Full Text:   <558>

Summary:  <171>

CLC number: 

On-line Access: 2024-02-01

Received: 2023-09-19

Revision Accepted: 2023-11-27

Crosschecked: 2024-02-01

Cited: 0

Clicked: 1323

Citations:  Bibtex RefMan EndNote GB/T7714


Shengwen TANG


-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2024 Vol.25 No.2 P.97-115


Stress relaxation properties of calcium silicate hydrate: a molecular dynamics study

Author(s):  Zhicheng GENG, Shengwen TANG, Yang WANG, Hubao A, Zhen HE, Kai WU, Lei WANG

Affiliation(s):  State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan 430072, China; more

Corresponding email(s):   tangsw@whu.edu.cn

Key Words:  Calcium silicate hydrate (C-S-H), Stress relaxation, Ca/Si ratio, Temperature, Water content, Atomic simulation

Share this article to: More |Next Article >>>

Zhicheng GENG, Shengwen TANG, Yang WANG, Hubao A, Zhen HE, Kai WU, Lei WANG. Stress relaxation properties of calcium silicate hydrate: a molecular dynamics study[J]. Journal of Zhejiang University Science A, 2024, 25(2): 97-115.

@article{title="Stress relaxation properties of calcium silicate hydrate: a molecular dynamics study",
author="Zhicheng GENG, Shengwen TANG, Yang WANG, Hubao A, Zhen HE, Kai WU, Lei WANG",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Stress relaxation properties of calcium silicate hydrate: a molecular dynamics study
%A Zhicheng GENG
%A Shengwen TANG
%A Yang WANG
%A Hubao A
%A Zhen HE
%A Kai WU
%J Journal of Zhejiang University SCIENCE A
%V 25
%N 2
%P 97-115
%@ 1673-565X
%D 2024
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2300476

T1 - Stress relaxation properties of calcium silicate hydrate: a molecular dynamics study
A1 - Zhicheng GENG
A1 - Shengwen TANG
A1 - Yang WANG
A1 - Hubao A
A1 - Zhen HE
A1 - Kai WU
A1 - Lei WANG
J0 - Journal of Zhejiang University Science A
VL - 25
IS - 2
SP - 97
EP - 115
%@ 1673-565X
Y1 - 2024
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2300476

The time-dependent viscoelastic response of cement-based materials to applied deformation is far from fully understood at the atomic level. calcium silicate hydrate (C-S-H), the main hydration product of Portland cement, is responsible for the viscoelastic mechanism of cement-based materials. In this study, a molecular model of C-S-H was developed to explain the stress relaxation characteristics of C-S-H at different initial deformation states, ca/Si ratios, temperatures, and water contents, which cannot be accessed experimentally. The stress relaxation of C-S-H occurs regardless of whether it is subjected to initial shear, tensile, or compressive deformation, and shows a heterogeneous characteristic. Water plays a crucial role in the stress relaxation process. A large ca/Si ratio and high temperature reduce the cohesion between the calcium-silicate layer and the interlayer region, and the viscosity of the interlayer region, thereby accelerating the stress relaxation of C-S-H. The effect of the hydrogen bond network and the morphology of C-S-H on the evolution of the stress relaxation characteristics of C-S-H at different water contents was elucidated by nonaffine mean squared displacement. Our results shed light on the stress relaxation characteristics of C-S-H from a microscopic perspective, bridging the gap between the microscopic phenomena and the underlying atomic-level mechanisms.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Abdolhosseini QomiMJ, KrakowiakKJ, BauchyM, et al., 2014. Combinatorial molecular optimization of cement hydrates. Nature Communications, 5:4960.

[2]AlizadehR, BeaudoinJJ, RakiL, 2010. Viscoelastic nature of calcium silicate hydrate. Cement and Concrete Composites, 32(5):369-376.

[3]AllenAJ, ThomasJJ, JenningsHM, 2007. Composition and density of nanoscale calcium‍–‍silicate‍–‍hydrate in cement. Nature Materials, 6(4):311-316.

[4]ArayroJ, DufresneA, ZhouTT, et al., 2018. Thermodynamics, kinetics, and mechanics of cesium sorption in cement paste: a multiscale assessment. Physical Review Materials, 2(5):053608.

[5]AtutisM, ValivonisJ, AtutisE, 2018. Experimental study of concrete beams prestressed with basalt fiber reinforced polymers. Part II: stress relaxation phenomenon. Composite Structures, 202:344-354.

[6]BazantZP, ChernJC, 1985. Concrete creep at variable humidity: constitutive law and mechanism. Materials and Structures, 18(1):1-20.

[7]BažantZP, HauggaardAB, BawejaS, et al., 1997. Microprestress-solidification theory for concrete creep. I: aging and drying effects. Journal of Engineering Mechanics, 123(11):1188-1194.

[8]BeushausenH, MasukuC, MoyoP, 2012. Relaxation characteristics of cement mortar subjected to tensile strain. Materials and Structures, 45(8):1181-1188.

[9]BrooksJJ, NevilleAM, 1976. Relaxation of stress in concrete and its relation to creep. Journal Proceedings, 73(4):‍227-232.

[10]ChenJ, FangL, ChenHQ, et al., 2022. The loading speed facilitating stress relaxation behaviors of surface-modified silicon: a molecular dynamics study. Journal of Molecular Modeling, 28(6):160.

[11]ChenJK, QianC, 2017. Loading history dependence of retardation time of calcium-silicate-hydrate. Construction and Building Materials, 147:558-565.

[12]CiarellaS, SciortinoF, EllenbroekWG, 2018. Dynamics of vitrimers: defects as a highway to stress relaxation. Physical Review Letters, 121(5):058003.

[13]ConstantinidesG, UlmFJ, 2004. The effect of two types of C-S-H on the elasticity of cement-based materials: results from nanoindentation and micromechanical modeling. Cement and Concrete Research, 34(1):67-80.

[14]ConstantinidesG, UlmFJ, 2007. The nanogranular nature of C-S-H. Journal of the Mechanics and Physics of Solids, 55(1):64-90.

[15]CuestaA, SantacruzI, de la TorreAG, et al., 2021. Local structure and Ca/Si ratio in C-S-H gels from hydration of blends of tricalcium silicate and silica fume. Cement and Concrete Research, 143:106405.

[16]CyganRT, LiangJJ, KalinichevAG, 2004. Molecular models of hydroxide, oxyhydroxide, and clay phases and the development of a general force field. The Journal of Physical Chemistry B, 108(4):1255-1266.

[17]DingH, ChenJK, 2019. Research on the resistivity attenuation law of cementitious conductive composites induced by stress relaxation. Construction and Building Materials, 206:347-354.

[18]DuHJ, PangSD, 2021. Long-term influence of nanosilica on the microstructures, strength, and durability of high-volume fly ash mortar. Journal of Materials in Civil Engineering, 33(8):04021185.

[19]FalkML, LangerJS, 1998. Dynamics of viscoplastic deformation in amorphous solids. Physical Review E, 57(6):7192-7205.

[20]FangGH, ZhangMZ, 2020. Multiscale micromechanical analysis of alkali-activated fly ash-slag paste. Cement and Concrete Research, 135:106141.

[21]FeldmanRF, 1972. Mechanism of creep of hydrated Portland cement paste. Cement and Concrete Research, 2(5):‍521-540.

[22]FengD, LiXF, WangXZ, et al., 2018. Capillary filling under nanoconfinement: the relationship between effective viscosity and water-wall interactions. International Journal of Heat and Mass Transfer, 118:900-910.

[23]Frech-BaronetJ, SorelliL, CharronJP, 2017. New evidences on the effect of the internal relative humidity on the creep and relaxation behaviour of a cement paste by micro-indentation techniques. Cement and Concrete Research, 91:39-51.

[24]FuQ, XieYJ, LongGC, et al., 2015. Temperature sensitivity and model of stress relaxation properties of cement and asphalt mortar. Construction and Building Materials, 84:1-11.

[25]GallucciE, ZhangX, ScrivenerKL, 2013. Effect of temperature on the microstructure of calcium silicate hydrate (C-S-H). Cement and Concrete Research, 53:185-195.

[26]GaoY, ZhangJ, HanP, 2013. Determination of stress relaxation parameters of concrete in tension at early-age by ring test. Construction and Building Materials, 41:152-164.

[27]GiorlaAB, DunantCF, 2018. Microstructural effects in the simulation of creep of concrete. Cement and Concrete Research, 105:44-53.

[28]GowersRJ, CarboneP, 2015. A multiscale approach to model hydrogen bonding: the case of polyamide. The Journal of Chemical Physics, 142(22):224907.

[29]HanGZ, FangZK, ChenMD, 2010. Modified Eyring viscosity equation and calculation of activation energy based on the liquid quasi-lattice model. Science China Physics, Mechanics and Astronomy, 53(10):1853-1860.

[30]HouDS, MaHY, YuZ, et al., 2014a. Calcium silicate hydrate from dry to saturated state: structure, dynamics and mechanical properties. Acta Materialia, 67:81-94.

[31]HouDS, ZhuY, LuYY, et al., 2014b. Mechanical properties of calcium silicate hydrate (C-S-H) at nano-scale: a molecular dynamics study. Materials Chemistry and Physics, 146(3):503-511.

[32]HouDS, ZhaoTJ, MaHY, et al., 2015a. Reactive molecular simulation on water confined in the nanopores of the calcium silicate hydrate gel: structure, reactivity, and mechanical properties. The Journal of Physical Chemistry C, 119(3):1346-1358.

[33]HouDS, ZhangJR, LiZJ, et al., 2015b. Uniaxial tension study of calcium silicate hydrate (C-S-H): structure, dynamics and mechanical properties. Materials and Structures, 48(11):3811-3824.

[34]HouDS, LiZJ, ZhaoTJ, et al., 2015c. Water transport in the nano-pore of the calcium silicate phase: reactivity, structure and dynamics. Physical Chemistry Chemical Physics, 17(2):1411-1423.

[35]HouDS, YuJ, JinZQ, et al., 2018a. Molecular dynamics study on calcium silicate hydrate subjected to tension loading and water attack: structural evolution, dynamics degradation and reactivity mechanism. Physical Chemistry Chemical Physics, 20(16):11130-11144.

[36]HouDS, JiaYT, YuJ, et al., 2018b. Transport properties of sulfate and chloride ions confined between calcium silicate hydrate surfaces: a molecular dynamics study. The Journal of Physical Chemistry C, 122(49):28021-28032.

[37]JanaR, PastewkaL, 2019. Correlations of non-affine displacements in metallic glasses through the yield transition. Journal of Physics: Materials, 2(4):045006.

[38]JenningsHM, 2004. Colloid model of C-S-H and implications to the problem of creep and shrinkage. Materials and Structures Aims, 37(1):59-70.

[39]KaiMF, ZhangLW, LiewKM, 2021. New insights into creep characteristics of calcium silicate hydrates at molecular level. Cement and Concrete Research, 142:106366.

[40]LiB, LiN, BrouwersHJH, et al., 2020. Understanding hydrogen bonding in calcium silicate hydrate combining solid-state NMR and first principle calculations. Construction and Building Materials, 233:117347.

[41]LiJ, YuQJ, HuangHL, et al., 2019. Effects of Ca/Si ratio, aluminum and magnesium on the carbonation behavior of calcium silicate hydrate. Materials, 12(8):1268.

[42]LiX, GrasleyZC, GarbocziEJ, et al., 2015. Modeling the apparent and intrinsic viscoelastic relaxation of hydrating cement paste. Cement and Concrete Composites, 55:‍322-330.

[43]LiXD, GrasleyZC, BullardJW, et al., 2018. Creep and relaxation of cement paste caused by stress-induced dissolution of hydrated solid components. Journal of the American Ceramic Society, 101(9):4237-4255.

[44]LiZM, ZhangSZ, LiangXH, et al., 2020. Cracking potential of alkali-activated slag and fly ash concrete subjected to restrained autogenous shrinkage. Cement and Concrete Composites, 114:103767.

[45]LiangCY, ZhengQ, JiangJY, et al., 2022. Calcium silicate hydrate colloid at different humidities: microstructure, deformation mechanism, and mechanical properties. Acta Materialia, 228:117740.

[46]LiuWH, ZhangLW, LiewKM, 2020. Modeling of crack bridging and failure in heterogeneous composite materials: a damage-plastic multiphase model. Journal of the Mechanics and Physics of Solids, 143:104072.

[47]LothenbachB, ScrivenerK, HootonRD, 2011. Supplementary cementitious materials. Cement and Concrete Research, 41(12):1244-1256.

[48]ManzanoH, PellenqRJM, UlmFJ, et al., 2012. Hydration of calcium oxide surface predicted by reactive force field molecular dynamics. Langmuir, 28(9):4187-4197.

[49]ManzanoH, MasoeroE, Lopez-ArbeloaI, et al., 2013. Shear deformations in calcium silicate hydrates. Soft Matter, 9(30):7333-7341.

[50]MaruyamaI, IgarashiG, NishiokaY, 2015. Bimodal behavior of C-S-H interpreted from short-term length change and water vapor sorption isotherms of hardened cement paste. Cement and Concrete Research, 73:158-168.

[51]MasoumiS, ZareS, ValipourH, et al., 2019. Effective interactions between calcium‍-silicate-hydrate nanolayers. The Journal of Physical Chemistry C, 123(8):4755-4766.

[52]MorshedifardA, MasoumiS, Abdolhosseini QomiMJ, 2018. Nanoscale origins of creep in calcium silicate hydrates. Nature Communications, 9(1):1785.

[53]MortazaviB, JavvajiB, ShojaeiF, et al., 2021a. Exceptional piezoelectricity, high thermal conductivity and stiffness and promising photocatalysis in two-dimensional MoSi2N4 family confirmed by first-principles. Nano Energy, 82:105716.

[54]MortazaviB, SilaniM, PodryabinkinEV, et al., 2021b. First-principles multiscale modeling of mechanical properties in graphene/borophene heterostructures empowered by machine-learning interatomic potentials. Advanced Materials, 33(35):2102807.

[55]PellenqRJM, KushimaA, ShahsavariR, et al., 2009. A realistic molecular model of cement hydrates. Proceedings of the National Academy of Sciences of the United States of America, 106(38):16102-16107.

[56]PitmanMC, van DuinACT, 2012. Dynamics of confined reactive water in smectite clay‍–‍zeolite composites. Journal of the American Chemical Society, 134(6):3042-3053.

[57]PriezjevNV, 2017. Collective nonaffine displacements in amorphous materials during large-amplitude oscillatory shear. Physical Review E, 95(2):023002.

[58]RichardsonIG, 1999. The nature of C-S-H in hardened cements. Cement and Concrete Research, 29(8):1131-1147.

[59]RongH, DongW, ZhaoXY, et al., 2021. Investigation on multi-cracks initiation and propagation of fiber reinforced concrete in restrained shrinkage ring tests. Theoretical and Applied Fracture Mechanics, 111:102856.

[60]RossiP, 1997. Strain rate effects in concrete structures: the LCPC experience. Materials and Structures, 30(1):54-62.

[61]ScrivenerKL, KirkpatrickRJ, 2008. Innovation in use and research on cementitious material. Cement and Concrete Research, 38(2):128-136.

[62]ShahsavariR, PellenqRJM, UlmFJ, 2011. Empirical force fields for complex hydrated calcio-silicate layered materials. Physical Chemistry Chemical Physics, 13(3):‍1002-1011.

[63]ShimizuF, OgataS, LiJ, 2007. Theory of shear banding in metallic glasses and molecular dynamics calculations. Materials Transactions, 48(11):2923-2927.

[64]ShishegaranA, KhaliliMR, KaramiB, et al., 2020. Computational predictions for estimating the maximum deflection of reinforced concrete panels subjected to the blast load. International Journal of Impact Engineering, 139:103527.

[65]TalebiH, SilaniM, BordasSPA, et al., 2014. A computational library for multiscale modeling of material failure. Computational Mechanics, 53(5):1047-1071.

[66]TamtsiaBT, BeaudoinJJ, 2000. Basic creep of hardened cement paste: a re-examination of the role of water. Cement and Concrete Research, 30(9):1465-1475.

[67]TangC, WongCH, 2015. Effect of atomic-level stresses on local dynamic and mechanical properties in CuxZr100-x metallic glasses: a molecular dynamics study. Intermetallics, 58:50-55.

[68]TianHW, StephanD, LothenbachB, et al., 2021. Influence of foreign ions on calcium silicate hydrate under hydrothermal conditions: a review. Construction and Building Materials, 301:124071.

[69]ToddBD, DaivisPJ, 2017. Nonequilibrium Molecular Dynamics: Theory, Algorithms and Applications. Cambridge University Press, Cambridge, UK.

[70]VandewalleL, NemegeerD, BalazsL, et al., 2002. Design of steel fibre reinforced concrete using the σ‍-‍w method: principles and applications. Materials and Structures, 35:262-278.

[71]VenkovicN, SorelliL, MartirenaF, 2014. Nanoindentation study of calcium silicate hydrates in concrete produced with effective microorganisms-based bioplasticizer. Cement and Concrete Composites, 49:127-139.

[72]WangJW, KalinichevAG, KirkpatrickRJ, 2004. Molecular modeling of water structure in nano-pores between brucite (001) surfaces. Geochimica et Cosmochimica Acta, 68(16):3351-3365.

[73]WangXF, BaoYW, LiuXG, et al., 2015. The stress relaxation of cement clinkers under high temperature. Frontiers of Mechanical Engineering, 10(4):413-417.

[74]WangZP, ChenYT, XuLL, et al., 2022. Insight into the local C-S-H structure and its evolution mechanism controlled by curing regime and Ca/Si ratio. Construction and Building Materials, 333:127388.

[75]YangXS, WangYJ, WangGY, et al., 2016. Time, stress, and temperature-dependent deformation in nanostructured copper: stress relaxation tests and simulations. Acta Materialia, 108:252-263.

[76]YoussefM, PellenqRJM, YildizB, 2011. Glassy nature of water in an ultraconfining disordered material: the case of calcium‍–‍silicate‍–‍hydrate. Journal of the American Chemical Society, 133(8):2499-2510.

[77]ZhangMZ, YeG, van BreugelK, 2011. Microstructure-based modeling of water diffusivity in cement paste. Construction and Building Materials, 25(4):2046-2052.

[78]ZhangT, QinWZ, 2006. Tensile creep due to restraining stresses in high-strength concrete at early ages. Cement and Concrete Research, 36(3):584-591.

[79]ZhangY, ZhouQ, JuJW, et al., 2021. New insights into the mechanism governing the elasticity of calcium silicate hydrate gels exposed to high temperature: a molecular dynamics study. Cement and Concrete Research, 141:106333.

[80]ZhengQ, JiangJY, LiXL, et al., 2021. In situ TEM observation of calcium silicate hydrate nanostructure at high temperatures. Cement and Concrete Research, 149:106579.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE