Hardness-packing density scaling relations for cohesive-frictional porous materials

Journal of the Mechanics and Physics of Solids

Volumn 56, Issue 3, 2008, Pages 924-952

  Cariou, Sophie ^a,b   Ulm, Franz Josef ^a   Dormieux, Luc ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITÉ PARIS EST   (France)

Author keywords

Cohesive frictional porous materials; Hardness; Indentation analysis; Packing density; Strength homogenization

Indexed keywords

COMPUTER SIMULATION; ELASTOPLASTICITY; FINITE ELEMENT METHOD; HOMOGENIZATION METHOD; MEASUREMENT THEORY; MICROSTRUCTURE; NANOINDENTATION; OPTIMIZATION; POROSITY;

COHESIVE-FRICTIONAL POROUS MATERIALS; PACKING DENSITY; STRENGTH HOMOGENIZATION;

POROUS MATERIALS;

EID: 39049155220     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.06.011     Document Type: Article

References (63)

1. Anderheggen E., and Knopfel H. Finite element limit analysis using linear programming. Int. J. Solids Struct. 8 (1972) 1413-1431
2. Barthélémy J.F., and Dormieux L. Détermination du critère de rupture macroscopique d'un milieu poreux par homogénéisation non linéaire. C.R. Méc. 331 (2003) 77-84
3. Bathe K.J. Finite Element Procedures (1996), Prentice-Hall, Upper Saddle River, NJ
4. Borodich F.M., and Keer L.M. Evaluation of elastic modulus of materials by adhesive (no-slip) nanoindentation. Proc. R. Soc. London Ser. A 460 (2004) 507-514
5. Borodich F.M., Keer L.M., and Korach C.S. Analytical study of fundamental nanoindentation test relations for indenters of non-ideal shapes. Nanotechnology 14 (2003) 803-808
6. Bottero A., Negre R., Pastor J., and Turgeman S. Finite element method and limit analysis theory for soil mechanics problems. Comput. Methods Appl. Mech. Eng. 22 (1980) 131-149
7. Brinell, J.A., 1901. Memoire sur les epreuves a bille en acier. In: Congres International des Methodes d'Essai des Materiaux de Construction, vol. 2, Paris, pp. 83-94.
8. Bucaille J.L., Stauss S., Felder E., and Michler J. Determination of plastic properties of metals by instrumented indentation using different sharp indenters. Acta Materialia 51 (2003) 1663-1678
9. Cariou, S., Ulm, F.-J., 2006. The effect of the packing density on the indentation hardness of cohesive-frictional porous materials. MIT-CEE Res. Rep. 06-01. M.Sc. Dissertation, Cambridge, MA.
10. Cheng Y.-T., and Cheng C.-M. Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R44 (2004) 91-149
11. Chitkara N.R., and Butt M.A. Numerical construction of axisymmetric slip-line fields for indentation of thick blocks by rigid conical indenters and friction at the tool-metal interface. Int. J. Mech. Sci. 34 11 (1992) 849-862
12. Chollacoop N., Dao M., and Suresh S. Depth-sensing instrumented indentation with dual sharp indenters. Acta Materialia 51 (2003) 3713-3729
13. Constantinides G., Ulm F.-J., and can Vleit K.J. On the use of nanoindentation for cementitious materials. Mater. Struct. (special issue of Concr. Sci. Eng.) 205 (2003) 191-196
14. Constantinides G., and Ulm F.-J. The nanogranular nature of C-S-H. J. Mech. Phys. Solids 55 (2007) 64-90
15. Cowin S. Bone poroelasticity. J. Biomech. 32 (1999) 217-238
16. DiCarlo A., Yang H.T.Y., and Chandrasekar S. Semi-inverse method for predicting stress-strain relationship from cone indentations. J. Mater. Res. 18 9 (2003) 2068-2078
17. Donev A., Cisse I., Sachs D., Variano E.A., Stillinger F.H., Connely R., Torquato S., and Chaikin P.M. Improving the density of jammed disordered packings using ellipsoids. Science 303 (2004) 990-993
18. Dormieux L., Molinari A., and Kondo D. Micromechanical approach to the behaviour of poroelastic materials. J. Mech. Phys. Solids 50 (2002) 2203-2231
19. Dormieux L., Kondo D., and Ulm F.-J. Microporomechanics (2006), Wiley, Chichester, UK
20. Fremond, M., Salençon, J., 1973. Limit analysis by finite element methods. In: Palmer, A.C. (Ed.), Proceedings of Symposium on Role of Plasticity in Soil Mechanics, Cambridge, UK
21. Futakawa M., Wakui T., Tanabe Y., and Ioka I. Identification of the constitutive equation by the indentation technique using plural indenters with different apex angles. J. Mater. Res. 16 8 (2001) 2283-2292
22. Ganneau F.P., Constantinides G., and Ulm F.-J. Dual-indentation technique for the assessment of strength properties of cohesive-frictional material. Int. J. Solids Struct. 43 (2006) 1727-1745
23. Gologanu, M., Leblond, J.-B., Perrin, G., Devaux, J., 1997. Recent extensions of Gurson's model for porous ductile metals. In: Suquet, P. (Ed.), Continuum Micromechanics, CISM Courses and Lectures No. 377. Springer, Wien/New York, pp. 61-130.
24. Gurson A.L. Continuum theory of ductile rupture by void nucleation and growth: part I-yield criteria and flow rules for porous ductile media. ASME J. Eng. Mater. Technol. 99 (1977) 2-15
25. Hellmich C., and Ulm F.-J. Drained and undrained poroelastic properties of healthy and pathological bone: a poro-micromechanical investigation. Transport Porous Med. 58 (2005) 243-268
26. Hershey A.V. The elasticity of an isotropic aggregate of anisotropic cubic crystals. ASME J. Appl. Mech. 21 (1954) 236-240
27. Hill R. The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids 15 (1967) 79-95
28. Jaeger H.M., and Nagel S.R. Physics of granular state. Science 255 5051 (1992) 1523-1531
29. Jennings H.M. Colloid model of C-S-H and implications to the problem of creep and shrinkage. Mater. Struct. (special issue of Concr. Sci. Eng.) 37 265 (2004) 59-70
30. Johnson K.L. Contact Mechanics (1985), Cambridge University Press, Cambridge, UK (9th printing 2003)
31. Krabbenhoft K., Lyamin A.V., Hjiaj M., and Sloan S.W. A new discontinuous upper bound limit analysis formulation. Int. J. Numer. Methods Eng. 63 (2005) 1069-1088
32. Kreher W. Residual-stresses and stored elastic energy of composites and polycrystals. J. Mech. Phys. Solids 38 1 (1990) 115-128
33. Kröner E. Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls. Z. Phys. 151 (1958) 504-518
34. Leblond, J.-B., 2003. Mécanique de la rupture fragile et ductile. Etudes en mécanique des matériaux et des structures. Hermes Science Paris, France.
35. Locket F.J. Indentation of a rigid/plastic material by a conical indenter. J. Mech. Phys. Solids 11 (1963) 345
36. Lyamin A.V., and Sloan S.W. Lower bound limit analysis using non-linear programming. Int. J. Numer. Anal. Methods Geomech. 26 (2002) 181-216
37. Lyamin A.V., and Sloan S.W. Upper bound limit analysis using linear finite elements and non-linear programming. Int. J. Numer. Methods Eng. 55 (2002) 573-611
38. Lysmer L. Limit analysis of plane problems in soil mechanics. ASCE J. Soil Mech. Found. Div. 96 (1970) 1311-1334
39. Mori T., and Tanaka K. Average stress in matrix and average energy of materials with misfitting inclusions. Acta Metall. 21 (1973) 571-574
40. MOSEK ApS, Denmark, 2002. The MOSEK optimization tools version 2.5 (revision 51)-user's manual and reference . Download from 〈http://www.mosek.com/〉.
41. Nix W.D., and Gao H. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 55 (1998) 64-90
42. Onoda G.Y., and Liniger E.G. Random loose packings of uniform spheres and the dilatancy onset. Phys. Rev. Lett. 64 22 (1990) 2727-2730
43. Pastor, J., 1976. Application de l'analyse limite a l'etude de la stabilite des pentes et des talus. Ph.D. Dissertation, USMG, Grenoble, France.
44. Pastor J., and Turgeman S. Mise en oeuvre numerique des methodes de l'analyse limite pour les materiaux de Von Mises et de Coulomb standards en deformation plane. Mech. Res. Commun. 3 (1976) 469-476
45. Peng J., Roos C., and Terlaky T. Self-regularity: A New Paradigm for Primal-dual Interior Point Algorithms (2002), Princeton University Press, Oxford, Princeton, NJ
46. Renegar J. A mathematical view of interior-point methods in convex optimization. MPS-SIAM Series on Optimization (2001), SIAM, Philadelphia, PA
47. Richardson I.G. Tobermorite/jennite- and tobermorite/calcium hydroxide-based models for the structure of C-S-H: applicability to hardened pastes of tricalcium silicate, β-dicalcium silicate, Portland cement, and blends of Portland cement with blast-furnace slag, metakaolin, or silica fume. Cem. Concr. Res. 34 (2004) 1733-1777
48. Salençon, J., 1983. Calcul à la rupture et analyse limite. Presses de l'Ecole nationale des ponts et chaussées, Paris, France.
49. Scott T.E., and Abousleiman Y. Acoustic measurements of the anisotropy of dynamic elastic and poromechanics moduli under three stress/strain path. J. Eng. Mech. ASCE 131 9 (2005) 937-946
50. Sloan S.W. Lower bound limit analysis using finite elements and linear programming. Int. J. Numer. Anal. Methods Geomech. 12 (1988) 61-77
51. Sloan S.W. A steepest edge active set algorithm for solving sparse linear programming problems. Int. J. Numer. Anal. Methods Geomech. 12 (1988) 2671-2685
52. Sloan S.W., and Kleeman P.W. Upper bound limit analysis with discontinuous velocity fields. Comput. Methods Appl. Mech. Eng. 127 (1995) 293-314
53. Sloane N.J.A. Kepler's conjecture confirmed. Nature 395 (1998) 435-436
54. Suquet, P., 1982. Plasticité et homogénéisation. Thèse de Doctorat d'Etat, Université Pierre et Marie Curie, Paris, France.
55. Suquet, P., 1997. Effective properties of nonlinear composites. In: Suquet, P. (Ed.), Continuum Micromechanics, CISM Courses and Lectures No. 377. Springer, Wien/New York, pp. 197-264.
56. Swaddiwudhipong S., Tho K.K., Liu Z.S., and Zeng K. Material characterization based on dual indenters. Int. J. Solids Struct. 42 (2005) 69-83
57. Tabor D. A simple theory of static and dynamic hardness. Proc. R. Soc. London Ser. A 192 (1948) 247 (cited from Johnson, K.L., 1985. Contact Mechanics. Cambridge University Press, Cambridge, UK (9th printing 2003))
58. Tennis P.D., and Jennings H.M. A model for two types of calcium silicate hydrate in the microstructure of portland cement pastes. Cem. Concr. Res. 30 (2000) 855-863
59. Trillat M., and Pastor J. Limit analysis and Gurson's model. Eur. J. Mech. A/Solids 24 5 (2005) 800-819
60. Turgeman, S., 1976. Etude des fondations sollicitees a l'arrachement par la theorie de l'analyse limite. Ph.D. Dissertation, USMG, Grenoble, France.
61. Ulm F.-J., and Abousleiman Y. The nanogranular nature of shale. Acta Geotech. 1 (2006) 77-88
62. Ulm F.-J., Constantinides G., and Heukamp F.H. Is concrete a poromechanics material?-A multiscale investigation of poroelastic properties. Mater. Struct. (special issue of Concr. Sci. Eng.) 37 265 (2004) 43-58
63. Zaoui A. Continuum micromechanics: survey. J. Eng. Mech. (ASCE) 128 8 (2002) 808-816