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Original Articles

Stiffness and stress fluctuations in dental cement paste: a continuum micromechanics approach

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 3332-3350 | Received 29 Apr 2022, Accepted 29 Apr 2022, Published online: 23 May 2022

References

  • P. Laurent, J. Camps, M. De Méo, J. Déjou, and I. About , Induction of specific cell responses to a Ca3SiO5-based posterior restorative material, Dent Mater., vol. 24, no. 11, pp. 1486–1494, 2008. DOI: 10.1016/j.dental.2008.02.020.
  • P. Laurent, and J. Camps, Biodentine induces TGF-β1 release from human pulp cells and early dental pulp mineralization, Int. Endodon. J., vol. 45, no. 5, pp. 439–448, 2012. DOI: 10.1111/j.1365-2591.2011.01995.x
  • P. Dohnalík, B.L. Pichler, L. Zelaya-Lainez, O. Lahayne, G. Richard, and C. Hellmich, Micromechanics of dental cement paste, J. Mech. Behav. Biomed. Mater., vol. 124, pp. 104863, 2021. DOI: 10.1016/j.jmbbm.2021.104863.
  • G. Constantinides, and F.-J. Ulm, 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., vol. 34, no. 1, pp. 67–80, 2004. DOI: 10.1016/S0008-8846(03)00230-8.
  • G. Constantinides, The elastic properties of calcium leached cement pastes and mortars: A multi-scale investigation, Master’s thesis, Massachusetts Institute of Technology, 2002.
  • M. Miller, C. Bobko, M. Vandamme, and F.-J. Ulm, Surface roughness criteria for cement paste nanoindentation, Cement Concrete Res., vol. 38, no. 4, pp. 467–476, 2008. DOI: 10.1016/j.cemconres.2007.11.014.
  • E. Donnelly, S.P. Baker, A.L. Boskey, and M.C. van der Meulen, Effects of surface roughness and maximum load on the mechanical properties of cancellous bone measured by nanoindentation, J. Biomed. Mater. Res. A., vol. 77, no. 2, pp. 426–435, 2006. DOI: 10.1002/jbm.a.30633.
  • W.C. Oliver, and G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res., vol. 7, no. 6, pp. 1564–1583, 1992. DOI: 10.1557/JMR.1992.1564.
  • Q. Li, A.P. Hurt, and N.J. Coleman, The application of 29Si NMR spectroscopy to the analysis of calcium silicate-based cement using Biodentine as an example, JFB, vol. 10, no. 2, pp. 25, 2019. DOI: 10.3390/jfb10020025.
  • J. Taplin, A method for following the hydration reaction in Portland cement paste, Austral. J. Appl. Sci., vol. 10, pp. 329–345, 1959.
  • S. Diamond, and D. Bonen, Microstructure of hardened cement paste—a new interpretation, J. Am. Ceram. Soc., vol. 76, no. 12, pp. 2993–2999, 1993. DOI: 10.1111/j.1151-2916.1993.tb06600.x.
  • P.D. Tennis, and H.M. Jennings, A model for two types of calcium silicate hydrate in the microstructure of Portland cement pastes, Cement Concrete Res., vol. 30, no. 6, pp. 855–863, 2000. DOI: 10.1016/S0008-8846(00)00257-X.
  • H.M. Jennings, A model for the microstructure of calcium silicate hydrate in cement paste, Cement Concrete Res., vol. 30, no. 1, pp. 101–116, 2000. DOI: 10.1016/S0008-8846(99)00209-4.
  • M. Königsberger, C. Hellmich, and B. Pichler, Densification of C-S-H is mainly driven by available precipitation space, as quantified through an analytical cement hydration model based on NMR data, Cement Concrete Res., vol. 88, pp. 170–183, 2016. DOI: 10.1016/j.cemconres.2016.04.006.
  • Y. Ma, G. Ye, and J. Hu, Micro-mechanical properties of alkali-activated fly ash evaluated by nanoindentation, Construct. Build. Mater., vol. 147, pp. 407–416, 2017. DOI: 10.1016/j.conbuildmat.2017.04.176.
  • M. Königsberger, L. Zelaya-Lainez, O. Lahayne, B.L. Pichler, and C. Hellmich, Nanoindentation-probed Oliver-Pharr half-spaces in alkali-activated slag-fly ash pastes: Multimethod identification of microelasticity and hardness, Mech. Adv. Mater. Struct., vol. 2021, pp. 1–12, 2021. DOI: 10.1080/15376494.2021.1941450.
  • R.J. Hussey, and J. Wilson, Advanced Technical Ceramics Directory and Databook, Springer Science & Business Media, Berlin, Heidelberg, 1998.
  • B. Pichler, and C. Hellmich, Upscaling quasi-brittle strength of cement paste and mortar: A multi-scale engineering mechanics model, Cement Concrete Res., vol. 41, no. 5, pp. 467–476, 2011. DOI: 10.1016/j.cemconres.2011.01.010.
  • B. Budiansky, and R.J. O’Connell, Elastic moduli of a cracked solid, Int. J. Solids Struct., vol. 12, no. 2, pp. 81–97, 1976. DOI: 10.1016/0020-7683(76)90044-5.
  • V. Pensée, D. Kondo, and L. Dormieux, Micromechanical analysis of anisotropic damage in brittle materials, J. Eng. Mech., vol. 128, no. 8, pp. 889–897, 2002. DOI: 10.1061/(ASCE)0733-9399(2002)128:8(889).
  • Z. Hashin, Analysis of composite materials—a survey, J. Appl. Mech., vol. 50, no. 3, pp. 481–505, 1983. DOI: 10.1115/1.3167081.
  • M. Königsberger, B. Pichler, and C. Hellmich, Multiscale poro-elasticity of densifying calcium-silicate hydrates in cement paste: An experimentally validated continuum micromechanics approach, Int. J. Eng. Sci., vol. 147, pp. 103196, 2020. DOI: 10.1016/j.ijengsci.2019.103196.
  • R. Hill, Elastic properties of reinforced solids: Some theoretical principles, J. Mech. Phys. Solids, vol. 11, no. 5, pp. 357–372, 1963. DOI: 10.1016/0022-5096(63)90036-X.
  • R. Hill, Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, vol. 13, no. 2, pp. 89–101, 1965. DOI: 10.1016/0022-5096(65)90023-2.
  • R. Hill, A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, vol. 13, no. 4, pp. 213–222, 1965. DOI: 10.1016/0022-5096(65)90010-4.
  • A. Zaoui, Continuum micromechanics: Survey, J. Eng. Mech., vol. 128, no. 8, pp. 808–816, 2002. DOI: 10.1061/(ASCE)0733-9399(2002)128:8(808).
  • J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond.: Ser. A. 396, vol. 241, no. 1226, pp. 376, 1957. DOI: 10.1098/rspa.1957.0133
  • N. Laws, The determination of stress and strain concentrations at an ellipsoidal inclusion in an anisotropic material, J. Elasticity, vol. 7, no. 1, pp. 91–97, 1977. DOI: 10.1007/BF00041133.
  • L. Dormieux, D. Kondo, and F.-J. Ulm, Microporomechanics, John Wiley & Sons, Hoboken, NJ, 2006.
  • Q.-Z. Zhu, J. Shao, and D. Kondo, A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction effects, Eur. J. Mech. A. Solids, vol. 30, no. 3, pp. 316–325, 2011. DOI: 10.1016/j.euromechsol.2010.12.005.
  • B. Pichler, C. Hellmich, and H.A. Mang, A combined fracture-micromechanics model for tensile strain-softening in brittle materials, based on propagation of interacting microcracks, Int. J. Numer. Anal. Meth. Geomech., vol. 31, no. 2, pp. 111–132, 2007. DOI: 10.1002/nag.544.
  • V. Deudé, L. Dormieux, D. Kondo, and S. Maghous, Micromechanical approach to nonlinear poroelasticity: Application to cracked rocks, J. Eng. Mech., vol. 128, no. 8, pp. 848–855, 2002. DOI: 10.1061/(ASCE)0733-9399(2002)128:8(848).
  • M. Irfan-ul-Hassan, B. Pichler, R. Reihsner, and C. Hellmich, Elastic and creep properties of young cement paste, as determined from hourly repeated minute-long quasi-static tests, Cement Concrete Res., vol. 82, pp. 36–49, 2016. DOI: 10.1016/j.cemconres.2015.11.007.
  • D. Johnson, The triangular distribution as a proxy for the beta distribution in risk analysis, J. R. Statist. Soc. D., vol. 46, no. 3, pp. 387–398, 1997. DOI: 10.1111/1467-9884.00091.
  • M.A. Chaudhry, A. Qadir, M. Rafique, and S. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math., vol. 78, no. 1, pp. 19–32, 1997. DOI: 10.1016/S0377-0427(96)00102-1.
  • O. Bernard, F.-J. Ulm, and E. Lemarchand, A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials, Cement Concrete Res., vol. 33, no. 9, pp. 1293–1309, 2003. DOI: 10.1016/S0008-8846(03)00039-5.
  • E. Stora, Q.-C. He, and B. Bary, Influence of inclusion shapes on the effective linear elastic properties of hardened cement pastes, Cement Concrete Res., vol. 36, no. 7, pp. 1330–1344, 2006. DOI: 10.1016/j.cemconres.2006.02.007.
  • J. Sanahuja, L. Dormieux, and G. Chanvillard, Modelling elasticity of a hydrating cement paste, Cement Concrete Res., vol. 37, no. 10, pp. 1427–1439, 2007. DOI: 10.1016/j.cemconres.2007.07.003.
  • B. Pichler, C. Hellmich, and J. Eberhardsteiner, Spherical and acicular representation of hydrates in a micromechanical model for cement paste: Prediction of early-age elasticity and strength, Acta Mech., vol. 203, no. 3–4, pp. 137–162, 2009. DOI: 10.1007/s00707-008-0007-9.
  • G. Constantinides, F.-J. Ulm, and K. Van Vliet, On the use of nanoindentation for cementitious materials, Mat. Struct., vol. 36, no. 3, pp. 191–196, 2003. DOI: 10.1007/BF02479557.
  • M. Vandamme, and F.-J. Ulm, Nanogranular origin of concrete creep, Proc. Natl. Acad. Sci. U. S. A., vol. 106, no. 26, pp. 10552–10557, 2009. DOI: 10.1073/pnas.0901033106.
  • J.J. Chen, L. Sorelli, M. Vandamme, F.-J. Ulm, and G. Chanvillard, A coupled nanoindentation/SEM-EDS study on low water/cement ratio Portland cement paste: Evidence for C-S-H/Ca(OH)2 nanocomposites, J. Am. Ceram. Soc., vol. 93, no. 5, pp. 1484–1493, 2010. DOI: 10.1111/j.1551-2916.2009.03599.x.
  • W. Da Silva, J. Němeček, and P. Štemberk, Methodology for nanoindentation-assisted prediction of macroscale elastic properties of high performance cementitious composites, Cement Concrete Res., vol. 45, pp. 57–68, 2014. DOI: 10.1016/j.cemconcomp.2013.09.013.
  • L. Brown, P.G. Allison, and F. Sanchez, Use of nanoindentation phase characterization and homogenization to estimate the elastic modulus of heterogeneously decalcified cement pastes, Mater. Des., vol. 142, pp. 308–318, 2018. DOI: 10.1016/j.matdes.2018.01.030.
  • E. Ford, A. Arora, B. Mobasher, C.G. Hoover, and N. Neithalath, Elucidating the nano-mechanical behavior of multi-component binders for ultra-high performance concrete, Construct. Build. Mater., vol. 243, pp. 118214, 2020. DOI: 10.1016/j.conbuildmat.2020.118214.
  • L. Sorelli, G. Constantinides, F.-J. Ulm, and F. Toutlemonde, The nano-mechanical signature of ultra high performance concrete by statistical nanoindentation techniques, Cement Concrete Res., vol. 38, no. 12, pp. 1447–1456, 2008. DOI: 10.1016/j.cemconres.2008.09.002.
  • J. Němeček, V. Králík, and J. Vondřejc, Micromechanical analysis of heterogeneous structural materials, Cement Concrete Compos., vol. 36, pp. 85–92, 2013. DOI: 10.1016/j.cemconcomp.2012.06.015.
  • L. Göbel, C. Bos, R. Schwaiger, A. Flohr, and A. Osburg, Micromechanics-based investigation of the elastic properties of polymer-modified cementitious materials using nanoindentation and semi-analytical modeling, Cement Concrete Compos., vol. 88, pp. 100–114, 2018. DOI: 10.1016/j.cemconcomp.2018.01.010.
  • Y. Li, P. Wang, and Z. Wang, Evaluation of elastic modulus of cement paste corroded in bring solution with advanced homogenization method, Construct. Build. Mater., vol. 157, pp. 600–609, 2017. DOI: 10.1016/j.conbuildmat.2017.09.133.
  • X. Gao, Y. Wei, and W. Huang, Effect of individual phases on multiscale modeling mechanical properties of hardened cement paste, Construct. Build. Mater., vol. 153, pp. 25–35, 2017. DOI: 10.1016/j.conbuildmat.2017.07.074.
  • Y. Li, Y. Liu, and R. Wang, Evaluation of the elastic modulus of concrete based on indentation test and multi-scale homogenization method, J. Build. Eng., vol. 43, pp. 102758, 2021. DOI: 10.1016/j.jobe.2021.102758.
  • D. Stefaniuk, P. Niewiadomski, M. Musial, and D. Lydzba, Elastic properties of self-compacting concrete modified with nanoparticles: Multiscale approach, Arch. Civil Mech. Eng., vol. 19, no. 4, pp. 1150–1162, 2019. DOI: 10.1016/j.acme.2019.06.006.
  • S. Liang, Y. Wei, and Z. Wu, Multiscale modeling elastic properties of cement-based materials considering imperfect interface effect, Construct. Build. Mater., vol. 154, pp. 567–579, 2017. DOI: 10.1016/j.conbuildmat.2017.07.196.
  • D. Damien, Y. Wang, and Y. Xi, Prediction of elastic properties of cementitious materials based on multiphase and multiscale micromechanics theory, J. Eng. Mech., vol. 145, no. 10, pp. 04019074, 2019. DOI: 10.1061/(ASCE)EM.1943-7889.0001650.
  • Y. Benveniste, A new approach to the application of Mori-Tanaka’s theory in composite materials, Mech. Mater., vol. 6, no. 2, pp. 147–157, 1987. DOI: 10.1016/0167-6636(87)90005-6.
  • C. Kohlhauser, and C. Hellmich, Ultrasonic contact pulse transmission for elastic wave velocity and stiffness determination: Influence of specimen geometry and porosity, Eng. Struct., vol. 47, pp. 115–133, 2013. DOI: 10.1016/j.engstruct.2012.10.027.
  • W. Drugan, and J. Willis, A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, J. Mech. Phys. Solids, vol. 44, no. 4, pp. 497–524, 1996. DOI: 10.1016/0022-5096(96)00007-5.
  • V. Pensée, and Q.-C. He, Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media, Int. J. Solids Struct., vol. 44, no. 7-8, pp. 2225–2243, 2007. DOI: 10.1016/j.ijsolstr.2006.07.003.
  • C. Kohlhauser, and C. Hellmich, Determination of Poisson’s ratios in isotropic, transversely isotropic, and orthotropic materials by means of combined ultrasonic-mechanical testing of normal stiffnesses: Application to metals and wood, Eur. J. Mech. A Solids, vol. 33, pp. 82–98, 2012. DOI: 10.1016/j.euromechsol.2011.11.009.
  • J.M. Carcione, Wave fields in real media: Wave propagation in anisotropic, anelastic, porous and electromagnetic media, Elsevier, New York, NY, 2007.
  • J. Achenbach, Wave propagation in elastic solids, One-dimensional motion of an elastic continuum, Elsevier, New York, NY, 1973.