A texture tensor to quantify deformations

Granular Matter

Volumn 5, Issue 2, 2003, Pages 67-70

  Aubouy, Miguel ^a   Jiang, Yi ^b   Glazier, James A ^c   Graner, François ^d  

^a CEA GRENOBLE   (France)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c INDIANA UNIVERSITY   (United States)

^d UNIV GRENOBLE ALPES   (France)

Author keywords

Connected network; Deformation and plasticity; Elasticity of disordered media; Strain

Indexed keywords

DEFORMATION; ELASTICITY; PLASTICITY; STRAIN;

ELASTIC STRAIN;

GRANULAR MATERIALS;

EID: 0042855732     PISSN: 14345021     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10035-003-0126-x     Document Type: Article

References (25)

1. C. Truesdell & W. Noll, The Non-Linear Field Theories of Mechanics, in Handbuch des Physik, vol III/3, S. Flügge ed., Springer-Verlag, Heidelberg, 1965
2. S. Alexander, Phys. Reports 296 (1998), p. 65
3. L. Landau & E. M. Lifschitz, In Theory of Elasticity, 3rd Edition, Reed Educational and Professional Publishing Ltd. 1986
4. L. E. Malvern, In Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Inc. New Jersey, 1969
5. A. Green & W. Zerna, In Theoretical Elasticity, 2nd edition (Clarendon Press, Oxford) 1968; A. Green and J. Adkins, in Large Elastic Deformations, 2nd edition (Clarendon Press, Oxford) 1970
6. A. Green & W. Zerna, In Theoretical Elasticity, 2nd edition (Clarendon Press, Oxford) 1968; A. Green and J. Adkins, in Large Elastic Deformations, 2nd edition (Clarendon Press, Oxford) 1970
7. I. Goldhirsch & C. Goldenberg, On the Microscopic Foundations of Elasticity. Submitted to Eur. Phys. J., cond-mat/0203360 (2002)
8. G. Durand, J. Weiss & F. Graner, Measure of the deformation tensor of polar ice from the microstructure: application on the Dome Concordia ice core. In preparation
9. D. A. Reinelt & A. M. Kraynik, J. Rheol. 44 (2000), p. 453
10. In equilibrium, with no external forces even at the boundaries, the stress is uniformly zero. Because we consider isotropic sites, we expect that the lack of force implies statistical isotropy on a mesoscopic scale. A prestressed reference state differs qualitatively (see [2] pp. 112-126).
11. S. Alesker, GAFA Geom. Funct. Anal. 8 (1998), p. 402; Geometriae dedicata 74 (1999), p. 241; Ann. of Math. 149 (1999), p. 977
12. S. Alesker, GAFA Geom. Funct. Anal. 8 (1998), p. 402; Geometriae dedicata 74 (1999), p. 241; Ann. of Math. 149 (1999), p. 977
13. S. Alesker, GAFA Geom. Funct. Anal. 8 (1998), p. 402; Geometriae dedicata 74 (1999), p. 241; Ann. of Math. 149 (1999), p. 977
14. H. Muller, Rend. Circ. Mat. Palermo 2 (1953), p. 1
15. R. Duda & P. Hart, In Pattern Classification and Scene Analysis (J. Wiley and Sons) 1973, pp. 364-366
16. P.-G. De Gennes & J. Prost, In The Physics of Liquid Crystals, 2nd edition (Oxford University Press, Oxford) 1998
17. F. Volino, Ann. Phys. Fr. 22 (1997), p. 1 (in French)
18. P.-G. De Gennes, In On Rice and Snow, Nishina Memorial Lecture (1998)
19. Y. Jiang, P. J. Swart, A. Saxena, M. Asipauskas & J. A. Glazier, Phys. Rev. E 59 (1999), p. 5819
20. S. Khan & R. Armstrong, J. Non-Newtonian Fluid Mech 22 (1986), p. 1; 25 (1987), p. 61
21. S. Khan & R. Armstrong, J. Non-Newtonian Fluid Mech 22 (1986), p. 1; 25 (1987), p. 61
22. 2〉 /d. Note, however, that M does not distinguish the anisotropy of rank four tensors ("mechanical anisotropy"): for instance, M does not necessarily distinguish between crystals and glasses.
23. C. Massonet & S. Cescotto, in Mécanique des Matériaux (in French) (Bibliothèque des Universités, De Boeck, Bruxelles) 1994, pp. 29-31
24. G. Porte, J.-F. Berret & J. Harden, J. Phys. II France 7 (1997), p. 459
25. M. Asipauskas, M. Aubouy, Y. Jiang, F. Graner & J. A. Glazier. A texture tensor to quantify deformations: the Example of Two-Dimensional Flowing Foams. Companion paper, Granular Matter, 5 (2003), pp. 71-74