Entropy and Granular Materials: Model
Publication: Journal of Engineering Mechanics
Volume 126, Issue 6
Abstract
The macrostructure of a granular material is treated as an ensemble of microstates of like spheres where each microstate is identified by a coordination number and a corresponding porosity. The probability of occurrence of these finite numbers of microstates is constrained by measurable information concerning the macrostate and described by maximizing the information entropy subject to these constraints and the axioms of probability theory. The macrostate behavior is then deduced from the probabilities of occurrence of the microstates and their mechanical performance. Existing observations of phenomena in granular media as related to soils and liquids are discussed and explained in light of the proposed entropy maximization scheme. Critical tests to examine the viability of the entropy model are proposed.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Backman, B. F. ( 1976). “The principle of maximum entropy with application to problems in structural mechanics.” PhD thesis, University of Washington, Seattle.
2.
Backman, B. F., Brown, C. B., Jowitt, P. W., and Munro, J. ( 1983). “Statistical mechanics of granular materials.” Advances in the mechanics and flow of granular materials, M. Shahinpoor, ed., TransTech Publications, Clausthal, Germany, 259–272.
3.
Bagi, K. ( 1997). “Analysis of micro-variables through entropy principle.” Powders and grains 97, R. F. Behringer and J. T. Jenkins, eds., Balkema, Rotterdam, The Netherlands, 251–254.
4.
Bernal, J. D. (1959). “A geometrical approach to the structure of liquids.” Nature, 183, 141–147.
5.
Bernal, J. D. (1960). “Geometry of the structure of monatomic liquids.” Nature, 185, 68–70.
6.
Bernal, J. D. (1964). “The structure of liquids.” Proc., Royal Soc., London, 280, 299–322.
7.
Bernal, J. D., and Finney, J. L. (1968). “Problems of the pebble bed and granular materials.” EURATOM, 4190d,e, 403.
8.
Bernal, J. D., Knight, K. R., and Cherry, I. (1964). “Growth crystals from random close packing.” Nature, 202, 852–854.
9.
Berryman, J. G. ( 1983). “Definition of dense random packing.” Advances in the mechanics and flow of granular materials, M. Shahinpoor, ed., TransTech Publications, Clausthal, Germany, 1–18.
10.
Boerdijk, A. H. (1952). “Some remarks concerning close packing of equal spheres.” Philip's Res. Rep., 7, 303–313.
11.
Boussinesq, M. J. ( 1986). “Essai théorique sur l'equilibre d'élasticité des massifs purvérulents comparé à celui de massifs solides et sur la poussée des terres sans cohésion.” Mem. Couronnes et Mem. des Sav. Etrangers Pub. par l'Acad.-Belgique, T.XL, 1–180.
12.
Brillouin, L. ( 1962). Science and information theory. 2nd Ed., Academic, New York, 160.
13.
Brown, C. B. (1978). “The use of maximum entropy in the characteristics of granular media.” Proc., U.S.–Japan Continuum Mech. and Statistical Approaches in the Mech. of Granular Mat., S. C. Cowin and M. Setake, eds., Gakujutsu Bunken Fukyukai, Tokyo, 98–108.
14.
Brown, C. B., Elms, D. G., Hanson, M. T., Nikzad, K., and Worden, R. E. (2000). “Entropy and granular materials: Experiments.”J. Engrg. Mech., ASCE, 126(6), 605–610.
15.
Casagrande, A. (1936). “Characteristics of cohesionless soils affecting the stability of slopes and earth fills.” J. Boston Soc. of Civ. Engrs., 23, 13–32.
16.
Coveney, P. V. (1988). “The second law of thermodynamics: Entropy, Irreversibility and Dynamics.” Nature, 333, 409–415.
17.
Davis, R. A., and Deresiewicz, H. (1977). “A discrete probabilistic model for mechanical response of a granular medium.” Acta Mechanica, 27, 69–89.
18.
Duffy, J., and Mindlin, R. D. (1957). “Stress-strain relations and vibrations of a granular medium.” J. Appl. Mech., 24, 585–593.
19.
Filep, L. ( 1936). Egyenlo gombokbol allo halmazok. Vizugyi Kozlemonyek, Budapest.
20.
Finney, J. L. (1970). “Random packing and structure of simple liquids. 1: The geometry of random close packing.” Proc., Royal Soc., London, 319, 479–493.
21.
Graton, L. C., and Fraser, H. J. (1935). “Systematic packing of spheres—with particular attention to porosity and permeability.” J. Geol., 48, 785–909.
22.
Hilbert, D., and Cohn-Vossen, S. ( 1932). Anschauliche geometrie, Chapter 2, Reguläre Punktsysteme, Springer, Berlin, 28–79.
23.
Jenkins, J. T. ( 1987). “Balance laws and constitutive relations for rapid flows of granular materials.” Constitutive models of deformation, J. Chandra and R. P. Srivastav, eds., SIAM, Philadelphia, 109–119.
24.
Jowitt, P. W. and Munro, J. (1975). “The influence of void distribution and entropy on the engineering properties of granular media.” Proc., 2nd Int. Conf. on the Applications of Statistics and Probability in Soil and Struct. Engrg., 365–385.
25.
Jowitt, P. W. ( 1977). “Decision making in civil engineering systems.” PhD thesis, University of London, London.
26.
Kapur, J. N., and Kesavan, H. K. (1987). The generalized maximum principle (with applications). Sandford Educational Press, Waterloo.
27.
Mason, G. (1976). “General discussion of packing topic.” Trans. Faraday Soc., 75–76.
28.
Mogami, T. (1965). “A statistical theory of mechanics and granular materials.” J. Faculty of Engrg., University of Toyko, B, 28, 65–79.
29.
Mogami, T. (1969). “Mechanics of granular materials as a particulated mass.” Proc., 7th Int. Conf. on Soil Mech. and Found. Engrg., 1, 281–285.
30.
Mogami, T., and Imai, G. (1967). “On the failure of granular material.” Soils and Found., Tokyo, VII, 1–9.
31.
Morgenstern, N. R. (1963). “Maximum entropy of granular materials.” Nature, 200, 559–600.
32.
Roscoe, K. H., Schofield, A. N., and Wroth, C. P. (1958). “On the yielding of soils.” Géotechnique, London, 8, 22–63.
33.
Rothenburg, L. ( 1980). “Micro-mechanics of idealised granular materials.” PhD thesis, Carleton University, Ottawa.
34.
Scott, G. D. (1960). “Packaging of spheres.” Nature, 188, 908–909.
35.
Scott, G. D. (1962). “Radial distribution of the random packing of equal spheres.” Nature, 194, 956–957.
36.
Scott, G. D., Charlesworth, A. M., and Mak, M. K. (1964). “On the random packing of spheres.” Nature, 202, 611–612.
37.
Wart, R. J., Ackerman, N. L., and Shen, H. T. ( 1979). “Interpretation of critical void ratio using information theory.” Preprint, Atlanta Meeting, ASCE, New York.
38.
Westman, A. E. R., and Hugill, H. R. (1930). “The packing of particles.” J. Am. Ceramic Soc., 13, 767–779.
39.
Ziman, J. M. ( 1979). Models of disorder. Cambridge University Press, New York, 233–236.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 126 • Issue 6 • June 2000
Pages: 599 - 604
History
Received: Jul 6, 1999
Published online: Jun 1, 2000
Published in print: Jun 2000
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.