Definitions
Granular mechanics is defined as the mechanics of materials with granular texture in which the role of grain interactions is paramount. The description of the mechanical behavior of these material systems begins from the conception of grain interactions. From this point of departure, either discrete or continuum descriptions can be elaborated. Discrete models of granular materials aim to describe their behavior by tracking grain trajectories in simulated grain assemblies according to formulated equations of motions. The behavior at the scale of the grain assembly (the so-called “macroscopic” behavior) may then be deduced through certain averaging procedures. The formulations of grain-interaction models and the discrete and continuum descriptions of granular materials, based upon the variational methods, are described in the two companion chapters.
Granular Solids
Granular solids...
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References
Cundall PA, Strack ODL (1979) Discrete numerical-model for granular assemblies. Geotechnique 29:47–65
dell’Isola F, Romano A (1987) On the derivation of thermomechanical balance-equations for continuous systems with a nonmaterial interface. Int J Eng Sci 25:1459–1468
Duffy J, Mindlin RD (1957) Stress-strain relations and vibrations of a granular medium. J Appl Mech 24:585–593
Hara G (1935) Theorie der akustischen Schwingungsausbreitung in gekornten Substanzen und experimentelle Untersuchungen an. Kohlepulver Elektr Nachr Tech 12:191–200
Hertz H (1881) On the contact of elastic solids. J Reine Angew Math 92:156–171
Holtzman R, Silin DB, Patzek TW (2010) Frictional granular mechanics: a variational approach. Int J Numer Methods Eng 81:1259–1280
Huang SP, Misra A (2013) Micro-macro-shear-displacement behavior of contacting rough solids. Tribol Lett 51:431–436
Kruggel-Emden H, Wirtz S, Scherer V (2009) Applicable contact force models for the discrete element method: the single particle perspective. J Press Vessel Technol 131:024001
Kuhn MR (2017) Granular geomechanics. Elsevier, London, UK
Li H, Lykotrafitis G (2012) Two-component coarse-grained molecular-dynamics model for the human erythrocyte membrane. Biophys J 102:75–84
Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435:1079
Matuttis H-G, Chen J (2014) Understanding the discrete element method: simulation of non-spherical particles for granular and multi-body systems. Wiley, Hoboken
Mindlin RD (1949) Compliance of elastic bodies in contact. J Appl Mech 16:259–268
Mindlin RD, Deresiewicz H (1953) Elastic spheres in contact under varying oblique forces. J Appl Mech Trans ASME 20:327–344
Misra A (1998) Particle kinematics in sheared rod assemblies. In: Physics of dry granular media. Springer, Dordrecht, Netherlands pp 261–266
Misra A, Jiang H (1997) Measured kinematic fields in the biaxial shear of granular materials. Comput Geotech 20:267–285. https://doi.org/10.1016/S0266-352x(97)00006-2
Misra A, Singh V, Darabi M (2017) Asphalt pavement rutting simulated using granular micromechanics based rate dependent damage-plasticity model. Int J Pavement Eng (accepted). https://doi.org/10.1080/10298436.2017.1380804
Placidi L (2015) A variational approach for a nonlinear 1-dimensional second gradient continuum damage model. Contin Mech Thermodyn 27:623–638. https://doi.org/10.1007/s00161-014-0338-9
Placidi L (2016) A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Contin Mech Thermodyn 28:119–137. https://doi.org/10.1007/s00161-014-0405-2
Radjaï F, Dubois F (2011) Discrete-element modeling of granular materials. Wiley-ISTE, London, UK
Sibille L, Hadda N, Nicot F, Tordesillas A, Darve F (2015) Granular plasticity, a contribution from discrete mechanics. J Mech Phys Solids 75:119–139
Tordesillas A, Zhang J, Behringer R (2009) Buckling force chains in dense granular assemblies: physical and numerical experiments. Geomech Geoeng Int J 4:3–16
Trollope D, Burman B (1980) Physical and numerical experiments with granular wedges. Geotechnique 30:137–157
Turco E (2018a) Discrete is it enough? The revival of Piola–Hencky keynotes to analyze three-dimensional Elastica. Contin Mech Thermodyn 30(5):1039–1057
Turco E (2018b) In-plane shear loading of granular membranes modeled as a Lagrangian assembly of rotating elastic particles. Mech Res Commun 92:61
Turco E, Rizzi NL (2016) Pantographic structures presenting statistically distributed defects: numerical investigations of the effects on deformation fields. Mech Res Commun 77:65–69
Turco E, Giorgio I, Misra A, dell’Isola F (2017) King post truss as a motif for internal structure of (meta) material with controlled elastic properties. Roy Soc Open Sci 4:171153
Zhang L, Nguyen NGH, Lambert S, Nicot F, Prunier F, Djeran-Maigre I (2017) The role of force chains in granular materials: from statics to dynamics. Eur J Environ Civ Eng 21:874–895
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The work is supported in part by the United States National Science Foundation grant CMMI-1727433
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Misra, A., Placidi, L., Turco, E. (2019). Variational Methods for Discrete Models of Granular Materials. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_172-1
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DOI: https://doi.org/10.1007/978-3-662-53605-6_172-1
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