Abstract
The equations of motion for dilatant granular material are obtained from a Hamiltonian variational principle of local type in the conservative case. The propagation of nonlinear waves in a region with uniform state is studied by means of an asymptotic approach that has already appeared useful in an investigation on wave propagation in bubbly liquids and in fluid mixtures. When the grains are assumed to be incompressible, it is shown that the material behaves as a continuum with latent microstructure.
Sommario
Si ricavano le equazioni di moto per i materiali granulari dilatanti da un principio variazionale Hamiltoniano di tipo locale nel caso conservativo. Si studia la propagazione delle onde non lineari in una regione di stato costante per mezzo di un approccio asintotico già rivelatosi utile nello studio della propagazione di onde nei liquidi con bolle e nelle miscele di fluidi. Quando si supponga che i granuli siano incomprimibili, si dimostra che il materiale si comporta come un continuo con microstruttura latente.
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References
Goodman, M. A. and Cowin, S. C., ‘A continuum theory for granular materials’,Arch. Rational Mech. Anal.,44 (1972) 249–266.
Passman, S. L., Nunziato, J. W., Bailey, P. B. and Thomas, J. P. jr., ‘Shearing flows of granular materials’,J. Engng. Mech. Div. ASCE,4 (1980) 773–783.
Nunziato, J. W. and Walsh, E. K., ‘One-dimensional shock waves in uniformly distributed granular materials’,Int. J. Solids Structures,14 (1978) 681–689.
Cowin, S. C. and Nunziato, J. W., ‘Waves of dilatancy in a granular material with incompressible granules’,Int. J. Engng. Sci.,19 (1981) 993–1008.
Jenkins, J. T., ‘Static equilibrium of granular Materials’,J. Appl. Mech.,42 (1975) 603–606.
Passman, S. L., Nunziato, J. W. and Walsh, E. K., ‘A theory of multiphase mixtures’ in: Truesdell, C. (Ed),Rational Thermodynamics, Springer-Verlag, New York, 1984, pp. 286–325.
Arthur, J. R. F. and Menzies, B. K., ‘Inherent anisotropy in sand’,Geotechnique,22 (1972) 115–129.
Capriz, G.,Continua with Microstructure, Springer-Verlag, Berlin, 1989.
Savage, S. B., ‘Gravity flow of cohesionless granular materials in chutes and channels’,J. Fluid Mech.,92 (1979) 53–96.
Capriz, G. and Podio Guidugli, P., ‘Materials with spherical structure’,Arch. Rational Mech. Anal.,75 (1981) 269–279.
Cowin, S. C., ‘A theory for the flow of granular materials’,Powder Technology,9 (1974) 61–69.
Cowin, S. C., ‘Microstructural continuum models for granular materials’ in: Cowin, S. C. and Satake, M. (Eds.),Proceedings of the U.S.-Japan Seminar on Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials, Gakujutsu Bunken Fukyu-Kai, Tokyo, 1978.
Passman, S. L., ‘Mixtures of granular materials’,Int. J. Engng. Sci.,15 (1977) 117–129.
Bedford, A. and Drumheller, D. S., ‘On volume fraction theories for discretized materials’,Acta Mechanica,48 (1983) 173–184.
Whitham, G. B.,Linear and Non-Linear Waves, John Wiley and Sons, New York, 1974.
Fusco, D. and Oliveri, F., ‘Derivation of a non-linear model equation for wave propagation in bubbly liquids’,Meccanica,24 (1989) 15–25.
Oliveri, F., ‘Nonlinear wave propagation in a non-diffusive model of bubbly liquids’,Acta Mechanica,83 (1990) 135–148.
Giovine, P. and Oliveri, F., ‘Wave features related to a model of compressible immiscible mixtures of two perfect fluids’,Acta Mechanica,96 (1993) 85–96.
Buyevich, Y. A. and Shchelchkova, I. N., ‘Flow of dense suspensions’,Prog. Aerospace Sci.,18 (1978) 121–150.
Bampi, F. and Morro, A., ‘connection between variational principles in Eulerian and Lagrangian descriptions’,J. Math. Phys.,25 (1984) 2418–2421.
Goodman, M. A. and Cowin, S. C., ‘A variational principle for granular materials’,ZAMM,56 (1976) 281–286.
Gelfand, I. M. and Fomin, S. V.,Calculus of Variations, Prentice-Hall, Englewood Cliffs, New Jersey, 1963.
Nunziato, J. W. and Cowin, S. C., ‘A nonlinear theory of elastic materials with voids’,Arch. Rational Mech. Anal.,72 (1979) 175–201.
Bowen, R. M., ‘Compressible porous media models by use of the theory of mixtures’,Int. J. Engng. Sci.,20 (1982) 697–735.
Fusco, D., ‘Some comments on wave motion described by non-homogeneous quasilinear first order hyperbolic systems’,Meccanica,17 (1982) 128–137.
Germain, P., ‘Progressive waves’,Jahrbuch 1971 der DGLR (1971) 11–29.
Choquet-Bruhat, Y., ‘Ondes asymptotiques et approchées pour des systèmes d'équations aux dérivées partielles non linéaires’,J. Math. Pure et Appliquée,48 (1969) 117–158.
Boillat, G., ‘Ondes asymptotiques non linéaires’,Ann. Mat. Pura e Applicata,61 (1976) 31–44.
Jeffrey, A. and Kawahara, T.,Asymptotic Methods in Nonlinear Wave Theory, Pitman, London, 1982.
Lamb, G. L. jr.,Elements of Soliton Theory, John Wiley and Sons, New York, 1980.
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Giovine, P., Oliveri, F. Dynamics and wave propagation in dilatant granular materials. Meccanica 30, 341–357 (1995). https://doi.org/10.1007/BF00993418
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DOI: https://doi.org/10.1007/BF00993418