The role of self-organization during confined comminution of granular materials

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences - Tập 368 Số 1910 - Trang 231-247 - 2010
Oded Ben-Nun1, Itai Einav1
1School of Civil Engineering, J05, The University of Sydney, Sydney, New South Wales 2006, Australia

Tóm tắt

During confined comminution of granular materials a power-law grain size distribution (gsd) frequently evolves. We consider this power law as a hint for fractal topology if self-similar patterns appear across the scales. We demonstrate that this ultimate topology is mostly affected by the rules that define the self-organization of the fragment subunits, which agrees well with observations from simplistic models of cellular automata. There is, however, a major difference that highlights the novelty of the current work: here the conclusion is based on a comprehensive study using two-dimensional ‘crushable’ discrete-element simulations that do not neglect physical conservation laws. Motivated by the paradigm of self-organized criticality, we further demonstrate that in uniaxial compression the emerging ultimate fractal topology, as given by the fractal dimension, is generally insensitive to alteration of global index properties of initial porosity and initial gsd. Finally, we show that the fractal dimension in the confined crushing systems is approached irrespective of alteration of the criteria that define when particles crush.

Từ khóa


Tài liệu tham khảo

10.1103/PhysRevE.60.6890

Ashby W. R., 1962, Principles of the self-organising systems, 255

10.1007/s100510050476

10.1007/978-1-4757-5426-1

10.1103/PhysRevA.38.364

10.1016/0191-8141(89)90101-6

10.2307/1311089

10.1680/geot.2003.53.7.633

10.1680/geot.2004.54.2.131

10.1038/nature03698

10.1680/geot.1979.29.1.47

10.1016/0022-5096(72)90029-4

10.1016/j.jmps.2006.11.003

10.1098/rspa.2007.1898

Heath T. L., 1961, Apollonius of Perga:treatise on conic sections

Irwin G., 1957, Analysis of stresses and strains near the end of a crack traversing a plate, J. Appl. Mech, 24, 361, 10.1115/1.4011547

10.1016/0148-9062(67)90046-0

10.1061/(ASCE)1532-3641(2001)1:1(21)

10.1038/272710a0

Lang R. A.. 2002 Numerical simulation of comminution in granular materials with an application to fault gouge evolution. MSc thesis Texas A&M University USA.

10.1038/23819

10.1061/(ASCE)1090-0241(2005)131:10(1295)

10.1103/PhysRevLett.84.4160

10.1126/science.156.3775.636

10.1680/geot.2002.52.4.299

10.1016/S0022-5096(96)00058-0

10.3208/sandf.41.2_39

Nicolis G., 1977, Self-organisation in non-equilibrium systems:from dissipative structures to order through fluctuations

10.1103/PhysRevLett.77.274

Robertson D.. 2000 Numerical simulations of crushable aggregates. PhD dissertation University of Cambridge UK.

10.1007/BF00878033

10.1038/nature06060

10.1006/jtbi.1995.0040

Sukumaran B., 2006, Qualitative assessment of the influence of coordination number on crushing strength using DEM

Timoshenko S. P., 1970, Theory of elasticity

Tory E. M., 1983, Comments on some types of random packing, 75

10.1016/S0032-5910(99)00137-0

10.1029/JB091iB02p01921

Weibull W., 1951, A statistical distribution function of wide applicability, J. Appl. Mech, 18, 293, 10.1115/1.4010337

10.1038/311419a0

10.1038/35101595

10.1103/PhysRevE.72.011301

Thông tin
Thông tin xuất bản

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

Tập 368 Số 1910

231-247

Thông tin tác giả