Elastic constants for granular materials modeled as first-order strain-gradient continua

International Journal of Solids and Structures

Volumn 40, Issue 21, 2003, Pages 5565-5582

  Chang, C S ^a   Shi, Q ^a   Liao, C L ^b  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b Bureau of High Speed Rail   (Taiwan)

Author keywords

Couple stress model; Grain rotation; Granular material; Internal length; Strain gradient model; Stress strain relationship

Indexed keywords

ELASTICITY; PARTICLE SIZE ANALYSIS; STIFFNESS; STRAIN MEASUREMENT; STRESS ANALYSIS;

ELASTIC CONSTANTS;

GRANULAR MATERIALS;

GRANULAR MEDIUM; SOIL MECHANICS; STRAIN ANALYSIS; STRESS-STRAIN RELATIONSHIP;

EID: 0141456224     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(03)00328-7     Document Type: Article

References (42)

1. Altan B.S. Aifantis E.C. On some aspects in the special theory of gradient elasticity Journal of the Mechanical Behavior of Materials 8 1997 231-282
2. Bardenhagen S. Trianfyllidis N. Derivation of higher order gradient continuum theories in 2,3-D non-linear elasticity from periodic lattice models Journal of Mechanics and Physics of Solids 42 1994 111-139
3. Bazant Z.P. Pijaudier-Cabot G. Nonlocal continuum damage localization instability and convergence Journal of Applied Mechanics, ASME 55 1987 659-673
4. Benjamin E.M. Cornell J.A. Probability, Statistics, and Decision for Civil Engineers 1970 McGraw-Hill Book Company New York, NY
5. Beran M.J. McCoy J.J. The use of strain gradient theory for analysis of random media International Journal of Solids and Structures 6 1970 1267-1275
6. Chang C.S. Micromechanical modeling of constructive relations for granular material Satake M. Jenkins J.T. Micromechanics of Granular Materials 1988 271-279 Elsevier Amsterdam
7. Chang C.S. Models of granular materials with intrinsic length Journal of Physics IV, France 8 1998 71-78
8. Chang C.S. Gao J. Second-gradient constitutive theory for granular material with random packing structure International Journal of Solids and Structures 32 16 1995 2279-2293
9. Chang C.S. Gao J. Kinematic and static hypotheses for constitutive modeling of granulates considering particle rotation Acta Mechanica 115 1-4 1996 213-229
10. Chang C.S. Gao J. Wave propagation in a granular rod using high-gradient theory Journal of Engineering Mechanics, ASCE 123 1 1997 52-59
11. Chang C.S. Liao C. Constitutive relations for particulate medium with the effect of particle rotation International Journal of Solids and Structures 26 1990 437-453
12. Chang C.S. Ma L. Elastic material constants for isotropic granular solids with particle rotation International Journal of Solids and Structures 29 8 1992 1001-1018
13. Coleman B.D. Hodgdon M.L. On shear bands in ductile materials Archive of Rational Mechanics and Analysis 90 1985 219-247
14. Cosserat, E., Cosserat, F., 1909. Theorie des Corps Deformables. Paris. Librairie Scientifique A. Hermann et Fils
15. Day D.F. Weitsman Y. Strain-gradient effects in microlayers Journal of Engineering Mechanics, ASCE 92 EM5 1966 67-86
16. De Borst R. Muhlhaus H.-B. Gradient-dependent plasticity: Formulation and algorithmic aspects International Journal of Numerical Methods in Engineering 35 1992 521-539
17. Eringen A.C. Theory of micropolar elasticity Liebowitz H. Fracture, An Advance Treatise 1968 Academic Press New York
18. Fleck N.A. Huchinson J.W. A Pomenological theory for strain gradient effects in plasticity Journal of Mechanics, Physics and Solids 41 12 1993 1825-1857
19. Gunther W. Zur Statik und Kinematik des Cosseratschen Kontinuums Abhandhungen der Braunschweigischen Wissenschafftlichen Gesellschaft Goltze, Gottingen 10 1958 195-213
20. Jenkins J.T. Volume change in small strain axisymmetric deformations of a granular material Satake M. Jenkins J.T. Micromechanics of Granular Materials 1988 143-152 Elsevier Amsterdam
21. Koiter W.T. Couple-stresses in the theory of elasticity, I - II Proceedings of the Royal Netherlands Academy of Sciences B 67 1964 17-44
22. Kruyt N.P. Statics and kinematics of discrete Cosserat-type granular materials International Journal of Solids and Structures 40 2003 511-534
23. Kruyt N.P. Rothenburg L. Statistics of the elastic behaviour of granular materials International Journal of Solids and Structures 38 28-29 2001 4879-4899
24. Kruyt N.P. Rothenburg L. Micromechanical bounds for the effective elastic moduli of granular materials International Journal of Solids and Structures 39 2 2002 311-324
25. Luding S. Latzel M. Volk W. Diebels S. Herrmann H.J. From discrete element simulations to a continuum model Computer Methods in Applied Mechanics and Engineering 191 1-2 2001 21-28
26. Mindlin R.D. Second gradient of strain and surface-tension in linear elasticity International Journal of Solids and Structures 1 1965 417-438
27. Mindlin R.D. Microstructure in linear elasticity Archive of Rational Mechanics and Analysis 16 1969 51-78
28. Mindlin R.D. Eshel N.N. On first strain-gradient theories in linear elasticity International Journal of Solids and Structures 4 1968 109-124
29. Mindlin R.D. Tiersten H.F. Effect of couple stresses in linear elasticity Archive of Rational Mechanics and Analysis 11, 1962 415-418
30. Muhlhaus H.-B. Oka F. Dispersion and wave propagation in discrete and continuous models for granular materials International Journal of Solids and Structures 33 1996 2841-2858
31. Oden J.T. Rigsby D.M. Cornett D. On the numerical solution of a class of problems in a linear first strain-gradient theory of elasticity International Journal for Numerical Methods in Engineering 2 1970 159-174
32. Pamin, J., 1944. Gradient-Dependent Plasticity in Numerical Simulation of Localization Phenomena, Dissertation, Delft University of Technology, Delft, Netherlands
33. Peerlings R.H.J. De Borst R. Brekelmans W.A.M. De Vree J.H.P. Gradient-enhanced damage for quasi-brittle materials International Journal for Numerical Methods in Engineering 39 1996 3391-3403
34. Rothenburg L. Selvadurai A.P.S. Micromechanical definitions of the Cauchy stress tensor for particular media Selvadurai A.P.S. Mechanics of Structured Media 1981 469-486 Elsevier Amsterdam
35. Shaefer H. Das Cosserat-Kontinuum Zeitschrift fur angewandte Mathematik und Mechanik 1967 485-498
36. Sluys, L.J., 1992. Wave Propagation, Localization and Dispersion in Softening Solids, Ph.D. thesis, Delft University of Technology
37. Suiker A.S.J. Chang C.S. Application of higher order tensor theory for formulating enhanced continuum models Acta Mechanica 142 2000 223-234
38. Suiker A.S.J. Chang C.S. deBorst R. Esveld C. Surface waves in a stratified half space with enhanced continuum properties, Part-1--Formulation of the boundary value problem European Journal of Mechanics Solids 18 1999 749-768
39. Suiker A.S.J. de Borst R. Chang C.S. Micromechanical modeling of granular material. Part 1: Derivation of a second-gradient micro-polar constitutive theory Acta Mechanica 149 2001 161-180
40. Toupin R.A. Elastic materials with couple-stresses Archive of Rational Mechanics and Analysis 11 1962 385-414
41. Wallton K. The effective elastic moduli of a random packing of spheres Journal of Mechanics and Physics of Solids 35 1987 213-226
42. Zervos A. Papanastasiou P. Vardoulakis I. A finite element displacement formulation for gradient elastoplasicity International Journal for Numerical Methods in Engineering 50 6 2001 1369-1388