Abstract
For a quasi-statically sheared granular system, the deformation of individual particles leads to reversible energy storage that sustains elastic stress. But, the system would subsequently relax because particles jiggle and slide. By employing the complete continuum mechanical theory, also known as Granular Solid Hydrodynamics (GSH), the elastic energy and its relaxation (denoted by granular temperature) are both calculated and explained. For a dense assembly, it is found that the elastic energy and energy dissipation rate reach peak values simultaneously, as it reaches peak strength. To observe the mesoscale characteristics, a two-dimension biaxial test is simulated with a discrete element method. The motion of particles and the evolution of force networks are exhibited at different strain values. The discrete element simulations results are helpful to understand GSH results.
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References
Gudehus, G., Jiang, Y.M., Liu, M.: Seismo- and thermodynamics of granular solids. Granul. Matter doi:10.1007/s10035-010-0229-0 (2010)
Kuhn M.R.: Structured deformation in granular materials. Mech. Mater. 31, 407–429 (1999)
Oda M., Kazama H.: Micro-structure of shear band and its relation to the mechanism of dilatancy and failure of dense granular soils. Géotechnique 48(4), 465–481 (1998)
Luding S.: Shear flow modeling of cohesive and frictional fine powder. Powder Technol. 158, 45–50 (2005)
Ord A., Hobbs B., Regenauer-lieb K.: Shear band emergence in granular materials: a numerical study. Int. J. Numer. Anal. Methods Geomech. 31, 373–393 (2007)
Houlsby G.T.: The work input to an unsaturated granular material. Géotechnique 47(1), 193–196 (1997)
Sheng D., Sloan S.W., Gens A.: A constitutive model for unsaturated soils: thermodynamical and computational aspects. Comput. Mech. 33(6), 453–465 (2004)
Li X.S.: Thermodynamics-based constitutive framework for unsaturated soils. 1: theory. Géotechnique 57(5), 411–422 (2007)
Welker, P.R., McNamara, S.C.: What triggers failure in frictional granular assemblies? Phys. Rev. E 79, 061305
Jiang Y., Liu M.: Granular solid hydrodynamics. Granul. Matter 11(3), 139–156 (2009)
Mahle, S., Jiang, Y., Liu, M.: The critical state as a steady-state solution of granular solid hydrodynamics. arXiv:1006.5131v3 [physics.geo-ph]
Bi, Z., Sun, Q., Jin, F. et al.: Numerical study on energy transformation in granular matter under biaxial compression. Granul. Matter. doi:10.1007/s10035-011-0262-7 (2011)
Sitharam T.G., Vinod J.S.: Critical state behaviour of granular materials from isotropic and rebounded paths: DEM simulations. Granul. Matter 11, 33–42 (2009)
Chapman S., Cowling T.G.: The Mathematical Theory of Non-uniform Gases. Cambridge University Press, Cambridge (1953)
Tillemans H., Herrmann H.J.: Simulating deformations of granular solids under shear. Phys. A 217, 261–288 (1995)
Bretz M., Zaretzki R., Field S.B. et al.: Broad distribution of stick-slip events in slowly sheared granular media: table-top production of a Gutenberg-Richter-like distribution. Europhys. Lett. 74, 1116–1122 (2006)
Bak P., Christensen K., Danon L. et al.: Unified scaling law for earthquakes. Phys. Rev. Lett. 88, 178501 (2002)
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Sun, Q., Song, S., Jin, F. et al. Elastic energy and relaxation in triaxial compressions. Granular Matter 13, 743–750 (2011). https://doi.org/10.1007/s10035-011-0288-x
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DOI: https://doi.org/10.1007/s10035-011-0288-x