Specimen Size Effect in Discrete Element Simulations of Granular Assemblies
Publication: Journal of Engineering Mechanics
Volume 135, Issue 6
Abstract
The paper addresses the question of whether the number of particles in a noncemented granular assembly will affect the mechanical characteristics of the assembly: its strength and stiffness. The question is answered by applying the discrete element method to assemblies of different sizes. To isolate the effect of assembly size, apart from the scatter that usually accompanies such simulations, multiple assemblies were tested. The two-dimensional assemblies had nearly identical initial porosities and fabrics, and they were all loaded in biaxial compression. Two different boundaries were tested: periodic and wall boundaries. We find that the peak compressive strength decreases with assembly size for both types of boundaries and over a range of assembly sizes that contain 256 particles to over 66,000 particles. Stiffness is only slightly reduced and only with wall boundaries. Deformation is less uniform in the larger assemblies, with deformation concentrated in a smaller fraction of the assembly area. An analysis of deformation patterning shows that at least a few thousand particles are required for realistic microband patterning.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was partially supported by the Bolyai Janos Scholarship and by the OTKA UNSPECIFIED48906 Grant.
References
Bagi, K. (1996). “Stress and strain in granular assemblies.” Mech. Mater., 22(3), 165–177.
Bagi, K. (2005). “An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies.” Granular Matter, 7(1), 31–43.
Bazant, Z. P., Gettu, R., and Kazemi, M. T. (1991). “Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves.” Int. J. Rock Mech. Min. Sci., 28(1), 43–51.
Bazant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC, Boca Raton, Fla.
Cundall, P. A., Drescher, A., and Strack, O. D. L. (1982). “Numerical experiments on granular assemblies.” Deformation and failure of granular materials, P. A. Vermeer and H. J. Luger, eds., Balkema, Rotterdam, The Netherlands, 355–370.
Cundall, P. A., and Strack, O. D. L. (1979). “A discrete numerical model for granular assemblies.” Geotechnique, 29(1), 47–65.
Drescher, A., and de Josselin de Jong, G. (1972). “Photoelastic verification of a mechanical model for the flow of a granular material.” J. Mech. Phys. Solids, 20(5), 337–351.
Konishi, J., and Naruse, F. (1988). “A note on fabric in terms of voids.” Micromechanics of granular materials, M. Satake and J. T. Jenkins, eds., Elsevier Science, Amsterdam, The Netherlands, 39–46.
Kuhn, M. R. (1997). “Deformation measures for granular materials.” Mechanics of deformations and flow of particulate materials, C. S. Chang, A. Misra, R. Y. Liang, and M. Babic, eds., ASCE, New York, 91–104.
Kuhn, M. R. (1999). “Structured deformation in granular materials.” Mech. Mater., 31, 407–429.
Kuhn, M. R. (2006). “Oval and OvalPlot: Programs for analyzing dense particle assemblies with the discrete element method.” ⟨http://faculty.up.edu/kuhn/oval/doc/oval_0618.pdf⟩ (June 1, 2006).
McKinney, K. R., and Rice, R. W. (1981). “Specimen size effect in fracture toughness testing of heterogeneous ceramics by the notch beam method.” Fracture mechanics methods for ceramics, rocks and concrete, ASTM STP 745, S. W. Freiman and E. R. Fuller, eds., ASTM, Philadelphia, 118–126.
Thornton, C., and Barnes, D. J. (1986). “Computer simulated deformation of compact granular assemblies.” Acta Mech., 64(1–2), 45–61.
Walsh, P. F. (1972). “Fracture of plain concrete.” Indian Concr. J., 46(11), 469–476.
Walton, K. (1986). “The effective elastic moduli of a random packing of spheres.” J. Mech. Phys. Solids, 35(2), 213–226.
Weibull, W. (1939). “A statistical theory of the strength of materials.” Proc. Royal Swedish Acad. Eng. Sci., 151(1), 1–45.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 6 • June 2009
Pages: 485 - 492
Copyright
© 2009 ASCE.
History
Received: Jan 4, 2007
Accepted: Sep 26, 2008
Published online: May 15, 2009
Published in print: Jun 2009
Notes
Note. Associate Editor: Anil Misra
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.