Some fundamental aspects of the continuumization problem in granular media

Peters, John F.

doi:10.1007/s10665-004-2117-2

Cited by 6 publications

(6 citation statements)

References 16 publications

(23 reference statements)

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“…The brackets indicate the average fluctuating velocity across the entire assembly. A second comparison is to the non-affine strain which is a measure of the observed deviation of a grain cluster from that expected if the deformation was solely attributable to the affine strain tensor [9,[29][30][31][32]48]. A scalar measure of the non-affine deformation for each grain cluster can be calculated and averaged over the whole assembly to obtain a macroscopic measure [9,30].…”

Section: B Energy Measures In Granular Assembliesmentioning

confidence: 99%

“…This means that a costly calculation of a networks' minimal cycle basis can be circumvented further opening the method to greater practical use in real sands where hundreds of thousands of grains are the norm. Macroscopic averages of this quantity across the entire assembly of grains correlates strongly with the fluctuating kinetic energy [26][27][28], including non-affine deformation measures that use full structural and kinematic information available in numerical experiments [9,[29][30][31][32]. We argue that our method can be applied to the current state of experimental measurements where standard measures are not possible.…”

Section: Introductionmentioning

confidence: 99%

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Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution

2014

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Recent advances in high-resolution measurements means it is now possible to identify and track the local "fabric" or contact topology of individual grains in a deforming sand throughout loading history. These provide compelling impetus to the development of methods for inferring changes in the contact forces and energies at multiple spatiotemporal scales, using information on grain contacts alone. Here we develop a surrogate measure of the fluctuating kinetic energy based on changes in the local contact topology of individual grains. We demonstrate the method for dense granular materials under quasistatic biaxial shear. In these systems, the initially stable and solidlike response eventually gives way to liquidlike behavior and global failure. This crossover in mechanical behavior, akin to a phase transition, is marked by bursts of kinetic energy and frictional dissipation. Mechanisms underlying this release of energy include the buckling of major load-bearing structures known as force chains. These columns of grains represent major repositories for stored strain energy. Stored energy initially accumulates at all of the contacts along the force chain, but is released collectively when the chain overloads and buckles. The exact quantification of the buildup and release of energy in force chains, and the manner in which force chain buckling propagates in the sample (i.e., diffuse and systemwide versus localized into shear bands), requires detailed knowledge of contact forces. To date, however, the forces at grain contacts continue to elude measurement in natural granular materials like sand. Here, using data from computer simulations, we show that a proxy for the fluctuating kinetic energy in dense granular materials can be suitably constructed solely from the evolving properties of the grain's local contact topology. Our approach directly relates the evolution of fabric to energy flux and makes possible research into the propagation of failure from measurements of grain contacts in real granular materials.

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Section: B Energy Measures In Granular Assembliesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution

2014

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“…In particular, later work by Tordesillas et al (2010) investigated the relationship between localization and meso-scale features such as force chains. Another trend in recent years is multi-scale analysis using hierarchical continuum theories, as employed by Liu (2004 and2005) to both regularize the boundary value problem and to provide a framework for incorporating information from microscale information.…”

Section: Non-local Theoriesmentioning

confidence: 99%

Patterned Nonaffine Motion in Granular Media

Peters

Walizer

2013

J. Eng. Mech.

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Vortex-like flow patterns often are observed in experiments on granular media for which uniform strain is expected based on the loading boundary conditions. These deformations become apparent when the motion associated with uniform strain is subtracted from the total particle motion. Besides presenting an interesting phenomenon that begs explanation, these vortex patterns suggest multi-scale structure to non-affine motion as suggested by modern continuum theories. Further, the rotational velocity field added to a uniform strain field produces a planar slip field. Thus, these structures are associated with the slip-band fields that eventually form and generally are associated with bifurcations in the solution path of the governing partial differential equations. A procedure is presented to extract these motion fields from discrete element simulations, along with conjugate forces associated with these motions. A key finding from the simulations is that the motions that eventually lead to shear band formation develop throughout the loading history rather than arising as a distinct bifurcation. Further, the pattern of rotational fields and, hence, the shear banding pattern are controlled by the boundary conditions. A question, only partly resolved here, is the origin of forces driving the rotational fields, considering no force exists at the boundaries in the case of frictionless platens. DISCLAIMER: The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. All product names and trademarks cited are the property of their respective owners. The findings of this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.

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“…The principle forms the basis of describing deformation of discrete particle systems. Any operator defined to extract deformation measures from particle motions is orthogonal to rigid-body motions (Peters 2005). Thus, a vector space can be defined from which all admissible deformations can be constructed as a linear combination of vectors that are orthogonal to the rigid body motions given by…”

Section: Rigid-body Motions and Deformationmentioning

confidence: 99%

Development of the particle-scale definition of stress and strain for the discrete element method : Report 3 in “Discrete nano-scale mechanics and simulations” series

Hodo¹,

Peters²,

Walizer³

et al. 2019

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The U.S. Army Engineer Research and Development Center (ERDC) solves the nation's toughest engineering and environmental challenges. ERDC develops innovative solutions in civil and military engineering, geospatial sciences, water resources, and environmental sciences for the Army, the Department of Defense, civilian agencies, and our nation's public good. Find out more at www.erdc.usace.army.mil. To search for other technical reports published by ERDC, visit the ERDC online library at http://acwc.sdp.sirsi.net/client/default.

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Some fundamental aspects of the continuumization problem in granular media

Cited by 6 publications

References 16 publications

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution

Mesoscale and macroscale kinetic energy fluxes from granular fabric evolution

Patterned Nonaffine Motion in Granular Media

Development of the particle-scale definition of stress and strain for the discrete element method : Report 3 in “Discrete nano-scale mechanics and simulations” series

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