Transmission of kinematic information in dense granular systems: local and nonlocal network sensing
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We study how kinematic information propagates in plane strain compression tests for two granular samples, one comprising glass beads and the other is sand. Of interest are the structures of directed networks constructed from static linear relationships among grain-scale kinematical measurements obtained using digital image correlation. The exact form and kinematical information used in each linear relationship is selected using a data modelling algorithm that appeals to the information theory description length philosophy encapsulated by the principle of Occam’s Razor. For both tests, we find that the observation sites with the most complicated relationships (i.e., those which require the x- and y-coordinates of the displacements of both neighboring and distant sites to best represent their own kinematics) are located in that region where the persistent shear band develops. The static linear relationships for these sites involve a length scale that is around 7–15 times the mean particle diameter, consistent with the observed thickness of the shear band in each sample. Our findings corroborate earlier evidence from the extant literature that the kinematics inside shear bands are necessarily nonlocal and further highlights the crucial importance of incorporating shear band kinematics in constitutive modelling. We shed new insights not only for constitutive modelling but also in the use of sensors to detect motion in deforming granular systems: that sensors with local sensing and monitoring capabilities are sufficient for distilling information on kinematic transmission—except in the shear band where nonlocal information, or information from spatially distant sensors, is a necessity.
KeywordsDigital image correlation Directed networks Granular media Kinematics Sensor networks
We thank Dr. John Peters for valuable insights and useful comments. This work was partially supported by the US Army Research Office (W911NF-11-1-0175), the Australian Research Council (DP0986876 and DP120104759), and the Melbourne Energy Institute (AT, DMW). ALR is supported by USA National Science Foundation (NSF) Grant CMMI-0748284.
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