Artykuły w czasopismach: „Granular Assemblies”

1

HIDAKA, Jusuke. "Numerical Experiments on Granular Assemblies." Journal of the Society of Powder Technology, Japan 29, nr 6 (1992): 465–71. http://dx.doi.org/10.4164/sptj.29.465.

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Suiker, Akke S. J., i Norman A. Fleck. "Frictional Collapse of Granular Assemblies". Journal of Applied Mechanics 71, nr 3 (1.05.2004): 350–58. http://dx.doi.org/10.1115/1.1753266.

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The frictional collapse of an assembly of equisized spheres is studied by a discrete element model. The macroscopic constitutive response is determined as a function of the level of Coulomb friction between particles. It is found that the level of Coulomb friction has a strong effect upon the relative proportion of sliding and rolling between particles, and consequently upon the macroscopic strength of the granular assembly. The discrete element predictions are shown to be in good agreement with experimental results obtained from triaxial tests on an aggregate of steel spheres. It is demonstrated that the shape of the collapse surface can be adequately represented by the Lade-Duncan continuum model.

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3

Melin, Stephan. "Wave propagation in granular assemblies". Physical Review E 49, nr 3 (1.03.1994): 2353–61. http://dx.doi.org/10.1103/physreve.49.2353.

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Benezet, J. C., P. Adamiec i M. Nemoz-Gaillard. "Study of real granular assemblies". Powder Technology 173, nr 2 (kwiecień 2007): 118–25. http://dx.doi.org/10.1016/j.powtec.2006.10.043.

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Manciu, Marian, Robert S. Sinkovits, Surajit Sen i Alan J. Hurd. "Nonlinear acoustics in granular assemblies". Granular Matter 3, nr 1-2 (1.01.2001): 33–39. http://dx.doi.org/10.1007/s100350000067.

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Sufian, Adnan, Adrian R. Russell, Andrew J. Whittle i Mohammad Saadatfar. "Pore Characterisation in Monodisperse Granular Assemblies". Applied Mechanics and Materials 846 (lipiec 2016): 583–88. http://dx.doi.org/10.4028/www.scientific.net/amm.846.583.

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The micro-scale geometric arrangement of pores was quantitatively characterised for monodisperse granular assemblies, particularly in relation to pore volume distribution and pore orientation characteristics. Using physical experiments and numerical simulations, the pore volume distribution was uniquely described by the analytical k-gamma distribution function [1-2]. A pore orientation tensor was defined to determine the preferred orientation of individual pores. This was subsequently used to define a global orientation tensor that revealed an isotropic pore network for the monodisperse granular assemblies considered in this study. The global orientation tensor was analytically linked to the parameters defining the pore volume distribution.

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Ning, Z., A. Khoubani i T. M. Evans. "Shear wave propagation in granular assemblies". Computers and Geotechnics 69 (wrzesień 2015): 615–26. http://dx.doi.org/10.1016/j.compgeo.2015.07.004.

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Bagi, Katalin. "Stress and strain in granular assemblies". Mechanics of Materials 22, nr 3 (marzec 1996): 165–77. http://dx.doi.org/10.1016/0167-6636(95)00044-5.

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Chen, Hui Liang, i Yu Ching Wu. "Viscoplastic Analysis of Mixed Polygonal Granular Material". Advanced Materials Research 446-449 (styczeń 2012): 3578–81. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.3578.

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In this paper, a series of mixed visco-plastic analyses for assembles of three types of asphalt are made using finite element method. Governing equations are derived for motion and deformation for particles, including coupling of rigid body motion and deformation for deformable bodies. Nonlinear viscous analysis is made for the assemblies using an implicit discrete element method. Among particles, three different contact types, cohering, rubbing and sliding, are taken into account. The numerical model is applied to simulate the compaction of aggregates consisting of mixed particles of different nonlinear viscous incompressible material. After minor modification, the application of the proposed numerical model to industry is possible.

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Okiy, Karinate Valentine. "Effect of Interparticle Friction on the Micromechanical Strength Characteristics of Three Dimensional Granular Media". International Journal of Engineering Research in Africa 16 (czerwiec 2015): 79–89. http://dx.doi.org/10.4028/www.scientific.net/jera.16.79.

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The role of interparticle friction on the micromechanical strength characteristics of granular assembly subjected to gradual shearing was analyzed. Three dimensional discrete element method (DEM) was applied in the simulation of quasi-static shearing of granular assemblies with varying interparticle frictional coefficients [µ= 0.10, 0.25, 0.50]. From the reported simulation results, analysis of the following was performed for varying interparticle frictional capacities.i. The normal and tangential stress contributions of weak and strong contacts to principal stress components.ii. Contribution of strong and weak contacts to principal and deviator stress.iii. Evolution of mechanical coordination number and fabric anisotropy of strong contact forces.From this analysis, it is safe to conclude that interparticle friction has a direct effect on the major and minor principal stress components in sheared granular assemblies. Consequently, increasing interparticle friction capacity enhances macroscopic shear strength in sheared granular assemblies. Likewise, at the peak shear strength of the sheared granular media, there exists a maximum fabric anisotropy of strong contact forces and this corresponds to a minimum value of mechanical coordination number (minimum possible number of load bearing contacts per particle).

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Russell, Adrian R., David Muir Wood i Mamoru Kikumoto. "Crushing of particles in idealised granular assemblies". Journal of the Mechanics and Physics of Solids 57, nr 8 (sierpień 2009): 1293–313. http://dx.doi.org/10.1016/j.jmps.2009.04.009.

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Thornton, C., i D. J. Barnes. "Computer simulated deformation of compact granular assemblies". Acta Mechanica 64, nr 1-2 (grudzień 1986): 45–61. http://dx.doi.org/10.1007/bf01180097.

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Liao, Ching L., Tian C. Chan, Akke S. J. Suiker i Ching S. Chang. "Pressure-dependent elastic moduli of granular assemblies". International Journal for Numerical and Analytical Methods in Geomechanics 24, nr 3 (marzec 2000): 265–79. http://dx.doi.org/10.1002/(sici)1096-9853(200003)24:3<265::aid-nag65>3.0.co;2-x.

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Judes Sujatha, S., Z. K. Jahanger, S. Barbhuiya i S. Joseph Antony. "Fabrics-Shear Strength Links of Silicon-Based Granular Assemblies". Journal of Mechanics 36, nr 3 (2.12.2019): 323–30. http://dx.doi.org/10.1017/jmech.2019.47.

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ABSTRACTSilicon (Si)-based materials are sought in different engineering applications including Civil, Mechanical, Chemical, Materials, Energy and Minerals engineering. Silicon and Silicon dioxide are processed extensively in the industries in granular form, for example to develop durable concrete, shock and fracture resistant materials, biological, optical, mechanical and electronic devices which offer significant advantages over existing technologies. Here we focus on the constitutive behaviour of Si-based granular materials under mechanical shearing. In the recent times, it is widely recognised in the literature that the microscopic origin of shear strength in granular assemblies are associated with their ability to establish anisotropic networks (fabrics) comprising strong-force transmitting inter-particle contacts under shear loading. Strong contacts pertain to the relatively small number of contacts carrying greater than the average normal contact force. However, information on how such fabrics evolve in Si-based assemblies under mechanical loading, and their link to bulk shear strength of such assemblies are scarce in the literature. Using discrete element method (DEM), here we present results on how Si-based granular assemblies develop shear strength and their internal fabric structures under bi-axial quasi-static compression loading. Based on the analysis, a simple constitutive relation is presented for the bulk shear strength of the Si-based assemblies relating with their internal fabric anisotropy of the heavily loaded contacts. These findings could help to develop structure-processing property relations of Si-based materials in future, which originate at the microscale.

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15

Zhu, C. Y., A. Shukla i M. H. Sadd. "Prediction of Dynamic Contact Loads in Granular Assemblies". Journal of Applied Mechanics 58, nr 2 (1.06.1991): 341–46. http://dx.doi.org/10.1115/1.2897191.

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An experimental-numerical hybrid technique has been developed to predict the intergranular contact load transfer in granular media subjected to explosive loading. The granular media were simulated by assemblies of circular disks in contact. The peak contact load transfer coefficients (i. e., the ratio of the maximum output contact load to the input contact load as a function of the contact angles) of a given particle were obtained through controlled experimental studies. These coefficients, along with the principle of superposition, were then used to predict the peak contact loads in several regular as well as irregular assemblies of disks. The predicted results compared favorably with the experimental data for several different assemblies.

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Azéma, Emilien, David Cantor i Itthichai Preechawuttipong. "Independence of shear strength with particle size dispersity still valid in polyhedral particle assemblies". EPJ Web of Conferences 249 (2021): 06009. http://dx.doi.org/10.1051/epjconf/202124906009.

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A very staggering result that has been constantly highlighted in granular media is that the shear strength of granular assemblies is independent of the particle size dispersity. In other words, a packing composed of monodisperse particles has similar strength properties to those of polydisperse systems. This has been shown numerically for the simplified case of disc and polygon assemblies in 2D and spheres in 3D. In this paper, we use three-dimensional contact dynamics simulations to revisit these results for the more complex case of assemblies composed of highly polydisperse rigid polyhedra. Although non-spherical shapes induce more intricated spatial correlations than spherical shapes because of the multiple contact types (i.e., vertex-face, edge-edge, edge-face, face-face), our numerical data provide evidence that the shear strength independence as the particle size dispersity increases still holds up for assemblies of polyhedra. We explain this finding from compensation mechanisms at the micro-scale between geometrical and mechanical anisotropies developed within the assemblies.

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17

Park, Jung i Kwak. "Effect of Initial Granular Structure on the Evolution of Contact Force Chains". Applied Sciences 9, nr 22 (6.11.2019): 4735. http://dx.doi.org/10.3390/app9224735.

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The effect of initial granular structural conditions on load transmission patterns was experimentally investigated. Two types of granular structures were prepared by laminating cylindrical model particles of different diameters, to which photoelastic sheets were attached. Two-dimensional, reflective photoelasticity tests were performed under two granular conditions: (1) a uniform structure without initial defects and (2) with initial local imperfections at the bottom of the granular assembly. Two granular assemblies were tested for uniaxial compressive loading and shallow foundation loading conditions. For macroscopic analyses of the load–displacement relationship, the photoelastic response of individual particles was measured to microscopically observe the distribution of the main contact force chains within each granular assembly. Furthermore, the effect of initial local defects on the bearing capacity of granular assemblies was examined by confirming particle movement and the expansion of initial local defects in the granular assembly via particle image velocimetry (PIV). As a result, a completely different form of internal contact force chain was developed from the beginning of loading to the final failure stage, depending upon whether or not initial local instability existed in the granular assembly. In particular, a significant effect on the bearing capacity was found under shallow foundation loading conditions.

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18

Wensrich, Christopher M., Erich H. Kisi, Vladimir Luzin, Oliver Kirstein, Alexander L. Smith i Jian Feng Zhang. "Neutron Diffraction Techniques in Granular Mechanics". Materials Science Forum 905 (sierpień 2017): 190–95. http://dx.doi.org/10.4028/www.scientific.net/msf.905.190.

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Granular materials demonstrate unique mechanical properties stemming from their discrete nature. At large length scales granular assemblies are often viewed from the perspective of continuum theory where they show complex behaviour such as elastic and plastic anisotropy related to the load and deformation history. This complex behaviour is inextricably linked to the micromechanics of load sharing and force transmission at the particle level. At these scales, bulk stress is not shared homogeneously between particles, but rather by a network of `force chains' that form a skeleton supporting the vast majority of the applied load. The formation and failure of these structures govern much of the bulk behaviour of these materials. Neutron diffraction techniques are now providing a window into the mechanics of granular materials at both bulk and particle scales. Through a combination of tomographic neutron imaging and diffraction based strain measurement it is now possible to directly examine the stress within individual particles in granular assemblies. Results of these experiments in two and three dimensions are presented and the outlook for this approach to studying the mechanics of granular materials is discussed.

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19

Shukla, A., C. Y. Zhu i Y. Xu. "Dynamic Stresses in Granular Assemblies with Microstructural Defects". Journal of Engineering Mechanics 118, nr 1 (styczeń 1992): 190–201. http://dx.doi.org/10.1061/(asce)0733-9399(1992)118:1(190).

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Bagi, Katalin. "Analysis of microstructural strain tensors for granular assemblies". International Journal of Solids and Structures 43, nr 10 (maj 2006): 3166–84. http://dx.doi.org/10.1016/j.ijsolstr.2005.07.016.

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Nicodemi, Mario. "Force Correlations and Arch Formation in Granular Assemblies". Physical Review Letters 80, nr 6 (9.02.1998): 1340–43. http://dx.doi.org/10.1103/physrevlett.80.1340.

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Younes, N., A. Wautier, R. Wan, O. Millet, F. Nicot i R. Bouchard. "DEM-LBM coupling for partially saturated granular assemblies". Computers and Geotechnics 162 (październik 2023): 105677. http://dx.doi.org/10.1016/j.compgeo.2023.105677.

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Cárdenas-Barrantes, Manuel, David Cantor, Jonathan Barés, Mathieu Renouf i Emilien Azéma. "Three-dimensional compaction of soft granular packings". Soft Matter 18, nr 2 (2022): 312–21. http://dx.doi.org/10.1039/d1sm01241j.

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Bathurst, R. J., i L. Rothenburg. "Micromechanical Aspects of Isotropic Granular Assemblies With Linear Contact Interactions". Journal of Applied Mechanics 55, nr 1 (1.03.1988): 17–23. http://dx.doi.org/10.1115/1.3173626.

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The paper presents a micromechanical analysis of plane granular assemblies of discs with a range of diameters, and interacting according to linear contact force-interparticle compliance relationships. Contacts are assumed to be fixed and indestructible. Macroscopically, the system is described in terms of a two-dimensional analogue of generalized Hooke’s law. Explicit expressions for elastic constants in terms of microstructure are derived for dense isotropic assemblies. It is shown that Poisson’s ratio for dense systems depends on the ratio of tangential to normal contact stiffnesses. The derived expression for Poisson’s ratio is verified by numerically simulating plane assemblies comprising 1000 particles. The effect of density on Poisson’s ratio is investigated using numerical simulations. The theory of dense plane systems is extended to dense three-dimensional systems comprising spheres. Finally, it is shown that Poisson’s result ν=1/4 is recovered for spherical particles with central interactions.

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Zhou, Bo, Ji Wei Li i Peng Shuai. "Effect of Grain Orientation Distribution on Anisotropy of Idealized Granular Materials". Applied Mechanics and Materials 174-177 (maj 2012): 24–29. http://dx.doi.org/10.4028/www.scientific.net/amm.174-177.24.

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Abstract. The regular grain orientation of granular materials is a common phenomenon in nature. Based on the research of grain shape effect on mechanical property of granular materials, two kinds of idealized shape grain (kind of long rod and square) assemblies with different grain orientation were studied by simulated biaxial compression test using Discrete Element Method. The significant orientation which can be computed as the mean value of all grain orientation is introduced to represent the orientation regularity of granular materials. In order to study the anisotropy, the mobilized friction angle and volumetric strain of assemblies with different significant orientation were obtained under both vertical and horizontal loading. The results show that the regular orientation of grains influences the movement such as motion and rotation obviously; with the increasing of significant orientation, peak mobilized friction angle of long rod grain assembly gradually increases under horizontal loading, and decreasing under vertical loading.

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Rothenburg, L., i R. J. Bathurst. "Micromechanical features of granular assemblies with planar elliptical particles". Géotechnique 42, nr 1 (marzec 1992): 79–95. http://dx.doi.org/10.1680/geot.1992.42.1.79.

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Tordesillas, Antoinette, Maya Muthuswamy i Stuart D. Walsh. "Mesoscale Measures of Nonaffine Deformation in Dense Granular Assemblies". Journal of Engineering Mechanics 134, nr 12 (grudzień 2008): 1095–113. http://dx.doi.org/10.1061/(asce)0733-9399(2008)134:12(1095).

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Tejada, Ignacio G., Luc Sibille, Bruno Chareyre, Chuheng Zhong i Didier Marot. "Multiscale modeling of transport of grains through granular assemblies". EPJ Web of Conferences 140 (2017): 15019. http://dx.doi.org/10.1051/epjconf/201714015019.

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Bagi, K. "Microstructural Stress Tensor of Granular Assemblies With Volume Forces". Journal of Applied Mechanics 66, nr 4 (1.12.1999): 934–36. http://dx.doi.org/10.1115/1.2791800.

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This paper focuses on the discrete expression of stress tensors of assemblies containing discrete particles with volumetric loads acting on them in addition to boundary forces. Instead of the concept of continuum point, a domain containing a finite number of grains is considered. This domain is replaced by a suitably chosen equivalent continuum whose average stress is expressed—assuming that the grains are in equilibrium—in terms of contact forces and properly defined branch vectors. Symmetry of the stress tensor is also analyzed.

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D'Addetta, G. A., E. Ramm, S. Diebels i W. Ehlers. "A particle center based homogenization strategy for granular assemblies". Engineering Computations 21, nr 2/3/4 (marzec 2004): 360–83. http://dx.doi.org/10.1108/02644400410519839.

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Zhao, Haiyang, Xizhong An, Yongli Wu i Xiaohong Yang. "Microscopic analyses of stress profile within confined granular assemblies". AIP Advances 8, nr 7 (lipiec 2018): 075124. http://dx.doi.org/10.1063/1.5041976.

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Suiker, Akke S. J., i René de Borst. "Enhanced continua and discrete lattices for modelling granular assemblies". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, nr 1836 (10.10.2005): 2543–80. http://dx.doi.org/10.1098/rsta.2005.1586.

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This article discusses the derivation of continuum models that can be used for modelling the inhomogeneous mechanical behaviour of granular assemblies. These so-called kinematically enhanced models are of the strain-gradient type and of the strain-gradient micro-polar type, and are derived by means of homogenizing the micro-structural interactions between discrete particles. By analysis of the body wave dispersion curves, the enhanced continuum models are compared to corresponding discrete lattice models. Accordingly, it can be examined up to which deformation level the continuum models are able to accurately describe the discrete particle behaviour. Further, the boundary conditions for the enhanced continuum models are formulated, and their stability is considered. It is demonstrated how to use the body wave dispersion relations for the assessment of stability.

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Santra, Sitangshu Bikas, Stefan Schwarzer i Hans Herrmann. "Fluid-induced particle-size segregation in sheared granular assemblies". Physical Review E 54, nr 5 (1.11.1996): 5066–72. http://dx.doi.org/10.1103/physreve.54.5066.

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Emeriault, Fabrice, i Ching S. Chang. "Anisotropic Elastic Moduli of Granular Assemblies from Micromechanical Approach". Journal of Engineering Mechanics 123, nr 12 (grudzień 1997): 1289–93. http://dx.doi.org/10.1061/(asce)0733-9399(1997)123:12(1289).

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Nicot, François, i Félix Darve. "Micro-mechanical investigation of material instability in granular assemblies". International Journal of Solids and Structures 43, nr 11-12 (czerwiec 2006): 3569–95. http://dx.doi.org/10.1016/j.ijsolstr.2005.07.008.

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Misra, Anil, i Payam Poorsolhjouy. "Micro-macro scale instability in 2D regular granular assemblies". Continuum Mechanics and Thermodynamics 27, nr 1-2 (28.12.2013): 63–82. http://dx.doi.org/10.1007/s00161-013-0330-9.

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Sibille, L., F. Nicot, F. V. Donzé i F. Darve. "Material instability in granular assemblies from fundamentally different models". International Journal for Numerical and Analytical Methods in Geomechanics 31, nr 3 (2007): 457–81. http://dx.doi.org/10.1002/nag.591.

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Lammali, Walid, Jean-Noël Roux i Anh-Minh Tang. "Quasistatic response of loose cohesive granular materials". EPJ Web of Conferences 249 (2021): 14021. http://dx.doi.org/10.1051/epjconf/202124914021.

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DEM-simulated model cohesive assemblies of spherical grains of diameter d, with contact tensile strength F0, once prepared in loose states, are quasistatically subjected to growing isotropic pressure P, and then to triaxial compression, maintaining lateral stresses σ2 = σ3 = P while increasing axial stress σ1 = P + q and strain є1. Reduced pressure P* = d2P/F0 varies from 0.1 (cohesion dominated case, for which systems typically equilibrate with solid fraction Ф ≃ 0.35), to large values for which the cohesionless behavior is retrieved. In triaxial compression, while the moderate strain response (є1 ~ 0.1) is influenced by initial coordination numbers and mesoscale heterogeneities, the approach to the critical state, as both q (deviator) and Ф steadily increase, gets slower for smaller P*. Critical ratio q/P strongly increases for decreasing P*, as roughly predicted in an “effective stress” scheme. Anomalously small elastic moduli are observed in the gel-like structures. While extensive geometric rearrangements take place, no shear banding is observed. Loose cohesive granular assemblies are thus capable of large quasistatic stable plastic strains and ductile rupture.

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Galindo-Torres, Sergio Andres, Dorival Pedroso, David Williams i Hans Mühlhaus. "An Analysis of the Strength of Anisotropic Granular Assemblies via Discrete Methods". Applied Mechanics and Materials 553 (maj 2014): 525–30. http://dx.doi.org/10.4028/www.scientific.net/amm.553.525.

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This paper presents a study on the macroscopic strength characteristics of granular assemblies with three-dimensional complex-shaped particles. Different assemblies are considered, with both isotropic and anisotropic particle geometries. The study is conducted using the Discrete Element Method (DEM), with so-called sphero-polyhedral particles, and simulations of mechanical true triaxial tests for a range of Lode angles and confining pressures. The observed mathematical failure envelopes are investigated in the Haigh-Westergaard stress space, as well as on the deviatoric-mean pressure plane. It is verified that the DEM with non-spherical particles produces results that are qualitatively similar to experimental data and previous numerical results obtained with spherical elements. The simulations reproduce quite well the shear strength of assemblies of granular media, such as higher strength during compression than during extension. In contrast, by introducing anisotropy at the particle level, the shear strength parameters are greatly affected, and an isotropic failure criterion is no longer valid. It is observed that the strength of the anisotropic assembly depends on the direction of loading, as observed for real soils.

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Adilet, Sugirbay, Jian Zhao, Nukeshev Sayakhat, Jun Chen, Zagainov Nikolay, Lingxin Bu, Zhanar Sugirbayeva, Guangrui Hu, Muratkhan Marat i Zhiwei Wang. "Calibration Strategy to Determine the Interaction Properties of Fertilizer Particles Using Two Laboratory Tests and DEM". Agriculture 11, nr 7 (26.06.2021): 592. http://dx.doi.org/10.3390/agriculture11070592.

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Investigating the interactions of granular fertilizers with various types of equipment is an essential part of agricultural research. A numerical technique simulating the mechanical behavior of granular assemblies has the advantage of data trackings, such as the trajectories, velocities, and transient forces of the particles at any stage of the test. The interaction parameters were calibrated to simulate responses of granular fertilizers in EDEM, a discrete element method (DEM) software. Without a proper calibration of the interaction parameters between the granular fertilizers and various materials, the simulations may not represent the real behavior of the granular fertilizers. Therefore, in this study, a strategy is presented to identify and select a set of DEM input parameters of granular fertilizers using the central composite design (CCD) to establish the nonlinear relationship between the dynamic macroscopic granular fertilizer properties and the DEM parameters. The determined interaction properties can be used to simulate granular fertilizers in EDEM.

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Hentschel, H. George E., Prabhat K. Jaiswal, Chandana Mondal, Itamar Procaccia i Jacques Zylberg. "The sandpile revisited: computer assisted determination of constitutive relations and the breaking of scaling". Soft Matter 13, nr 29 (2017): 5008–20. http://dx.doi.org/10.1039/c7sm01060e.

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We revisit the problem of the stress distribution in a frictional sandpile with both normal and tangential (frictional) inter-granular forces, under gravity, equipped with a new numerical method of generating such assemblies.

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Nezamabadi, Saeid, Farhang Radjai, Serge Mora, Jean-Yves Delenne i Mojtaba Ghadiri. "Rheology of soft granular materials: uniaxial compression". EPJ Web of Conferences 249 (2021): 05008. http://dx.doi.org/10.1051/epjconf/202124905008.

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Soft granular materials are assemblies of highly deformable grains interacting via surface forces. The large grain deformations of these materials differ them from hard granular systems, in which, their behaviors are essentially governed by grain rearrangements. In this paper, we study the uniaxial compression of soft granular materials using a numerical approach based on the Material Point Method allowing for large grain deformations, coupled with the Contact Dynamics method for the treatment of unilateral frictional contacts between grains. Considering the neo-Hookean and elasto-plastic grains, the compaction of 2D soft granular packings is analyzed. We focus essentially on the evolution of the packing vertical stress as a function of the packing fraction and the predictive models are proposed.

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Kruyt, N. P., i L. Rothenburg. "Micromechanical Definition of the Strain Tensor for Granular Materials". Journal of Applied Mechanics 63, nr 3 (1.09.1996): 706–11. http://dx.doi.org/10.1115/1.2823353.

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In order to develop constitutive relations for granular materials from the micromechanical viewpoint, general expressions relating macroscopic stress and strain to contact forces and particle displacements are required. Such an expression for the stress tensor under quasi-static conditions is well established in the literature, but a corresponding expression for the strain tensor has been lacking so far. This paper presents such an expression for two-dimensional assemblies. This expression is verified by computer simulations of biaxial and shear tests. As a demonstration of the use of the developed expression, a study is made of the elastic moduli of two-dimensional, isotropic assemblies of bonded, nonrotating disks. Theoretical expressions are given for the elastic moduli in terms of micromechanical parameters, such as coordination number and contact stiffnesses. Comparison with the results from computer simulations show that the agreement is fairly good over a wide range of coordination numbers and contact stiffness ratios.

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He, Pengfei, Yuching Wu i Huiliang Chen. "The Compactions of Elasto-Plastic and Visco-Plastic Granular Assemblies". Open Journal of Civil Engineering 03, nr 01 (2013): 29–44. http://dx.doi.org/10.4236/ojce.2013.31005.

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Kuhn, Matthew R., i Katalin Bagi. "Specimen Size Effect in Discrete Element Simulations of Granular Assemblies". Journal of Engineering Mechanics 135, nr 6 (czerwiec 2009): 485–92. http://dx.doi.org/10.1061/(asce)0733-9399(2009)135:6(485).

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BATHURST, RICHARD J., i LEO ROTHENBURG. "INVESTIGATION OF MICROMECHANICAL FEATURES OF IDEALIZED GRANULAR ASSEMBLIES USING DEM". Engineering Computations 9, nr 2 (luty 1992): 199–210. http://dx.doi.org/10.1108/eb023859.

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Nicot, François, Luc Sibille, Frédéric Donze i Félix Darve. "From microscopic to macroscopic second-order work in granular assemblies". Mechanics of Materials 39, nr 7 (lipiec 2007): 664–84. http://dx.doi.org/10.1016/j.mechmat.2006.10.003.

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Chen, J., S. Supprasert, H. O-tani, K. Fujita, L. Wijerathne i M. Hori. "On elastic waves in granular assemblies: From a continuumnization viewpoint". Mechanics of Materials 109 (czerwiec 2017): 101–13. http://dx.doi.org/10.1016/j.mechmat.2017.04.002.

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Satake, M. "Tensorial form definitions of discrete-mechanical quantities for granular assemblies". International Journal of Solids and Structures 41, nr 21 (październik 2004): 5775–91. http://dx.doi.org/10.1016/j.ijsolstr.2004.05.046.

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Goddard, J. D. "On entropy estimates of contact forces in static granular assemblies". International Journal of Solids and Structures 41, nr 21 (październik 2004): 5851–61. http://dx.doi.org/10.1016/j.ijsolstr.2004.05.049.

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