Logarithmic Strengthening of Granular Materials with Shear Rate

R. R. Hartley, R. P. Behringer, S. Henkes, D. Bi, B. Chakraborty

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationPowders and Grains 2009
EditorsM Nakagawa, S Luding
Place of PublicationMelville
PublisherAmerican Institute of Physics
Pages1089-1092
Number of pages4
ISBN (Print)978-0-7354-0682-7
Publication statusPublished - 2009
Event6th International Conference on the Micromechanics of Granular Media - Golden
Duration: 13 Jul 200917 Jul 2009

Publication series

NameAIP conference proceedings
Volume1145

Conference

Conference6th International Conference on the Micromechanics of Granular Media
CityGolden
Period13/07/0917/07/09

Keywords

  • AEMMG
  • grains
  • granular matter
  • micromechanics of powders
  • powders

Cite this

Hartley, R. R., Behringer, R. P., Henkes, S., Bi, D., & Chakraborty, B. (2009). Logarithmic Strengthening of Granular Materials with Shear Rate. In M. Nakagawa, & S. Luding (Eds.), Powders and Grains 2009 (pp. 1089-1092). (AIP conference proceedings; Vol. 1145). Melville: American Institute of Physics.