A 2D granular medium with rotating particles

International Journal of Solids and Structures

Volumn 43, Issue 20, 2006, Pages 6194-6207

  Pavlov, I S ^a   Potapov, A I ^a   Maugin, G A ^b  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Cosserat continuum; Granular medium; Lattice model; Macroproperties; Microstructure

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; ELASTICITY; ELECTROMAGNETIC WAVE PROPAGATION; LATTICE VIBRATIONS; MATHEMATICAL MODELS; MICROSTRUCTURE; PARTICLES (PARTICULATE MATTER);

COSSERAT CONTINUUM; ELASTICITY CONSTANTS; LATTICE MODEL; MICROROTATIONS; ROTATING PARTICLES;

GRANULAR MATERIALS;

EID: 33846074844     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2005.06.012     Document Type: Article

References (38)

1. Askar A. Lattice Dynamical Foundations of Continuum Theories (1986), World Scientific, Singapore
2. Askar A., and Cakmak A.S. A structural model of micropolar continuum. Int. J. Eng. Sci. 6 (1968) 583-587
3. Bogdanov A.N., and Skvortsov A.T. Non-linear shear waves in a granular medium. Phys. Acoust. 38 3 (1992) 408-412
4. Born M., and Huang K. Dynamical Theory of Crystal Lattices (1954), Clarendon Press, Oxford
5. Brulin O., and Hsieh R.K.T. Mechanics of Micropolar Media (1982), World Scientific, Singapore
6. Chang C.S., and Ma L. A micromechanical-based micro-polar theory for deformation of granular solids. Int. J. Solids Struct. 28 (1994) 67-87
7. Christoffersen J., Mehrabadi M.M., and Nemat-Nasser S.A. A micromechanical description of granular material behavior. ASME, J. Appl. Mech. 48 (1981) 339-344
8. Emericault F., and Cambau B. Micromechanical modeling of anisotropic non-linear elasticity of granular medium. Int. J. Solids Struct. 33 18 (1996) 2591-2607
9. Eringen A.C. Theory of micropolar elasticity. In: Liebowitz H. (Ed). Fracture vol. II (1968), Academic Press, New York 622-729 (Chapter 7)
10. Eringen A.C. Microcontinuum Field Theories. 1: Foundation and Solids (1999), Springer Verlag, Inc, New York
11. Erofeyev V.I., and Rodyushkin V.M. Observation of dispersion of elastic waves in a granular composite. Phys. Acoust. 38 6 (1992) 1116-1117
12. Feynman R.P., Leighton R.B., and Sands M. The Feynman Lectures on Physics vol. 2 (1964), Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, Palo Alto, London
13. Forest S. Mechanics of generalized continua: construction by homogenization. J. Phys. IV 8/PR4 (1998) 39-48
14. Frantsevich I.N., Voronov F.F., and Bakuta S.A. In: Frantsevich I.N. (Ed). Elastic Constants and Elasticity Moduli of Metals and Nonmetals, Reference Book (1982), Naukova Dumka, Kiev (in Russian)
15. Gendelman O.V., and Manevitch L.I. The description of polyethylene crystal as a continuum with internal degrees of freedom. Int. J. Solids Struct. 33 12 (1996) 1781-1798
16. Grekova E.F., and Maugin G.A. Modelling of elastic magnetic crystals by means of multi-spin micromorphic media. Int. J. Eng. Sci. 43 5-6 (2005) 494-519
17. Gusev A.I. Effects of the nanocrystalline state in solids. Physics-Uspekhi 41 1 (1998) 49-76
18. Hirth J.P., and Lothe J. Theory of Dislocations (1970), McGraw-Hill Book Company, New York
19. Kosevich A.M. The Crystal Lattice (1999), Wiley-VCH, Berlin
20. Kunin I.A. Elastic Media with Microstructure vol. 2 (1983), Springer, Berlin
21. Limat L. Percolation and Cosserat elasticity-exact results on a deterministic fractal. Phys. Rev. B37 (1988) 672-675
22. Limat L. Effets rotationnels dans le cisaillement d'un milieu granulaire. C.R. Acad. Sci. Paris II-326 (1998) 501-509
23. Lisina S.A., Potapov A.I., and Nesterenko V.F. Non-linear granular medium with rotations of the particles. One-dimensional model. Phys. Acoust. 47 5 (2001) 666-674
24. Maugin G.A. Continuum Mechanics of Electromagnetic Solids (1988), North-Holland, Amsterdam
25. Maugin G.A. Non-linear Waves in Elastic Crystals (1999), Oxford University Press, UK
26. Misra A., and Chang C.S. Effective elastic moduli of heterogeneous granular solids. Int. J. Solids Struct. 30 18 (1993) 2547-2566
27. Muhlhaus H.-B., and Oka F. Dispersion and wave propagation in discrete and continuous models for granular materials. Int. J. Solids Struct. 33 19 (1996) 2841-2858
28. Nowacki W. Theory of Asymmetric Elasticity (1986), Pergamon, Oxford
29. In: Panin V.E. (Ed). Physical Mesomechanics of Heterogeneous Media and Computer-Aided Design of Materials (1998), Cambridge International Science Publishing
30. Potapov A.I., Pavlov I.S., and Maugin G.A. Non-linear wave interactions in 1D crystals with complex lattice. Wave Motion 29 (1999) 297-312
31. Potapov A.I., Pavlov I.S., Gorshkov K.A., and Maugin G.A. Non-linear interactions of solitary waves in a 2D lattice. Wave Motion 34 1 (2001) 83-95
32. Pouget J., Askar A., and Maugin G.A. Lattice model for elastic ferroelectric crystals: continuum approximation. Phys. Rev. B 33 (1986) 6304-6325
33. Pouget J., and Maugin G.A. Non-linear dynamics of oriented elastic solids-I-Basic equations, I-II-Propagation of solitons. J. Elasticity 22 (1989) 135-155 157-183
34. Savin G.N., Lukashev A.A., and Lysko E.M. Propagation of elastic waves in a solid with microstructure. Appl. Mech. 6 7 (1970) 48-52 (in Russian)
35. Schwartz L.M., Feng S., Thorpe M.F., and Sen P.N. Behavior of elastic depleted networks. Phys. Rev. B 32 (1985) 4607-4617
36. Stokes V.K. Theories of Fluids with Microstructure (1984), Springer-Verlag, Berlin
37. Suiker A.S.J., Metrikine A.V., and de Borst R. Comparison of wave propagation characteristics of the Cosserat continuum model and corresponding discrete lattice models. Int. J. Solids Struct. 38 (2001) 1563-1583
38. Valiev R.Z., and Alexandrov I.V. Nanostructural Materials Obtained by Intensive Plastic Deformation (2000), Logos Press, Moscow (in Russian)