참고문헌
- Abrams, D. (1918), Design of Concrete Mixtures, Structural Materials Research Laboratory, Lewis Institute, Chicago, USA.
- ACI Committee 318 (2008), Building code requirements for structural concrete (ACI 318-08) and commentary, American Concrete Institute.
- Bernard, O., UIm, F.J. and Lemarchand, E. (2003), "A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials", Cement. Concrete. Res., 33(9), 1293-1309. https://doi.org/10.1016/S0008-8846(03)00039-5
- Bary, B., Ben, M., Adam, E. and Montarnal, P (2009), "Numerical and analytical effective elastic properties of degraded cement pastes", Cement. Concrete. Res., 39(10), 902-912. https://doi.org/10.1016/j.cemconres.2009.06.012
- Bentz, D.P. (1995), A Three-Dimensional Cement Hydration and Microstructure Program. I. Hydration Rate, Heat of Hydration, and Chemical Shrinkage, NISTIR 5756, U.S. Department of Commerce.
- Bishnoi, S. and Scrivener, K.L. (2009a), "A new platform for modelling the hydration of cements", Cement. Concrete. Res., 39(4), 266-274. https://doi.org/10.1016/j.cemconres.2008.12.002
-
Bishnoi, S. and Scrivener, K.L. (2009b), "Studying nucleation and growth kinetics of alite hydration using
${\mu}ic$ ", Cement. Concrete. Res., 39(10), 849-860. https://doi.org/10.1016/j.cemconres.2009.07.004 - Bolomey, J. (1935), "Granulation et prevision de la resistance probable des betons", Travaux, 30, 228-232.
- Boumiz, A., Sorrentino, D., Vernet, C. and Tenoudji, F.C. (2000), "Modelling the development of the elastic moduli as a function of the hydration degree of cement pastes and mortars", RILEM Proceedings, PRO 13, Hydration and Setting: Why does Cement Set, an Interdisciplinary Approach, 295-316.
- Castaneda, P.P. and Willis, J.R. (1995), "The effect of spatial distribution on the effective behaviour of composite materials and cracked media", J. Mech. Phys. Solids., 43(12), 1919-1951. https://doi.org/10.1016/0022-5096(95)00058-Q
- Constantinides, G. and Ulm, F.J. (2004), "The effect of two types of C-S-H on the elasticity of cement-based materials: Results from nanoindentation and micromechanical modeling", Cement. Concrete. Res., 34(1), 67-80. https://doi.org/10.1016/S0008-8846(03)00230-8
- Courant, R. (1943), "Variational methods for the solution of problems of equilibrium and vibration", B. Am. Math. Soc., 49, 1-23.
- Do, H.Q., Bishnoi, S. and Scrivener, K.L. (2013), "Numerical simulation of porosity in cements", Transport. Porous. Med, 99(1), 101-117. https://doi.org/10.1007/s11242-013-0176-4
- Dunant, C.F., Bary, B., Giorla, A.B., Peniguel, C., Sanahuja, J., Toulemonde, C., Tran, A.B., Willot, F. and Yvonnet J. (2013), "A critical comparison of several numerical methods for computing effective properties of highly heterogeneous materials", Adv. Eng. Softw., 58, 1-12. https://doi.org/10.1016/j.advengsoft.2012.12.002
- EN 1992-1-1 (2004), Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings, CEN Technical Committee 250.
- Eshelby, J.D. (1957), "The determination of the elastic field of an ellipsoidal inclusion, and related problems", Proceedings of the Royal Society A, 241, 376-396. https://doi.org/10.1098/rspa.1957.0133
- Eshelby, J.D. (1959), "The elastic field outside an ellipsoidal inclusion", Proceedings of the Royal Society A, 252, 561-569. https://doi.org/10.1098/rspa.1959.0173
- Feret, R. (1892), "Sur Ie compacite des mortiers", Annales des Pants et Chaussees, 7, 5-164.
- Haecker, C.J., Garboczi, E.J., Bullard, J.W., Bohn, R.B., Sun, Z., Shah, S.P. and Voigt, T. (2005), "Modeling the linear elastic properties of Portland cement paste", Cement. Concrete. Res., 35(10), 1948-1960. https://doi.org/10.1016/j.cemconres.2005.05.001
- Hain, M. and Wriggers, P. (2008), "Numerical homogenization of hardened cement pastes", Comput. Mech., 42(2), 197-212. https://doi.org/10.1007/s00466-007-0211-9
- Hill, R. (1952), "The elastic behaviour of a crystalline aggregate", Proceedings of the Physical Society, 65, 349-354.
- Hill, R. (1965), "A self-consistent mechanics of composite materials", J. Mech. Phys. Solids., 13(4), 213-222. https://doi.org/10.1016/0022-5096(65)90010-4
- Hrennikoff, A.P. (1940), "Plane stress and bending of plates by method of articulated framework", Doctoral Dissertation, Massachusetts Institute of Technology, Boston.
- Huet, C. (1990), "Application of variational concepts to size effects in elastic heterogeneous bodies", Mech. Phys. Solids., 38(6), 813-841. https://doi.org/10.1016/0022-5096(90)90041-2
- Jennings, H.M. (2000), "A model for the microstructure of calcium silicate hydrate in cement paste", Cement. Concrete. Res., 30(1), 101-116. https://doi.org/10.1016/S0008-8846(99)00209-4
- Jennings, H.M. and Parrott, L.J. (1986), "Microstructural analysis of hardened alite paste, part II: microscopy and reaction products", J. Mater. Sci., 21(11), 4053-4059. https://doi.org/10.1007/BF02431651
- Mori, T and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta. Metall. Sin., 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
- Moulinec, H. and Suquet, P. (1994), "A fast numerical method for computing the linear and nonlinear properties of composites", Comptes Rendus de l'Academie des Sciences Paris, II, 318(11), 1417-1423.
- Nguyen, V.P., Stroeven, M. and Sluys, L.J. (2012a), "Multiscale failure modelling of concrete: micromechanical modelling, discontinuous homogenization and parallel computations", Comput. Method Appl. M., 201-204, 139-156. https://doi.org/10.1016/j.cma.2011.09.014
- Nguyen, V.P., Stroeven, M. and Sluys, L.J. (2012b), "Multiscale continuous and discontinuous modelling of heterogeneous materials: A review on recent developments", J. Multi. Model., 3(4), 1-42.
- Pichler, B., Hellmich, C. and Eberhardsteiner, J. (2009), "Spherical and acicular representation of hydrates in a micromechanical model for cement paste: prediction of early-age elasticity and strength", Acta. Mech., 203(3-4), 137-162. https://doi.org/10.1007/s00707-008-0007-9
- Powers, T.C. (1958), "Structure and physical properties of hardened portland cement paste", J. Am. Ceram. Soc., 41(1), 1-6.
- Reuss, A. (1929), "Berechnung der fliessgrenze von mischkristallen auf grund der plastizitatsbedingung fur einkristalle", J. Appl. Math. Mech., 9(1), 49-58.
- Sanahuja, J., Dormieux, L. and Chanvillard, G. (2007), "Modelling elasticity of a hydrating cement paste", Cement Concrete. Res., 37(10), 1427-1439. https://doi.org/10.1016/j.cemconres.2007.07.003
- Scherer, G.W, Zhang, J., Quintanilla, J.A. and Torquato, S. (2012), "Hydration and percolation at the setting point", Cement. Concrete. Res., 42(5), 665-672. https://doi.org/10.1016/j.cemconres.2012.02.003
- Smilauer, V. and Bittnar, Z. (2006), "Microstructure-based micromechanical prediction of elastic properties in hydrating cement paste", Cement. Concrete. Res., 36(9), 1708-1718. https://doi.org/10.1016/j.cemconres.2006.05.014
- Stefan, L.. Benboudjema. F., Torrenti. J.M. and Bissonnette, B. (2010), "Prediction of elastic properties of cement pastes at early ages", Comput. Mater. Sci. 47(3), 775-784. https://doi.org/10.1016/j.commatsci.2009.11.003
- Suquet, P. (1990), "A simplified method for the prediction of homogeneized elastici properties of composites with a periodic structure", Comptes Rendus de l'Academie des Sciences Paris, II, 311, 769-774.
- Thomas, J.J., Allen, A.J. and Jennings, H.M. (2009), "Hydration kinetics and microstructure development of normal and CaCl2-Accelerated tricalcium silicate pastes", J. Phys. Chem. C. 113(46), 19836-19844. https://doi.org/10.1021/jp907078u
- Vandamme, M. (2008), "The nanogranular origin of concrete creep: A nanoindentation investigation of microstructure and fundamental principles of calcium-silicate-hydrates", Doctoral Dissertation, Massachusetts Institute of Technology, Boston.
- Velez, K., Maximilien, S., Damidot, D., Fantozzi, G. and Sorrentino, F. (2001), "Determination by nanoindentation of elastic modulus and hardness of pure constituents of Portland cement clinker", Cement. Concrete. Res. 31(4), 555-561. https://doi.org/10.1016/S0008-8846(00)00505-6
- Voidt, W. (1887), "Theoretische studien uber die elasticitatsverhaltnisse der krystalle", Abhandlungen der Koniglichen Gesellschaft der Wissenschaften in Gottingen, 34, 3-51.
피인용 문헌
- Microstructural Modeling of Early-Age Creep in Hydrating Cement Paste vol.142, pp.11, 2016, https://doi.org/10.1061/(ASCE)EM.1943-7889.0001144
- Reduced-order modeling analysis of shell structures buckling using a co-rotational solid-shell element vol.70, 2017, https://doi.org/10.1016/j.ast.2017.08.036
- Microstructural modelling of the strength of mortars containing fly ash using µic vol.163, 2018, https://doi.org/10.1016/j.conbuildmat.2017.12.163
- Microstructural simulation and measurement of elastic modulus evolution of hydrating cement pastes vol.130, pp.None, 2015, https://doi.org/10.1016/j.cemconres.2020.106007
- Microstructural modelling of autogenous shrinkage in Portland cement paste at early age vol.37, pp.9, 2015, https://doi.org/10.1108/ec-08-2019-0353