Dippel, and D.E. Wolf, J. Phys. I 6, 5 (1996).

[c12] D. Ertas et al., Europhys. Lett. 56, 214 (2000); L.E. Silbert et al., Phys. Rev. E 64, 051302 (2002).

[c13] P.A. Cundall and O.D.L. Strack, Geotechnique 29, 47 (1979).

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Stick-slip dynamics of a granular layer under shear

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