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Journal articles on the topic 'Modelling granular materials'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

Einav, Itai. "Breakage mechanics—Part II: Modelling granular materials." Journal of the Mechanics and Physics of Solids 55, no. 6 (June 2007): 1298–320. http://dx.doi.org/10.1016/j.jmps.2006.11.004.

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2

Lade, Poul V., and Richard B. Nelson. "Modelling the elastic behaviour of granular materials." International Journal for Numerical and Analytical methods in Geomechanics 11, no. 5 (September 1987): 521–42. http://dx.doi.org/10.1002/nag.1610110507.

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3

Alonso-Marroquin, Fernando, Itai Einav, and Antoinette Tordesillas. "Developments in micromechanical modelling of granular materials." Granular Matter 13, no. 3 (May 3, 2011): 183–85. http://dx.doi.org/10.1007/s10035-011-0265-4.

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4

Harris, David. "Modelling Dense Granular Flows." Materials Science Forum 623 (May 2009): 49–59. http://dx.doi.org/10.4028/www.scientific.net/msf.623.49.

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In this paper we discuss properties of dense granular °ows and elaborate on some properties of a model which generalises the classical plastic potential model using elements of the double shearing model. It is shown how the model is embedded into a Cosserat continuum model. The proposed model recti¯es the ill-posedness of both the non-associated °ow rule and the double shearing model and may be used for both granular materials and also for metals which possess a micro-structure which is capable of rotation.

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5

Calvetti, Francesco. "Discrete modelling of granular materials and geotechnical problems." Revue européenne de génie civil 12, no. 7-8 (October 1, 2008): 951–65. http://dx.doi.org/10.3166/ejece.12.951-965.

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6

Lekarp, F., and A. Dawson. "Modelling permanent deformation behaviour of unbound granular materials." Construction and Building Materials 12, no. 1 (April 1998): 9–18. http://dx.doi.org/10.1016/s0950-0618(97)00078-0.

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7

Mizuseki, Hiroshi, Keiko Kikuchi, Kazumi Tanaka, Masahito Ishihara, and Yoshiyuki Kawazoe. "Modelling of Magnetic Multivalued Recording in Granular Materials." Japanese Journal of Applied Physics 37, Part 1, No. 4B (April 30, 1998): 2155–58. http://dx.doi.org/10.1143/jjap.37.2155.

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8

Xiao, Hongyi, Paul B. Umbanhowar, Julio M. Ottino, and Richard M. Lueptow. "Modelling density segregation in flowing bidisperse granular materials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (July 2016): 20150856. http://dx.doi.org/10.1098/rspa.2015.0856.

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Preventing segregation in flowing granular mixtures is an ongoing challenge for industrial processes that involve the handling of bulk solids. A recent continuum-based modelling approach accurately predicts spatial concentration fields in a variety of flow geometries for mixtures varying in particle size. This approach captures the interplay between advection, diffusion and segregation using kinematic information obtained from experiments and/or discrete element method (DEM) simulations combined with an empirically determined relation for the segregation velocity. Here, we extend the model to include density-driven segregation, thereby validating the approach for the two important cases of practical interest. DEM simulations of density bidisperse flows of mono-sized particles in a quasi-two-dimensional-bounded heap were performed to determine the dependence of the density-driven segregation velocity on local shear rate and particle concentration. The model yields theoretical predictions of segregation patterns that quantitatively match the DEM simulations over a range of density ratios and flow rates. Matching experiments reproduce the segregation patterns and quantitative segregation profiles obtained in both the simulations and the model, thereby demonstrating that the modelling approach captures the essential physics of density-driven segregation in granular heap flow.

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9

Calvetti, Francesco. "Discrete modelling of granular materials and geotechnical problems." European Journal of Environmental and Civil Engineering 12, no. 7-8 (August 2008): 951–65. http://dx.doi.org/10.1080/19648189.2008.9693055.

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10

Yohannes, Bereket, Danielle Tan, Lev Khazanovich, and K. M. Hill. "Mechanistic modelling of tests of unbound granular materials." International Journal of Pavement Engineering 15, no. 7 (April 9, 2013): 584–98. http://dx.doi.org/10.1080/10298436.2013.775442.

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11

Amoddeo, Antonino, and Pasquale Giovine. "Micromechanical modelling of granular materials and FEM simulations." Meccanica 54, no. 4-5 (December 17, 2018): 609–30. http://dx.doi.org/10.1007/s11012-018-00927-8.

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12

Weinhart, T., A. R. Thornton, and I. Einav. "Editorial: Modelling and computational challenges in granular materials." Computational Particle Mechanics 3, no. 3 (November 25, 2015): 291–92. http://dx.doi.org/10.1007/s40571-015-0091-2.

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13

Ghadimi, Behzad, Hamid Nikraz, Colin Leek, and Ainalem Nega. "A Comparison between Effects of Linear and Non-Linear Mechanistic Behaviour of Materials on the Layered Flexible Pavement Response." Advanced Materials Research 723 (August 2013): 12–21. http://dx.doi.org/10.4028/www.scientific.net/amr.723.12.

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Modelling granular pavement materials has a significant role in the pavement design procedure. Modelling can be through an experimental or numerical approach to predict the granular behaviour during cyclic loading. The current design process in Australia is based on linear elastic analysis of layers. The analysis is performed through a well-known program CIRCLY which is applied to model bound pavement material behaviour. The KENLAYER is one of the common pavement software models used for pavement design in the United States which performs non-linear analysis for granular materials. Alternatively, a general Finite Element program such as ABAQUS can be used to model the complicated behaviour of multilayer granular materials. This study is to compare results of numerical modelling with these three programs on two sample pavement models.

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14

Petrov, Maxim S., Vladimir V. Gaidukov, Radii M. Kadushnikov, Iliya V. Antonov, and Eugenii Yu Nurkanov. "Numerical Method for Modelling the Microstructure of Granular Materials." Powder Metallurgy and Metal Ceramics 43, no. 7/8 (July 2004): 330–35. http://dx.doi.org/10.1023/b:pmmc.0000048126.87171.f9.

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15

Sitharam, Thallak G. "Discrete element modelling of cyclic behaviour of granular materials." Geotechnical and Geological Engineering 21, no. 4 (2003): 297–329. http://dx.doi.org/10.1023/b:gege.0000006036.00597.0b.

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16

Gröger, Torsten, Ugur Tüzün, and David M. Heyes. "Modelling and measuring of cohesion in wet granular materials." Powder Technology 133, no. 1-3 (July 2003): 203–15. http://dx.doi.org/10.1016/s0032-5910(03)00093-7.

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17

Al Hattamleh, O., B. Muhunthan, and H. M. Zbib. "Gradient plasticity modelling of strain localization in granular materials." International Journal for Numerical and Analytical Methods in Geomechanics 28, no. 6 (April 19, 2004): 465–81. http://dx.doi.org/10.1002/nag.345.

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18

Avci, O., and W. Ehlers. "Granular materials: Parameter identification and modelling of localisation problems." PAMM 7, no. 1 (December 2007): 4060023–24. http://dx.doi.org/10.1002/pamm.200700356.

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19

Sosnowski, Marcin. "Computational domain discretization in numerical analysis of flow within granular materials." EPJ Web of Conferences 180 (2018): 02095. http://dx.doi.org/10.1051/epjconf/201818002095.

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The discretization of computational domain is a crucial step in Computational Fluid Dynamics (CFD) because it influences not only the numerical stability of the analysed model but also the agreement of obtained results and real data. Modelling flow in packed beds of granular materials is a very challenging task in terms of discretization due to the existence of narrow spaces between spherical granules contacting tangentially in a single point. Standard approach to this issue results in a low quality mesh and unreliable results in consequence. Therefore the common method is to reduce the diameter of the modelled granules in order to eliminate the single-point contact between the individual granules. The drawback of such method is the adulteration of flow and contact heat resistance among others. Therefore an innovative method is proposed in the paper: single-point contact is extended to a cylinder-shaped volume contact. Such approach eliminates the low quality mesh elements and simultaneously introduces only slight distortion to the flow as well as contact heat transfer. The performed analysis of numerous test cases prove the great potential of the proposed method of meshing the packed beds of granular materials.

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20

Ghadimi, Behzad, and Umair Hasan. "Review of Finite Element Simulation of Granular Materials." Applied Mechanics and Materials 709 (December 2014): 219–26. http://dx.doi.org/10.4028/www.scientific.net/amm.709.219.

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The behaviour of granular materials especially under dynamic loading has been under investigation for years. In recent years, the advancing computer technology makes it possible to model complicate behaviour under different loadings. In this review paper, major advances and researches in the field of providing conceptual model for behaviour of granular materials have been reviewed. The reviewers have tried to categorise the researches in term of their approach to modelling the mechanical behaviour of granular materials and then identify the gaps to provide ground for the future researches.

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21

Nataatmadja, A., and A. K. Parkin. "Characterization of granular materials for pavements." Canadian Geotechnical Journal 26, no. 4 (November 1, 1989): 725–30. http://dx.doi.org/10.1139/t89-083.

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For design and analysis of flexible pavements, a simple elastic model that does not require cumbersome calculation and also can rank materials according to their performance is clearly desirable. Early studies indicated that the resilient modulus of a granular material can be taken to be a function of the first invariant of stress, θ, although there is evidence that it is also dependent on the repeated deviator stress, qr. The limitations of some earlier models are discussed herein and a simple model for granular materials is proposed. The model is empirical in nature and based on repeated load triaxial testing with constant confining pressure. The application of this model in situations where the confining pressure is pulsed in phase with the deviator stress is also discussed. Key words: repeated load, triaxial test, resilient modulus, granular materials, modelling, pavement.

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22

Orlik-Kożdoń, Bożena, and Artur Nowoświat. "Modelling and testing of a granular insulating material." Journal of Building Physics 42, no. 1 (June 30, 2017): 6–15. http://dx.doi.org/10.1177/1744259117715715.

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In the following article, the Authors present the results of initial researches into a building component needed for thermal insulation. The building component is a elastic insulation plate made from recycling materials. The solution is protected by industry patter Elastyczna pyta izolacyjna No 23 621 for Silesian University of Technology Gliwice. The paper presents the determination method of effective thermal conductivity for granular materials. It is based on the geometrical model for the determination of granular medium structure, which is based on the theory of the highest-density arrangement of equal-sized spheres. The elaborated by the Authors modeling results, obtained on the basis of an innovative description (definition) of granular medium, were addressed to the commonly applied two-component medium. To verify the correctness of the calculation model proposed by the Authors, the results were subjected to validation, basing on the thermal conductivity of elastic plates in a hot plate apparatus.

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23

Niu, Qifei, and Chi Zhang. "Pore-scale modelling of complex conductivity of saturated granular materials." Near Surface Geophysics 15, no. 6 (October 1, 2017): 593–602. http://dx.doi.org/10.3997/1873-0604.2017055.

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24

Calvetti, F. "Limitations and perspectives of the micromechanical modelling of granular materials." Mathematical and Computer Modelling 37, no. 5-6 (March 2003): 485–95. http://dx.doi.org/10.1016/s0895-7177(03)00041-4.

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25

Vescovi, Dalila, Irene Redaelli, and Claudio di Prisco. "Modelling phase transition in granular materials: From discontinuum to continuum." International Journal of Solids and Structures 202 (October 2020): 495–510. http://dx.doi.org/10.1016/j.ijsolstr.2020.06.019.

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26

Woeller, David J. "Unbound granular materials: laboratory testing, in situ testing, and modelling." Canadian Geotechnical Journal 37, no. 6 (2000): 1399. http://dx.doi.org/10.1139/cgj-37-6-1399.

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27

NAON, B., C. SAIX, G. BERTHOMIEU, and J. C. BENET. "Modelling Convective Drying of Granular Materials : Application to Natural Rubber." Drying Technology 13, no. 3 (January 1995): 571–83. http://dx.doi.org/10.1080/07373939508916975.

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28

Xiao Ming Zheng and James M. Hill. "Boundary effects for Couette flow of granular materials: Dynamical modelling." Applied Mathematical Modelling 20, no. 1 (January 1996): 82–92. http://dx.doi.org/10.1016/0307-904x(95)00105-s.

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29

Karrech, A., A. Seibi, and D. Duhamel. "Finite element modelling of rate-dependent ratcheting in granular materials." Computers and Geotechnics 38, no. 2 (March 2011): 105–12. http://dx.doi.org/10.1016/j.compgeo.2010.08.012.

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30

Buonsanti, Michele, Giovanni Leonardi, and Francesco Scoppelliti. "Modelling Micro-Damage in Granular Solids." Key Engineering Materials 525-526 (November 2012): 497–500. http://dx.doi.org/10.4028/www.scientific.net/kem.525-526.497.

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The prediction of the spacing and opening of cracks in asphalt or concrete pavements, and particularly in airports (runway, taxiway and apron) is important for the durability assessment. A basic problem is the spacing of parallel planar cracks from a half space surface, approached and solved by numerous authors by means of macro-scale computational models. The calculated values of crack spacing are in relatively good agreement with the values reported in observations on asphalt concrete pavements. The constituents of granular solids are, fundamentally, made of grain in contact and, these materials are highly discontinuous and non-homogeneous with two or three phases (solid, voids with air or water), and finally binding among solid parts. The aim of this paper is to suggest a micromechanical approach in granular material solids, focusing the attention on a simple RVE (representative volume element) based on two rigid particles linked through an adhesive material (bitumen). Our final aim is to propose a micro-damageability parameter (interface loss) supposing the adhesion decreasing under the action of prescribed tangential and normal relative displacement. The reduction is attributed by progressive damage and comes with energy dissipation and moreover we assume unilateral contact conditions for normal displacement and Coulomb friction for the tangential displacement.

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31

Matuszek, Dominika. "Modelling selected parameters of granular elements in the mixing process." International Agrophysics 29, no. 1 (January 1, 2015): 75–81. http://dx.doi.org/10.1515/intag-2015-0002.

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Abstract This paper presents the effects of mixing non-homogeneous bicomponent granular structures by the flow method with the use of an inverted cone insert as a supporting element. The analysis of homogeneity of mixtures after 10 consecutive flows was carried out based on computer image analysis. Based on these tests, the use of a nonlinear regression for the modelling of two selected parameters of the process was proposed. Spatial dependence was described by the relation between the variance of the tracer distribution (dependent variable) and density ratio of the mixed components, and the diameter of the cone insert used (independent variables). The mathematical description was made with the use of a ‘nonlinear regression’ module. The results obtained in these tests proved that the use of supporting insert improves the degree of mixability of granular materials. The twodimensional model in the form of a quadratic function may be a formula for describing the influence of selected parameters on the homogeneity of a granulate mixture before the beginning of the mixing process.

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32

Tamura, S. "Granular modelling simulator for powder compaction processes." Metal Powder Report 47, no. 10 (October 1992): 53. http://dx.doi.org/10.1016/0026-0657(92)91928-d.

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33

Darde, Benjamin, Anh Minh Tang, Jean-Michel Pereira, Patrick Dangla, Jean-Noël Roux, Jean Talandier, and Minh Ngoc Vu. "Modelling the hydromechanical behaviour of expansive granular mixtures upon hydration." E3S Web of Conferences 195 (2020): 02006. http://dx.doi.org/10.1051/e3sconf/202019502006.

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Bentonite pellet-powder mixtures are candidate sealing materials in radioactive waste disposal concepts. The mixture is installed in galleries in dry state as a granular material. The material is progressively hydrated by the pore water of the host rock and becomes homogeneous. Before homogenisation, the granular structure controls the material behaviour. In the present work, a modelling approach able to address particular features of pellet-powder mixtures is introduced. Two domains are considered: i) granular, and ii) homogeneous. The material behaviour before homogenisation is studied through Discrete Element Method (DEM) simulations. Constitutive laws for the granular state are proposed from DEM results. The behaviour of the homogenised material is described by a modified Barcelona Basic Model (BBM). Transition from granular to homogeneous states depends on suction and relative volume fractions of pellets and powder. Swelling pressure tests performed in the laboratory are satisfactorily simulated using this approach.

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34

Van Aswegen, Elsabe, and Wynand J. Vdm Steyn. "Statistical Modelling of the Resilient Behaviour of Unbound Granular Material." Slovak Journal of Civil Engineering 21, no. 1 (March 1, 2013): 9–16. http://dx.doi.org/10.2478/sjce-2013-0002.

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Abstract The resilient behaviour of an unsaturated, unbound granular material is a primary input used in the mechanistic analysis of pavements incorporating such layers. Various models exist for the determination of the resilient behaviour, mainly based on the output of tri-axial laboratory testing. This paper describes an investigation where basic engineering properties such as grading, laboratory compaction characteristics and optimum moisture content are incorporated into the resilient behaviour model to quantify the effect of basic material properties on the resilient response of unsaturated, unbound granular materials. Such a resilient behaviour model will enable practitioners to estimate the behaviour of specific material, which might enable the use of available quality material that was discarded in the past. Data from tri-axial laboratory tests on materials originating from the Long Term Pavement Performance test sections are combined with basic engineering parameters of typical unbound granular material through a statistical modelling process to develop a model for predicting resilient behaviour, which can be used as a practical predictor of the expected behaviour during a Level 2 and/or Level 3 Mechanistic Empirical Pavement Design analysis. The work illustrates the process and the potential to develop a general resilient behaviour model for unbound granular materials incorporating saturation effects.

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35

Zhu, H. P., Y. H. Wu, and A. B. Yu. "Discrete and continuum modelling of granular flow." China Particuology 3, no. 6 (December 2005): 354–63. http://dx.doi.org/10.1016/s1672-2515(07)60215-2.

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36

Grickus, Armands, and Sharif Guseynov. "ON A MATHEMATICAL MODEL DESCRIBING OPTIMAL PROCESSING MECHANISM OF DISPERSED GRANULAR MATERIALS IN GRAVITATIONAL FLOW WITH HORIZONTAL OR INCLINED VIBRATING SIEVE CLASSIFYING SCREENS." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 3 (June 15, 2017): 69. http://dx.doi.org/10.17770/etr2017vol3.2547.

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The investigation of motion and gravitational processing of disperse granular materials is very important for solution of a wide spectrum of technological processes, including the chemical technology of treatment (with or without the decoration-compression procedure) of granular mineral fertilizers and their drying and sorting/separation by means of vibrating sieve classifying screens, in particular. In this work, we have used the apparatus of the theory of continuous media for the mathematical modelling of dynamics of disperse granular materials, and by this we assume that a property of these materials is the distribution of a solid granular component inside of them. The elaborated mathematical model is based on the volume conservation law for granular components, on the momentum conservation law, as well as on the equations for stress tensor in the granular mineral fertilizers and equations for description of the Coulomb granular mineral fertilizers.

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37

Mennicke, R. T., D. Bozec, V. G. Kravets, M. Vopsaroiu, J. A. D. Matthew, and S. M. Thompson. "Modelling the magnetorefractive effect in giant magnetoresistive granular and layered materials." Journal of Magnetism and Magnetic Materials 303, no. 1 (August 2006): 92–110. http://dx.doi.org/10.1016/j.jmmm.2005.10.233.

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38

Rahman, Mohammad Shafiqur, and Sigurdur Erlingsson. "Modelling the Moisture Dependent Permanent Deformation Behavior of Unbound Granular Materials." Procedia Engineering 143 (2016): 921–28. http://dx.doi.org/10.1016/j.proeng.2016.06.072.

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39

Josserand, C., P. Y. Lagrée, and D. Lhuillier. "Stationary shear flows of dense granular materials: a tentative continuum modelling." European Physical Journal E 14, no. 2 (June 2004): 127–35. http://dx.doi.org/10.1140/epje/i2003-10141-4.

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40

Alsaleh, Mustafa I., George Z. Voyiadjis, and Khalid A. Alshibli. "Modelling strain localization in granular materials using micropolar theory: mathematical formulations." International Journal for Numerical and Analytical Methods in Geomechanics 30, no. 15 (2006): 1501–24. http://dx.doi.org/10.1002/nag.533.

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41

Masad, E., B. Muhunthan, and C. Crowe. "Numerical modelling of fluid flow in microscopic images of granular materials." International Journal for Numerical and Analytical Methods in Geomechanics 26, no. 1 (2001): 53–74. http://dx.doi.org/10.1002/nag.192.

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42

Kirchner, Nina P. "Thermodynamically consistent modelling of abrasive granular materials. I Non–equilibrium theory." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458, no. 2025 (September 8, 2002): 2153–76. http://dx.doi.org/10.1098/rspa.2002.0963.

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43

He, Jun, Quansheng Liu, Zhijun Wu, and Xiangyu Xu. "Modelling transient heat conduction of granular materials by numerical manifold method." Engineering Analysis with Boundary Elements 86 (January 2018): 45–55. http://dx.doi.org/10.1016/j.enganabound.2017.10.011.

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44

Emeriault, F., and C. Claquin. "Micromechanical modelling of the anisotropic viscoelasticity of granular materials: statistical homogenization." Granular Matter 2, no. 4 (October 2000): 201–10. http://dx.doi.org/10.1007/pl00010914.

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45

Konrad, Jean-Marie, and Younes Salami. "Particle breakage in granular materials — a conceptual framework." Canadian Geotechnical Journal 55, no. 5 (May 2018): 710–19. http://dx.doi.org/10.1139/cgj-2017-0224.

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A simple, yet complete framework is introduced with the aim of modelling grain breakage in soils and crushable granular materials. The evolution of grain breakage is measured using a specific parameter of the grain-size distribution. The evolution of this new breakage parameter is related to the applied mechanical work, which allows the predictions to be independent of the stress paths. The correlation function proposed is trilinear, and is capable of describing the initiation, development, and stabilization of breakage. The initial state, coupled with three additional parameters, is used to calibrate this function. The three parameters are related to a grain specific quantity representing the strength of the particles that form the granular medium. The theory of fractal fragmentation is adopted, and the final state is considered to be unique and described by a single parameter: the fractal dimension. When tested against experimental results, this model was able to correctly predict the crushable behavior of a sand.

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46

Millet, Olivier, Shuitao Gu, and Djimédo Kondo. "A 2D micromechanical modelling of anisotropy in granular media." Comptes Rendus Mécanique 335, no. 4 (April 2007): 231–37. http://dx.doi.org/10.1016/j.crme.2007.03.005.

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47

Hayakawa, Hisao, and Daniel C. Hong. "Dynamics of Granular Compaction." International Journal of Bifurcation and Chaos 07, no. 05 (May 1997): 1159–65. http://dx.doi.org/10.1142/s0218127497000960.

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We investigate the way the disordered granular materials organize themselves in a vibrating bed, the intensity of which is given by the dimensionless parameter Γ. Based on the recognition that an assembly of mono-disperse and cohesionless granular materials is a collection of spinless hard sphere Fermions, we first demonstrate that the time averaged steady state density profile for weak excitation with Γ ≈ 1 is given by the Fermi distribution. This is consistent with the observed experimental data and the results of Molecular dynamics. We then present a dynamic model to study the dynamics of granular compaction, namely the dynamic evolution of the initial state ultimately relaxing toward this steady state. Our preliminary investigation reveals that the relaxation is exponential, which is not inconsistent with the available experimental data for low Γ.

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48

Потапов, Игорь Иванович, and Ольга Владимировна Решетникова. "Usage of composite kernel in the SPH method for simulating the movement of granular materials." Вычислительные технологии, no. 1(26) (April 2, 2021): 50–61. http://dx.doi.org/10.25743/ict.2021.26.1.004.

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В работе для моделирования движения сыпучей среды используется метод сглаженных частиц. Для аппроксимации искомых функций предложено новое составное ядро малой связности. Основой для разработки ядра послужило требование к условию о сохранении плотности единичной SPH-частицы. Выполнение данного условия позволяет правильно моделировать поле плотности на границах расчетной области, а также в случаях структурных изменений каркаса гранулированных частиц сыпучей среды. Из анализа решения задачи гидростатики методом SPH получена оценка значения масштаба сглаживающей длины ядра для двумерного случая. Выполнен расчет процесса обрушения гранулированного “столба” и проведено сравнение полученных численных результатов моделирования с экспериментальными данными. The purpose of the study is to improve the practice of the SPH methodology which is applied for modelling of movement in the various media. The basis of the SPH-approximation of the function fields is formed by the forms of the smoothing kernel and its derivatives. Popular forms of smoothing kernels are characterized by the presence of significant fatal approximation errors when modelling granular media. Methodology. The state of granular medium is described by the classical motion and mass conservation equations. Each granule of the medium corresponds to a separate SPH particle. To approximate the density and pressure fields in the SPH particle, a new combination of the smoothing core and its first derivative forms is proposed. Results. The proposed new composite core fulfills the conditions of mass conservation and density recovery in the particle during SPH modeling. It is shown that the new composite core is characterized by a minimum error of pressure gradient approximation - about 2%. A new estimate for the velocity of propagation of an elastic wave in a medium, sufficient to obtain a correct numerical solution, is proposed. A comparative analysis of the obtained solutions with experimental data is made. Findings. The proposed composite shape of the smoothing kernel allows correct simulation of the motion of a granular medium by the SPH method. Its compactness (unit smoothing radius and unit smoothing length) makes it possible to correctly reconstruct the density field at the boundaries of the computational domain and in cases of structural changes in the framework of the granular medium. The numerical solution of the problem of the collapse of a column of granules obtained using the proposed composite core shows good agreement with experimental data.

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Zhu, Ning, Dennj De Meo, and Erkan Oterkus. "Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics." Materials 9, no. 12 (December 2, 2016): 977. http://dx.doi.org/10.3390/ma9120977.

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Sweijen, T., B. Chareyre, S. M. Hassanizadeh, and N. K. Karadimitriou. "Grain-scale modelling of swelling granular materials; application to super absorbent polymers." Powder Technology 318 (August 2017): 411–22. http://dx.doi.org/10.1016/j.powtec.2017.06.015.

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