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References

1

Jennings, H.M., and Xi, Y., "Microstructurally Based Mechanisms for Modeling Shrinkage of Cement Paste at Multiple Levels," Creep and Shrinkage of Concrete, ed. Z.P. Bazant and I. Carol, (E and FN Spon, London 1994), pp. 85-102.

2

Garboczi, E.J., "Computational Materials Science of Cement Based Materials," Materials and Structures, 26, 1993, pp. 191-195.

3

Bentz, D.P.; Quenard, D.A.; Baroghel-Bouny, V.; Garboczi, E.J.; and Jennings, H.M., "Modelling Drying Shrinkage of Cement Paste and Mortar: Part 1. Structural Models from Nanometers to Millimeters," Materials and Structures 28, 450-458 (1995).

4

D.P. Bentz, E.J. Garboczi, and D.A. Quenard, "Modelling drying shrinkage in porous materials: Application to porous Vycor glass," Mod. and Sim. in Mater. Eng. and Sci., 6, 211-236 (1998).

5

Mura, T., Micromechanics of Defects in Solids, Second Edition, (Martinus Nijhoff, Hingham, MA, 1987).

6

Hashin, Z., "Analysis of Composite Materials-A Survey," Journal of Applied Mechanics, 50, 1983, pp. 481-505.

7

Garboczi, E.J., and Day, A.R., "An Algorithm for Computing the Effective Linear Elastic Properties of Heterogeneous Materials: 3-D Results for Composites with Equal Phase Poisson Ratios," J. Mech. Phys. Solids 43, 1349-1362 (1995).

8

Bentz, D.P.; Coveney, P.V.; Garboczi, E.J.; Kleyn, M.F.; and Stutzman, P.E., "Computer Automaton Simulations of Cement Hydration and Microstructure Development," Modelling and Simulations in Materials Science and Engineering, 2, 1994, pp. 783-808;

D.P. Bentz and E.J. Garboczi, NISTIR 4746, "Guide to Using HYDRA3D: A Three-Dimensional Digital-Image-Based Cement Microstructural Model" (1992) (Updated manual).

9

Eischen, J.W., and Torquato, S., "Determining Elastic Behavior of Composites by the Boundary Element Method," Journal of Applied Physics, 74 (1), 1993, pp. 159-170.

10

Scrivener, K.L., "The Microstructure of Concrete," Materials Science of Concrete I, ed. J.P. Skalny, (American Ceramic Society, Westerville OH, 1989), pp. 127-161.

11

Bentz, D.P.; Schlangen, E.; and Garboczi, E.J., "Computer Simulation of Interfacial Zone Microstructure and Its Effect on the Properties of Cement-Based Composites," in Materials Science of Concrete IV, ed. J.P. Skalny and S. Mindess, (American Ceramic Society, Westerville OH, 1995).

12

Winslow, D.N.; Cohen, M.D.; Bentz, D.P.; Snyder, K.A.; and Garboczi, E.J., "Percolation and Porosity in Mortars and Concretes," Cem. and Conc. Res., 24, 1994, pp. 25-37.

13

Schlangen, E., and van Mier, J.G.M., "Fracture Modelling of Granular Materials," Computational Methods in Materials Science, ed. J.E. Mark, M.E. Glicksman, and S.P. Marsh, (MRS Symposium Proceedings, Vol. 278, Pittsburgh PA), pp. 153-158.

14

Garboczi, E.J.; Bentz, D.P.; and Schwartz, L.M., "Modelling the Influence of the Interfacial Zone on the DC Electrical Conductivity of Mortar," J. of Adv. Cem. Bas. Mat. 2, 169- 181 (1995).

15

Zimmerman, R.W.; King, M.S.; and Monteiro, P.J.M., "The Elastic Moduli of Mortar as a Porous-Granular Material," Cem. Conc. Res., 16, 1986, pp. 239-245.

16

Hashin, Z., and Shtrikman, S., "A Variational Approach to the Elastic Behaviour of Multiphase Materials," J. Mech. Phs. Solids, 11, 1963, pp. 127-140.

17

Thorpe, M.F., and Sen, P.N., "Elastic Moduli of Two-Dimensional Composite Continua with Elliptical Inclusions," J. Acoust. Soc. Am., 77, 1985, pp. 1674-1680.

18

Snyder, K.A.; Garboczi, E.J.; and Day, A.R., "The Elastic Moduli of Simple Two- Dimensional Isotropic Composites: Computer Simulation and Effective Medium Theory," J. Appl. Phys., 72 (12), 1992, pp. 5948-5955.

19

Rosen, B.W. and Hashin, Z., "Effective Thermal Expansion Coefficients and Specific Heats of Composite Materials," Int. J. Engng. Sci., 8, 1970, pp. 157-173.

20

Nilsen, A.U. and Monteiro, P.J.M., "Concrete: A Three Phase Material," Cement and Concrete Research, 23, 1993, pp. 147-151.

21

Le Roy, R. and de Larrard, F., Discussion on "Concrete: A Three Phase Material," Cement and Concrete Research, 24, 1994, pp. 189-193.

22

Cohen, M.D.; Goldman, A.; and Chen. W-F., "The Role of Silica Fume in Mortar: Transition Zone vs. Bulk Paste Modification," Cement and Concrete Research, 24, 1994, pp. 95- 98.

23

Helmuth, R.A., and Turk, D.H., "Elastic moduli of hardened portland cement and tricalcium silicate pastes: Effect of porosity," Highw. Res. Board, Spec. Rep., 90, 1966, 135-144.

24

D.P. Bentz, E.J. Garboczi, and P.E. Stutzman, "Computer modelling of the interfacial zone in concrete," Interfaces in Cementitious Composites, ed. J. Maso (E. and F. Spon, London, 1993), pp. 107-116.

25

Mindess, S., "Interfaces in Concrete," Materials Science of Concrete I, ed. J.P. Skalny, (American Ceramic Society, Westerville OH, 1989), pp. 163-180.

26

Scrivener, K.L., and Gartner, E.M., "Microstructural Gradients in Cement Paste around Aggregate Particles," Bonding in Cementitious Composites, ed. S. Mindess and S.P. Shah, (Materials Research Society, Pittsburgh PA, 1987), pp. 77-85.

27

A.I. Rashed and R.B Williamson, J. Mater. Res. 6, pp. 2004-20012 (1991).

28

Pickett, G., "Effect of Aggregate on Shrinkage of Concrete and a Hypothesis Concerning Shrinkage," J. Am. Concr. Inst, 52 (5), 1956, pp. 581-590.

29

Hansen, W., "Constitutive Model for Predicting Ultimate Drying Shrinkage of Concrete," J. Am. Ceram. Soc., 70 (5), 1987, pp. 329-332.

30

Garboczi, E.J., and Bentz, D.P., "Digital Simulation of the Aggregate-Cement Paste Interfacial Zone in Concrete," J. Mater. Res., 6 (1), 1991, pp. 196-201.

31

Bentz, D.P.; Stutzman, P.E.; and Garboczi, E.J., "Experimental and Simulation Studies of the Interfacial Zone in Concrete," Cem. Concr. Res., 22 (5), 1992, pp. 891-902.

32

Bentz, D.P., and Garboczi, E.J., "Simulation Studies of the Effects of Mineral Admixtures on the Cement Paste-Aggregate Interfacial Zone," ACI Mat. J., 88 (5), 1991, pp. 518-529.

33

Coverdale, R.T., "Microstructural Analysis of Cement Paste Using a Computer Model of Impedance Spectroscopy," Ph.D. Thesis, Northwestern University, 1991.

34

Birchall, J.D.; Howard, A.J.; and Bailey, J.E., "On the Hydration of Portland Cement," Proc. R. Soc. Lond., A360, 1978, pp. 445-453.

35

Kittel, C. Introduction to Solid State Physics, (John Wiley and Sons, New York, 1986), pp. 75.

36

Breton, D., Carles-Gibergues, A., Ballivy, G., and Grandet, J., "Contribution to the Formation Mechanism of the Transition Zone Between Rock and Cement Paste,", Cem. Conc. Res. 23, 1993, pp. 335-346.

37

Bourdette, B., Ringot, E., and Ollivier, J.P., "Modelling of the Transition Zone Porosity," submitted to Cem. Conc. Res.

38

Monteiro, P.J.M.; Maso, J.C.; and Ollivier, J.P., "The Aggregate-Mortar Interface," Cem. Concr. Res., 15, 1985, pp. 953-958.

39

Detwiler, R.J.; Monteiro, P.J.M.; Wenk, H.R.; and Zhong, Z., "Texture of calcium hydroxide near the cement paste-aggregate interface," Cem. Concr. Res., 18, 1989, pp. 823-829.

40

Watt, J.P. and Peselnick, L., "Clarification of the Hashin-Shtrikman Bounds on the Effective Elastic Moduli of Polycrystals with Hexagonal, Trigonal, and Tetragonal Symmetries," J. Appl. Phys., 51, 1980, pp. 1525-1531.

41

Holuj, F.; Drozdowski, M.; and Czajkowski, M., "Brillouin Spectrum of Ca(OH)2," Solid State Communications, 56, 1985, pp. 1019-1021.

42

Wittman, F.H., "Estimation of the Modulus of Elasticity of Calcium Hydroxide," Cem. and Conc. Res., 16, 1986, pp. 971-972.

43

E.J. Garboczi and D.P. Bentz, "Analytical formulas for interfacial transition zone properties," J. Adv. Cement-Based Mat., 6, 1997, pp. 99-108.

44

M.P. Lutz and P.J.M. Monteiro, "Effect of the transition zone on the bulk modulus of concrete," in Microstructure of Cement-Based Systems/Bonding and Interfaces in Cementitious Materials, edited by S. Diamond, S. Mindess, F.P. Glasser, L.W. Roberts, J.P. Skalny, and L.D. Wakeley, Vol. 370 (Materials Research Society, Pittsburgh, 1995), pp. 413-418.