Ken Kamrin's blog
https://imechanica.org/blog/16468
enNEW.Mech 2017 @ MIT | Registration deadline info
https://imechanica.org/node/21630
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/74">conference</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormal"><span>The 8th annual New England Workshop on the Mechan</span><span>ics of Materials and Structures </span><span>(</span><a href="http://2017.newmech.org/" target="_blank" data-saferedirecturl="https://www.google.com/url?hl=en&q=http://2017.newmech.org/&source=gmail&ust=1506542077482000&usg=AFQjCNG2RuIFjDam38Y62qfDQYTsit9L7Q"><span>NEW.Mech 2017</span></a><span>) is taking place at MIT on <strong><span class="aBn" data-term="goog_1076545635"><span class="aQJ">October 14, 2017</span></span></strong></span><span>. We would like to let you know that the registration deadline for submitting an e-poster or teaser talk is <strong><span class="aBn" data-term="goog_1076545636"><span class="aQJ">October 4</span></span> </strong>and<strong> </strong>the registration deadline<strong> </strong>for general admission is</span><span> <strong><span class="aBn" data-term="goog_1076545637"><span class="aQJ">October 11</span></span></strong>. </span><span>We are also glad to note that the registration for </span><a href="http://2017.newmech.org/" target="_blank" data-saferedirecturl="https://www.google.com/url?hl=en&q=http://2017.newmech.org/&source=gmail&ust=1506542077483000&usg=AFQjCNELT7s20KBCKtdFghi_SqnZ3iFsOA"><span>NEW.Mech 2017</span></a><span> is free. Please do register to secure your seat. Submission of teaser talks and/or e-posters can be done during online registration. You can directly register at </span><a href="http://newmech.org/register" target="_blank" data-saferedirecturl="https://www.google.com/url?hl=en&q=http://newmech.org/register&source=gmail&ust=1506542077483000&usg=AFQjCNH5omIJrIRJ3SxCe2aJ_5BPA-ik0w"><span>http://newmech.org/register</span></a><span>. </span></p>
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<p class="MsoNormal"><span>Our confirmed invited speakers and the titles of their talks are:</span></p>
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<p><a href="http://2017.newmech.org/people/huajian-gao" target="_blank" data-saferedirecturl="https://www.google.com/url?hl=en&q=http://2017.newmech.org/people/huajian-gao&source=gmail&ust=1506542077482000&usg=AFQjCNHcpXsz4ef0V9ULuJzIKSzCnv1C8A"><strong><span>Huajian Gao</span></strong></a><span class="m_-6241741057646650006gmail-apple-converted-space"><span> </span></span><span>– Professor of Engineering, Brown University<br />Talk Title: <em>Mechanics of cell interaction with low-dimensional nanomaterials</em></span></p>
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<p><a href="http://2017.newmech.org/people/john-w-hutchinson" target="_blank" data-saferedirecturl="https://www.google.com/url?hl=en&q=http://2017.newmech.org/people/john-w-hutchinson&source=gmail&ust=1506542077482000&usg=AFQjCNEuu-f7rOjLL05e9fP_UJ1ndH6U-A"><strong><span>John W. Hutchinson</span></strong></a><span class="m_-6241741057646650006gmail-apple-converted-space"><strong><span> </span></strong></span><span>– Professor of Engineering, Harvard University<br />Talk Title: <em>Shell buckling—the old and the new</em></span></p>
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<p><a href="http://2017.newmech.org/people/subra-suresh" target="_blank" data-saferedirecturl="https://www.google.com/url?hl=en&q=http://2017.newmech.org/people/subra-suresh&source=gmail&ust=1506542077483000&usg=AFQjCNFprdT9aJaTdw5cSMepTPm-iVdXgA"><strong><span>Subra Suresh</span></strong></a><span> – President-Designate, Nanyang Technological University, Singapore & Vannevar Bush Professor of Engineering Emeritus, MIT</span></p>
<p><span>Talk Title: <em>Cell mechanics and human diseases</em></span></p>
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<p><a href="http://2017.newmech.org/people/franz-josef-ulm" target="_blank" data-saferedirecturl="https://www.google.com/url?hl=en&q=http://2017.newmech.org/people/franz-josef-ulm&source=gmail&ust=1506542077483000&usg=AFQjCNFv46KTypV7t2cRMLkx0HRzHPey5w"><strong><span>Franz-Josef Ulm</span></strong></a><span class="m_-6241741057646650006gmail-apple-converted-space"><strong><span> </span></strong></span><span>– Professor of Civil & Environmental Engineering, MIT</span></p>
<p><span>Talk Title:<span class="m_-6241741057646650006gmail-apple-converted-space"> </span><em>Urban physics: Is Boston a liquid or a solid? A quantitative mechanics approach to cities' sustainability and resilience</em></span></p>
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<p class="MsoNormal"><span>NEW.Mech 2017 is supported by the following sponsors, </span><span>whom we graciously acknowledge:</span></p>
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<p class="MsoNormal"><span>- MIT Department of Civil and Environmental Engineering</span></p>
<p class="MsoNormal"><span>- MIT Department of Mechanical Engineering</span></p>
<p class="MsoNormal"><span>- MIT Department of Materials Science and Engineering</span></p>
<p class="MsoNormal"><span>- MIT Program in Polymers and Soft Matter</span></p>
<p class="MsoNormal"><span>- MIT Center for Materials Science and Engineering</span></p>
<p class="MsoNormal"><span>- North American Center for Research on Advanced Materials</span></p>
<p class="MsoNormal"><span>- Votorantim Cimentos</span></p>
<p class="MsoNormal"><span>- Multi-Scale Material Science for Energy and Environment</span></p>
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<p class="MsoNormal"><span>We look forward to seeing you at </span><span>NEW.Mech 2017</span><span>! The conference poster is attached.</span></p>
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<p class="MsoNormal"><span>Best regards,</span></p>
<p class="MsoNormal"><span>The NEW.Mech 2017 Organizers:</span></p>
<p class="MsoNormal"><span>Tal Cohen, Xuanhe Zhao, Ken Kamrin, Niels Holten-Andersen</span></p>
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</div></div></div>Tue, 26 Sep 2017 20:19:35 +0000Ken Kamrin21630 at https://imechanica.orghttps://imechanica.org/node/21630#commentshttps://imechanica.org/crss/node/21630Journal Club Theme of July 2013: Predicting granular flows: A new size-dependent constitutive model
https://imechanica.org/node/14929
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Since Coulomb initiated the topic over 200 years ago, continuum modeling of granular materials has remained an infamously difficult subject. Granular matter is common in everyday life (soil, sand, food grains, pharmaceuticals, etc) and second only to water as the most handled type of industrial material. However, a predictive, general constitutive relation for granular flow is lacking. This has become an expensive world-wide setback, since geotechnical and industrial flows are often on space- and time-scales too large for discrete particle simulation. It begs us to ask: Is there any hope for a "Navier-Stokes" equivalent for sand? With a view toward this question, in this journal club entry I'll outline some encouraging recent results based on a new model obtained with collaborators Georg Koval (of INSA Strasbourg) and recently-former postdoc David Henann (just started as Mech E faculty at Brown). See papers [1] and [2] for full details.
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Throughout, we limit the discussion to well-developed flows, in order to make the problem more tractable. This focus is part of a bigger strategy --- once we understand the well-developed state, it instructs the long-time behavior when developing critical-state-like models for the transients.</p>
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<strong><em>Inertial (local) rheology</em></strong>
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Our story begins in the mid-2000's, with the advent of the <em>inertial rheology</em> for granular flow, developed by a group of southern French researchers [3,4]. As reported in <a href="node/7028">my prior journal club entry</a>, the premise of the model can be extracted logically from dimensional arguments in a simple shear cell (see notational details below). In the end, for a given quasi-monodisperse granular composition, the result is a local rheology of the form
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<p><img src="http://web.mit.edu/kkamrin/www/simple_shearing.png" alt="simple shearing" width="654" height="150" align="left" /></p>
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Of note, the function f is empirically fit and demonstrates a clear yield criterion; f = 0 if τ/P = μ < μs for material parameter μs. The inertial rheology above has shown to work extremely well for steady-state, homogeneous simple shear flows.
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To broaden beyond simple shear, the relation can be written tensorially (i.e. presuming codirectionality and the Drucker-Prager yield surface), and instituted in general geometries as a 3D viscoplastic rheology [4], or as the flow rule in an elasto-viscoplastic rheology [5]. While these extensions give reasonable results for rapid flows, trouble quickly sets in.
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Despite how well the inertial rheology may work in homogeneous simple shear, it fails for slow non-uniform flows, even ones where the steady flow profile is locally simple shearing everywhere (say, annular shear flow) [6]. Of note, the model predictions tend to under-predict the size of flow features; rather, it happens that the grain size itself plays the key role in determining the width of such features. Moreover, we see creeping flow occurring in regions where stress levels are well beneath the μs value obtained from uniform simple shearing, as long as a flow gradient is present. These are tell-tale signs of nonlocality, set by a length-scale associated to the particle size, and consequently, well-developed granular rheology must be recast with nonlocal (or gradient-based) constitutive modeling. Since grains are commonly on our size-scale, the consequences of the nonlocality can be appreciated and noticed with the naked eye, in a truly remarkable fashion. Indeed one does not have to try hard to produce a flow where almost the entire profile is due to size-effects, and differs completely from the inertial rheology prediction.
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<strong><em>Extending to a nonlocal flow rule</em></strong>
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Our model, the <em>Nonlocal Granular Fluidity</em> (NGF) model, aims at resolving these issues, and can be backed out statistically from a micro-mechanism in which "flow aids flow" [7]. That is, a microscopic rearrangement event at some location can emit stress perturbations that affect material some distance away. Hence, in the continuum limit, it is both the mean applied stress and disturbances from neighboring flow (in the form of a Laplacian term scaled by the particle size) that together determine the shear-rate at some point. Mathematically, NGF resembles an implicit gradient theory, e.g. [8]. Omitting mathematical specifics here (see [2] for details), we note the following important features of the model:
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1) NGF couples the stress/strain-rate relation to a scalar field, the "granular fluidity", which satisfies a PDE calling on the grain-size.
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2) NGF reduces to the inertial relation in the absence of flow gradients (as it should).
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3) NGF necessitates only one new material parameter; an order-one dimensionless constant we call A, the nonlocal amplitude. The other parameters are borrowed directly from the inertial rheology. In total, NGF uses three material parameters.
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<strong><em>Results</em></strong>
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<p>The combined results of [1] and [2] show that the NGF model predicts flow and stress fields with a newfound level of accuracy, as verified over hundreds of geometries. </p>
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Our initial demonstrations in [1] were in the simplest 2D geometries --- flow in an annular cell, gravity-driven flow down a vertical chute, and dragging of a plate over granular bed. Its predictions matched data from discrete simulations of disk flows (c/o Georg Koval) in the analogous geometries for various different values of system size or gravity, over many orders of magnitude in flow speed. A single calibration of the material parameters was used throughout.
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With the success of the 2D prototype cases, the model was recast in 3D, and an Abaqus User-Element was created (c/o David Henann) to permit us to solve the NGF system in arbitrary 3D geometries [2]. We re-calibrated the model parameters for quasi-monodisperse 3D glass beads, and compared model predictions against experimental data for bead flows in many geometries. As a stringent test, we first compared NGF predictions in "split-bottom" flow geometries, a family of flow environments made famous over the last decade for having resisted all previous continuum models. It was shown in [2] that NGF is the first continuum model to quantitatively capture all features of the flows in these geometries. For example, see below (from [2]).
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<p><img src="http://web.mit.edu/kkamrin/www/split_bottom.png" alt="split bottom cell" width="652" height="282" /></p>
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(a) A schematic of the split-bottom geometry: Grains fill an annular trough split along its bottom at radius <em>Rs</em>. The outter portion is rotated while holding the inner portion fixed. (b,c) Model predictions for the flow field as measured by the revolution rate <em>ω(r,z) = νθ(r,z) / RΩ</em> for different filling heights <em>H</em>. Note the Heaviside profile at <em>z=0</em> spreading out <em>z</em> increases. (d) Comparing the predicted flow field on the top surface (<em>z=H</em>) to experimental data [9] for various filling heights <em>H</em>.
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We then applied the same model with same parameters in completely different flow environments and found equally high agreement with experimental data on glass bead flows, reflecting the geometric-generality of NGF. For example, see below (from [2]).
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<p><img src="http://web.mit.edu/kkamrin/www/other_flows.png" alt="other flow environments" width="644" height="207" /></p>
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(Left) Comparison of NGF prediction (solid line) to experimental flow data (symbols) in a 3D, gravity-compacted annular shear apparatus [10]. (Right) Comparison of NGF prediction (solid line) to experimental flow data (symbols) in a 3D plate-dragging geometry in the presence of gravity [11].
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<em><strong>More to do</strong></em>
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Despite the encouraging results, there remain several questions to answer. For instance, there are lingering issues about the form of fluidity boundary conditions, how exactly to incorporate transient effects and/or anisotropy internal variables within this framework, and the exact connection between grain properties and the nonlocal amplitude A. Please see the end of our paper [2] for a comprehensive discussion of the major open issues.
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Again, much appreciation to my collaborators Koval and Henann!
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</p><p>[1] <a href="http://prl.aps.org/abstract/PRL/v108/i17/e178301">Kamrin and Koval, Phys Rev Lett (2012)<br /></a>
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</p><p>[2] <a href="http://www.pnas.org/content/early/2013/03/27/1219153110.abstract">Henann and Kamrin, PNAS (2013)<br /></a>
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</p><p>[3] <a href="http://pre.aps.org/abstract/PRE/v72/i2/e021309">da Cruz et al, Phys Rev E (2005)</a> </p>
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</p><p>[4] <a href="http://www.nature.com/nature/journal/v441/n7094/abs/nature04801.html">Jop et al, Nature (2006)<br /></a>
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</p><p>[5] <a href="http://www.sciencedirect.com/science/article/pii/S0749641909000898">Kamrin, Int J Plasticity (2010)<br /></a>
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</p><p>[6] <a href="http://pre.aps.org/abstract/PRE/v79/i2/e021306">Koval et al, Phys Rev E (2009)<br /></a>
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</p><p>[7] <a href="http://prl.aps.org/abstract/PRL/v103/i3/e036001">Bocquet et al, Phys Rev Lett (2009)<br /></a>
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</p><p>[8] <a href="http://www.sciencedirect.com/science/article/pii/S0749641911001665">Anand et al, Int J Plasticity (2012)<br /></a>
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</p><p>[9] <a href="http://www.nature.com/nature/journal/v425/n6955/abs/425256a.html">Fenistein and van Hecke, Nature (2003)<br /></a>
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</p><p>[10] <a href="http://prl.aps.org/abstract/PRL/v85/i7/p1428_1">Losert et al, Phys Rev Lett (2000)<br /></a>
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<p>[11] <a href="http://pre.aps.org/abstract/PRE/v73/i1/e010301">Siavoshi et al, Phys Rev E (2006)</a> </p>
</div></div></div>Wed, 03 Jul 2013 05:17:13 +0000Ken Kamrin14929 at https://imechanica.orghttps://imechanica.org/node/14929#commentshttps://imechanica.org/crss/node/14929Journal Club Theme of November 2009: Steady granular flow
https://imechanica.org/node/7028
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How does sand flow? A surprisingly difficult question. This entry tells the story behind a model detailed in [6] for dry, dense, steady-flowing granular materials. </p>
<p>As an initial thought experiment, consider a long, 2D simple shear cell filled with viscoelastic disks. The disks are slightly bidisperse (to avoid crystal packings), and have average diameter <em>d</em> and mass <em>m</em>. The rough plates of the cell are compressed together with pressure <em>P</em> and sheared relative to each other at a rate <em>dv/dy</em>. Supposing the disks are always composed of the same material, we ask the question: How does the steady-state packing fraction <em>φ</em> and shear stress <em>τ</em> depend on the given parameters? Dimensional arguments are helpful here. Aside from <em>φ</em>, there are two other dimensionless groups that can be constructed: <em>I = (dv/dy) √(m/Pd)</em> is the normalized shear-rate, and <em>μ = τ/P</em> is the effective friction. The problem should have a unique steady behavior, so it follows that <em>μ = g(I)</em> and <em>φ = h(I)</em>, since <em>I</em> is the only dimensionless group determined solely from the problem setup. These dependences generalize "Bagnold scaling" [2]; Bagnold was the first to observe that at fixed packing fraction, the pressure exerted on the wall of a granular shear cell depends <em>quadratically</em> on the shear-rate.</p>
<p>Disk shear simulations of [3], revealed that the functions <em>g</em> and <em>h</em> always have a relatively simple form in the "inertial regime" (1e-3 < <em>I </em>< 1e-1), characteristic of shearing in day-to-day flows like an hourglass. Namely, <em>φ = h(I)</em> stays roughly constant at the random-close-packing value, and <em>μ = g(I) ≈ μ_s + β I</em> indicative of a rate-dependent flow stress with static yield criterion <em>μ_s</em>. Here, rate-sensitivity arises from the dominating role of impact dissipation in the inertial regime; increasing the normalized shear-rate increases both the frequency of collisions and the energy loss per collision.
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Next, the work of Jop <em>et al.</em> [5] extended these 2D results into a 3D rheology for monodisperse spheres by trying a straightforward re-interpretation: Replace <em>τ</em> and <em>dv/dy</em> with the equivalent shear stress and equivalent shear-rate, let <em>P</em> be the hydrostatic pressure, presume incompressibility, and enforce codirectionality to relate the direction of the deviatoric stress tensor to the deformation-rate tensor (non-associative). In essence, a Bingham fluid treatment of granular matter was proposed with Drucker-Prager yield criterion <em>μ_s</em>. The model was heralded as a major step forward, as it turned out to be capable of predicting highly inhomogeneous 3D flow profiles with accuracy. The applicability of the continuum rheology was bolstered in [7], where it was shown that the size-scale for RVE behavior in 3D inertial flow is generally a mere 5 particle diameters.</p>
<p>However, a key ingredient was missing. Bingham models give no stress computation in static regions (below <em>μ_s</em>). Solid-like zones are common in steady granular flow, and must be described in order for the law to be mechanically well-posed under admissible kinematic/traction boundary conditions. Thus, the next step was to splice a granular elasticity law into this framework, converting the Bingham model to an elasto-plastic model. The elasticity of a static granular material element is itself a complicated phenomenon, since even in the small-strain limit, the elastic response cannot be approximated as linear because grain assemblies do not support tension. The work of Jiang and Liu [4] proposed a nonlinear granular elasticity model, which expanded on successful mean-field theories of Hertzian contacts. With demonstrated experimental validation, both in terms of acoustic and static behavior, the Jiang-Liu elasticity law seemed to fit the bill.</p>
<p>My goal in [6] was to merge the Jiang-Liu elasticity model with the Jop flow law, to produce a unified granular constitutive law, which can be implemented in FEM, and used to predict steady stress and flow profiles throughout any 3D geometry. Following similar theories for thermodynamically compatible elasto-plasticity in [1], my approach was to presume a multiplicative Kröner-Lee decomposition of the deformation gradient. Running the model to steady-state as a VUMAT in ABAQUS, several flows were computed in different 3D geometries (e.g. silo, inclined chute, annular shear). The predicted flow and stress profiles compared favorably against the data of a number of experimental and discrete simulation studies.</p>
<p>While there is no shortage of remaining open questions in granular flow, it seems the most important to the study of dense, well-developed flow would be a general description of the "quasi-static" flow regime (<em>I < </em>1e-3), which characterizes many geological applications. Its rheology appears significantly more complex than the inertial regime, with rate-independent flow stresses and a non-local size dependence.
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<a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TXB-4FSCVJR-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a1bb386ef56f0aa0c71dd39fc2382e15">[1] L. Anand and C. Su. A theory for amorphous viscoplastic materials undergoing ﬁnite deformations, with application to metallic glasses. J. Mech. Phys. Solids, 53:1362–1396, 2005.</a><br /><a href="http://www.jstor.org/stable/99440"></a>
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<a href="http://www.jstor.org/stable/99440">[2] R. A. Bagnold. Experiments on a gravity free dispersion of large solid spheres in a newtonian ﬂuid under shear. Proc. Roy. Soc. London Ser. A, 225, 1954.</a><br /><a href="http://link.aps.org/doi/10.1103/PhysRevE.72.021309"></a>
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<a href="http://link.aps.org/doi/10.1103/PhysRevE.72.021309">[3] F. da Cruz, S. Emam, M. Prochnow, J. Roux, and F. Chevoir. Rheophysics of dense granular materials: Discrete simulation of plane shear ﬂows. Phys. Rev. E., 72:021309, 2005.</a> <br /><a href="http://link.aps.org/doi/10.1103/PhysRevLett.91.144301"></a>
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<a href="http://link.aps.org/doi/10.1103/PhysRevLett.91.144301">[4] Y. Jiang and M. Liu. Granular elasticity without the coulomb condition. Phys. Rev. Lett., 91:144301, 2003. </a> <br /><a href="http://www.nature.com/nature/journal/v441/n7094/full/nature04801.html"></a>
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<a href="http://www.nature.com/nature/journal/v441/n7094/full/nature04801.html">[5]</a> <a href="http://www.nature.com/nature/journal/v441/n7094/full/nature04801.html"> P. Jop, Y. Forterre, and O. Pouliquen. A constitutive law for dense granular ﬂows. Nature, 441:727, 2006. </a> <br /><a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TWX-4WRM6J2-6&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=54c95cce1e11c0b9ccedc56707e11b61"></a>
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<a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TWX-4WRM6J2-6&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=54c95cce1e11c0b9ccedc56707e11b61">[6] K. Kamrin. Nonlinear elasto-plastic model for dense granular ﬂow. (In press, Int. J. Plasticity) doi:10.1016/j.ijplas.2009.06.007. </a> <a href="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TXB-4VKP476-1&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1074876449&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=b2d75489d8ef2581f1b7b74d0cdca9c8"><br /></a>
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</div></div></div>Mon, 02 Nov 2009 22:23:22 +0000Ken Kamrin7028 at https://imechanica.orghttps://imechanica.org/node/7028#commentshttps://imechanica.org/crss/node/7028