### Abstract

Experiments on sheared granular materials show that the stresses grow as the first power of the log of the shear rate, ($) over circle gamma. We suggest that this may be evidence of the stress ensemble recently proposed by Henkes, O'Hern, and Chakraborty. The picture that we propose is that under steady shearing, the local force network builds up over time, and then fails when the force on the network exceeds a characteristic value. In analogy to soft glassy rheology, we assume that this is an activated process, but now, with the Boltzmann factor replaced by the stress ensemble analogue. We assume that the probability that a local part of the network fails is proportional to exp[(sigma - sigma(m))sigma(o)], where sigma is the local stress, sigma(m) is a failure threshold, and sigma(o) is related to the generalized temperature, alpha, of Henkes and Chakraborty. It is then possible to show that these assumptions lead to logarithmic increases in the stress as a function of gamma. This contrasts with the SGR result that the stress grows as the square root of log(gamma).

Original language | English |
---|---|

Title of host publication | Powders and Grains 2009 |

Editors | M Nakagawa, S Luding |

Place of Publication | Melville |

Publisher | American Institute of Physics |

Pages | 1089-1092 |

Number of pages | 4 |

ISBN (Print) | 978-0-7354-0682-7 |

Publication status | Published - 2009 |

Event | 6th International Conference on the Micromechanics of Granular Media - Golden Duration: 13 Jul 2009 → 17 Jul 2009 |

### Publication series

Name | AIP conference proceedings |
---|---|

Volume | 1145 |

### Conference

Conference | 6th International Conference on the Micromechanics of Granular Media |
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City | Golden |

Period | 13/07/09 → 17/07/09 |

### Keywords

- AEMMG
- grains
- granular matter
- micromechanics of powders
- powders

### Cite this

*Powders and Grains 2009*(pp. 1089-1092). (AIP conference proceedings; Vol. 1145). Melville: American Institute of Physics.

**Logarithmic Strengthening of Granular Materials with Shear Rate.** / Hartley, R. R.; Behringer, R. P.; Henkes, S.; Bi, D.; Chakraborty, B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Powders and Grains 2009.*AIP conference proceedings, vol. 1145, American Institute of Physics, Melville, pp. 1089-1092, 6th International Conference on the Micromechanics of Granular Media, Golden, 13/07/09.

}

TY - GEN

T1 - Logarithmic Strengthening of Granular Materials with Shear Rate

AU - Hartley, R. R.

AU - Behringer, R. P.

AU - Henkes, S.

AU - Bi, D.

AU - Chakraborty, B.

PY - 2009

Y1 - 2009

N2 - Experiments on sheared granular materials show that the stresses grow as the first power of the log of the shear rate, ($) over circle gamma. We suggest that this may be evidence of the stress ensemble recently proposed by Henkes, O'Hern, and Chakraborty. The picture that we propose is that under steady shearing, the local force network builds up over time, and then fails when the force on the network exceeds a characteristic value. In analogy to soft glassy rheology, we assume that this is an activated process, but now, with the Boltzmann factor replaced by the stress ensemble analogue. We assume that the probability that a local part of the network fails is proportional to exp[(sigma - sigma(m))sigma(o)], where sigma is the local stress, sigma(m) is a failure threshold, and sigma(o) is related to the generalized temperature, alpha, of Henkes and Chakraborty. It is then possible to show that these assumptions lead to logarithmic increases in the stress as a function of gamma. This contrasts with the SGR result that the stress grows as the square root of log(gamma).

AB - Experiments on sheared granular materials show that the stresses grow as the first power of the log of the shear rate, ($) over circle gamma. We suggest that this may be evidence of the stress ensemble recently proposed by Henkes, O'Hern, and Chakraborty. The picture that we propose is that under steady shearing, the local force network builds up over time, and then fails when the force on the network exceeds a characteristic value. In analogy to soft glassy rheology, we assume that this is an activated process, but now, with the Boltzmann factor replaced by the stress ensemble analogue. We assume that the probability that a local part of the network fails is proportional to exp[(sigma - sigma(m))sigma(o)], where sigma is the local stress, sigma(m) is a failure threshold, and sigma(o) is related to the generalized temperature, alpha, of Henkes and Chakraborty. It is then possible to show that these assumptions lead to logarithmic increases in the stress as a function of gamma. This contrasts with the SGR result that the stress grows as the square root of log(gamma).

KW - AEMMG

KW - grains

KW - granular matter

KW - micromechanics of powders

KW - powders

M3 - Conference contribution

SN - 978-0-7354-0682-7

T3 - AIP conference proceedings

SP - 1089

EP - 1092

BT - Powders and Grains 2009

A2 - Nakagawa, M

A2 - Luding, S

PB - American Institute of Physics

CY - Melville

ER -