A thermo-mechanical continuum theory with internal length for cohesionless granular materials : PPart I. A class of constitutive models

Continuum Mechanics and Thermodynamics

Volumn 17, Issue 8, 2006, Pages 545-576

  Fang, Chung ^a   Wang, Yongqi ^a   Hutter, Kolumban ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Goodman Cowin theory; Granular materials; Internal length; M ller Liu entropy principle

Indexed keywords

ENTROPY; GRANULAR MATERIALS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; SHEAR FLOW; THERMODYNAMIC PROPERTIES;

GOODMAN-COWIN THEORY; INDEPENDENT KINEMATIC FIELD QUANTITY; INTERNAL LENGTH; MÜLLER-LIU ENTROPY PRINCIPLE;

CONTINUUM MECHANICS;

EID: 33745666855     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-006-0007-8     Document Type: Article

References (52)

1. Goodman, M.A.: A continuum theory for the dynamical behavior of granular materials. Ph.D. Thesis, Tulane University, USA (1970)
2. Goodman, M.A., Cowin, S.C.: Two problems in the gravity flow of granular materials. J. Fluid Mech. 45, 321-339 (1971)
3. Goodman, M.A., Cowin, S.C.: A continuum theory for granular materials. Arch. Rational Mech. Anal. 44, 249-266 (1972)
4. Duran, J.: Sands, Powders and Grains. Springer, Berlin Heidelberg New York (2000)
5. Hutter, K.: Order and disorder in granular materials: experiment and theory. In: Hutter, K., Wilmański, K. (eds.), Kinetic and Continuum Theories of Granular and Porous Media, pp. 1-65. Springer, Berlin, Heidelberg, New York (2000)
6. Hutter, K., Rajagopal, K.R.: On flows of granular materials. Continuum. Mech. Thermodyn. 6, 81-139 (1994)
7. Savage, S.B.: Mechanics of granular flows. In: Hutter, K. (ed.), Continuum Mechanics in Environmental Sciences and Geophysics. Springer, Berlin Heidelberg New York, pp. 467-522 (1993)
8. Wang, Y., Hutter, K.: Granular material theories revisited. In: Balmforth, N.J., Provenzale, A. (eds.), Geomorphological Fluid Mechanics, pp. 79-107. Springer, Berlin Heidelberg New York (2001)
9. Fang, C.: A thermo-mechanical continuum theory with internal length of cohesionless granular materials. Ph.D. thesis, Darmstadt University of Technology, Germany (2005)
10. Chen, C.L., Ling, C.H.: Granular-flows rheology: role of shear-rate number in transition regime. J. Eng. Mech. 122, 469-480 (1996)
11. Coussot, P.: Steady, laminar flow of concentrated mud suspensions in open channels. J. Hydr. Res. 32(4), 535-550 (1994)
12. Massoudi, M., Boyle, E.J.: A review of theories for flowing granular materials with applications to fluidized beds and solids transport. U.S. Department of Energy Report, DOE/PETC/TR-91/8 (1991)
13. McTigue, D.F.: A non-linear constitutive model for granular materials: applications to gravity flows. J. Appl. Mech. 49, 291-296 (1982)
14. Rajagopal, K.R., Troy, W.C.: Massoudi, M.: Existence of solutions to the equations governing the flow of granular materials. Eur. J. Mech., B/Fluids 11, 265-276 (1992)
15. Savage, S.B.: Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92, 53-96 (1979)
16. Bowen, R.M.: Incompressible porous media models by use of the theory of mixtures. Int. J. Engng. Sci. 18, 1129-1148 (1980)
17. Sampaio, R.S., Williams, W.O.: J. de Mechanique 18, 19-45 (1979)
18. Bluhm, J., De Boer, R., Wilmański, K.: The thermodynamic structure of the two-component model of porous incompressible materials with true mass densities. Mech. Res. Reviews 22, 171-180 (1995)
19. Hutter, K., Laloui, L., Vulliet, L.: Thermodynamically based mixture models of saturated and unsaturated soils. Mech Cohesive-Frictional Mat. 4(4), 295-338 (1999)
20. Svendsen, B., Hutter, K.: On the thermodynamics of a mixture of Isotropic materials with constraints. Int. J. Engng. Sci. 33, 2021-2054 (1995)
21. Svendsen, B., Hutter, K.: On the thermodynamics of a mixture of isotropic materials with constraints. Int. J. Engng. Sci. 33, 2021-2054 (1995)
22. Cowin, S.C.: A theory for the flow of granular materials. Powder Technol. 9, 61-69 (1974)
23. Cowin, S.C.: Constitutive relations that imply a generalized Mohr-Coulomb criterion. Acta Mechanica. 20, 41-46 (1974)
24. Cowin, S.C.: Polar fluids. Phys. Fluids 11(9), 1919-1927 (1968)
25. Nunziato, J.W., Passman, S.L.: Gravitational flows of granular materials with incompressible grains. J. Rheology 24, 395-420 (1980)
26. Nunziato, J.W., Walsh, E.K.: On ideal multiphase mixtures with chemical reactions and diffusions. Arch. Rational Mech. Anal. 73, 285-311 (1980)
27. Passman, S.L., Nunziato, J.W., Bailey, P.B., Thomas, J.P.: Shearing flow of granular materials. J. Eng. Mech. Division, ASCE 106, 773-783 (1980)
28. Passman, S.L., Nunziato, J.W., Walsh, E.K.: A theory of multiphase mixtures. In: Truesdell, C. (ed.), Rational Thermodynamics, pp. 287-325. Springer, Berlin Heidelberg New York (1984)
29. Wang, Y., Hutter, K.: A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures. Granular Matter 1, 163-181 (1999)
30. Wang, Y., Hutter, K.: A constitutive theory of fluid-saturated granular materials and its application in gravitational flows. Rheol. Acta 38, 214-223 (1999)
31. Wang, Y., Hutter, K.: Shearing flows in a Goodman-Cowin type granular material-theory and numerical results. Part Sci. Technol. 17, 97-124 (1999)
32. Hutter, K.: The foundations of thermodynamics, its basic postulates and implications. A review of modern thermodynamics. Acta. Mechanica. 27, 1-54 (1977)
33. Wang, Y., Hutter, K.: Comparison of two entropy principles and their applications in granular flows with/without fluid. Arch. Mech. 51(5), 605-632 (1999)
34. Kirchner, N.: Thermodynamics of structured granular materials. Ph.D. Thesis, Darmstadt University of Technology, Germany (2001)
35. Kirchner, N.: Thermodynamically consistent modelling of abrasive granular materials. I: Non-equilibrium theory. Proc. R. Soc. Lond. A 458, 2153-2176 (2002)
36. Kirchner, N., Teufel, A.: Thermodynamically consistent modelling of abrasive granular materials. II: Thermodynamic equilibrium and applications to steady shear flows. Proc. R. Soc. Lond. A 458, 3053-3077 (2002)
37. Cowin, S.C., Goodman, M.A.: A variational principle for granular materials. ZAMM 56, 281-286 (1976)
38. Liu, I.-S.: Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rational Mech. Anal. 46, 131-148 (1972)
39. Liu, I.-S.: On the entropy supply in a classical and a relativistic fluid. Arch. Rational Mech. Anal. 50, 111-117 (1973)
40. Liu, I.-S.: Continuum Mechanics. Springer, Berlin Heidelberg New York (2002)
41. Liu, I.-S., Muller, I.: Thermodynamics of mixtures of fluids. In: Truesdell, C. (ed.), Rational Thermodynamics, Springer, Berlin Heidelberg New York (1984)
42. Truesdell, C., Noll, W.: The non-linear field theories of mechanics. In: Flügge, S. (ed.), Handbuch der Physik, III/3, Springer, Berlin Heidelberg New York (1965)
43. Wang, C.-C.: A new representation theorem for isotropic functions, Part I and Part II. Arc. Rational Mech. Anal. 36, 166-197, 198-223; Corrigendum, ibid. 43, 392-395 (1971)
44. Wang. C.-C., Liu, I.-S.: A note on material symmetry. Arch. Rational Mech. Anal. 74, 277-296 (1980)
45. Wilmański, K.: Thermo-Mechanics of Continua. Springer, Berlin Heidelberg New York (1998)
46. Nunziato, J.W., Cowin, S.C.: A nonlinear theory of elastic materials with voids. Arch. Rational Mech. Anal. 72, 175-201 (1979)
47. Cowin, S.C., Leslie, L.M.: On Kinetic Energy and Moment in Cesserat Continua. ZAMP 31, 247-260 (1980)
48. Vardoulakis, I., Aifantis, E.C.: A gradient flow theory of plasticity for granular materials. Acta Mechanica. 87, 197-217 (1991)
49. Terzaghi, K.: Theoretical Soil Mechanics. Wiley (1963)
50. Batchelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge University Press (1959)
51. Bradshaw, P.: An Introduction to Turbulence and Its Measurement. Pergamon Press, New York (1971)
52. Lesieur, M.: Turbulence in Fluids. Martinus Nijhoff Publishers, Dordrecht (1987)