Abstract
A temporal multiscale model was developed to characterize the damage that evolves in concrete structures throughout a complete scenario of dynamic fatigue loading. The damage was decomposed into quasistatic and dynamic components, and its evolution was controlled by introducing negative and positive feedback mechanisms. Fatigue damage evolution equations of the power law type were used together with a deduced temporal multiscale scheme to allow a computationally efficient finite-element method (FEM) simulation of the damage that evolves during the whole loading process. The validity and computational efficiency of the FEM model were assessed by comparing its predictions with published experimental data.
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Data Availability Statement
All numerical models and computer code generated during the study are available from the corresponding author by request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 52078361 and 51678439) and Innovation Program of Shanghai Municipal Education Commission (2017).
References
Aas-Jakobsen, K., and R. Lenschow. 1973. “Behavior of reinforced columns subjected to fatigue loading.” J. Am. Concr. Inst. 70 (3): 199–206. https://doi.org/10.14359/11198.
Alliche, A. 2004. “Damage model for fatigue loading of concrete.” Int. J. Fatigue 26 (9): 915–921. https://doi.org/10.1016/j.ijfatigue.2004.02.006.
Bažant, Z. P., and K. Xu. 1991. “Size effect in fatigue fracture of concrete.” ACI Mater. J. 88 (4): 390–399. https://doi.org/10.14359/1786.
Chen, G., J. Teng, J. Chen, and Q. Xiao. 2015. “Finite element modeling of debonding failures in FRP-strengthened RC beams: A dynamic approach.” Comput. Struct. 158 (Oct): 167–183. https://doi.org/10.1016/j.compstruc.2015.05.023.
Cornelissen, H. A., and H. W. Reinhardt. 1984. “Uniaxial tensile fatigue failure of concrete under constant-amplitude and programme loading.” Mag. Concr. Res. 36 (129): 216–226. https://doi.org/10.1680/macr.1984.36.129.216.
Ding, Z. 2016. “The fatigue constitutive relation of concrete and stochastic fatigue response of concrete structure.” Ph.D. thesis, Dept. College of Civil Engineering, Tongji Univ.
Gylltoft, K. 1984. “A fracture mechanics model for fatigue in concrete.” Matériaux et Constr. 17 (1): 55–58. https://doi.org/10.1007/BF02474057.
Hillerborg, A., M. Modéer, and P. E. Petersson. 1976. “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res. 6 (6): 773–781. https://doi.org/10.1016/0008-8846(76)90007-7.
Hillerborg, A., and P. E. Petersson. 1981. “Fracture mechanical calculations, test methods and results for concrete and similar materials.” Adv. Fract. Res. 4 (1): 1515–1522.
Hordijk, D. A. 1991. “Local approach to fatigue of concrete.” Ph.D. thesis, Dept. of Civil Engineering, Delft Univ. of Technology.
Horii, H., H. C. Shin, and T. M. Pallewatta. 1992. “Mechanism of fatigue crack growth in concrete.” Cem. Concr. Compos. 14 (2): 83–89. https://doi.org/10.1016/0958-9465(92)90002-D.
Kim, J. K., and Y. Y. Kim. 1996. “Experimental study of the fatigue behavior of high strength concrete.” Cem. Concr. Res. 26 (10): 1513–1523. https://doi.org/10.1016/0008-8846(96)00151-2.
Kolluru, S. V., E. F. O’Neil, J. S. Popovics, and S. P. Shah. 2000. “Crack propagation in flexural fatigue of concrete.” J. Eng. Mech. 126 (9): 891–898. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:9(891).
Li, J., and X. Ren. 2009. “Stochastic damage model for concrete based on energy equivalent strain.” Int. J. Solids Struct. 46 (11–12): 2407–2419. https://doi.org/10.1016/j.ijsolstr.2009.01.024.
Liang, J., X. Nie, M. Masud, J. Li, and Y. L. Mo. 2017. “A study on the simulation method for fatigue damage behavior of reinforced concrete structures.” Eng. Struct. 150 (Nov): 25–38. https://doi.org/10.1016/j.engstruct.2017.07.001.
Liang, J., X. Ren, and J. Li. 2016. “A competitive mechanism driven damage-plasticity model for fatigue behavior of concrete.” Int. J. Damage Mech. 25 (3): 377–399. https://doi.org/10.1177/1056789515586839.
Liu, F., and J. Zhou. 2018. “Experimental research on fatigue damage of reinforced concrete rectangular beam.” KSCE J. Civ. Eng. 22 (9): 3512–3523. https://doi.org/10.1007/s12205-018-1767-y.
Mai, S. H., F. Le-Corre, G. Foret, and B. Nedjar. 2012. “A continuum damage modeling of quasi-static fatigue strength of plain concrete.” Int. J. Fatigue 37 (Apr): 79–85. https://doi.org/10.1016/j.ijfatigue.2011.10.006.
Marigo, J. J. 1985. “Modelling of brittle and fatigue damage for elastic material by growth of microvoids.” Eng. Fract. Mech. 21 (4): 861–874. https://doi.org/10.1016/0013-7944(85)90093-1.
Ouyang, C., and S. P. Shah. 1991. “Geometry-dependent R-curve for quasi-brittle materials.” J. Am. Ceram. Soc. 74 (11): 2831–2836. https://doi.org/10.1111/j.1151-2916.1991.tb06851.x.
Papa, E., and A. Taliercio. 1996. “Anisotropic damage model for the multiaxial static and fatigue behaviour of plain concrete.” Eng. Fract. Mech. 55 (2): 163–179. https://doi.org/10.1016/0013-7944(96)00004-5.
Paris, P. C., M. P. Gomez, and W. E. P. Anderson. 1961. “A rational analytic theory of fatigue.” Trend Eng. 13 (1): 9.
Park, Y., A. H. Ang, and Y. K. Wen. 1985. “Seismic damage analysis of reinforced concrete buildings.” J. Struct. Eng. 111 (4): 740–757. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(740).
Petersson, P. E. 1981. “Crack growth and development of fracture zones in plain concrete and similar materials.” Ph.D. dissertation, Div. of Building Materials, Lund Univ.
Reinhardt, H. W. 1984. “Fracture mechanics of an elastic softening material like concrete.” Heron 29 (2): 1–42.
Reinhardt, H. W., H. A. W. Cornelissen, and D. A. Hordijk. 1986. “Tensile tests and failure analysis of concrete.” J. Struct. Eng. 112 (11): 2462–2477. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:11(2462).
Ren, X., S. Zeng, and J. Li. 2014. “A rate-dependent stochastic damage–plasticity model for quasi-brittle materials.” Comput. Mech. 55 (2): 267–285. https://doi.org/10.1007/s00466-014-1100-7.
Saito, M., and S. Imai. 1983. “Direct tensile fatigue of concrete by the use of friction grips.” J. Am. Concr. Inst. 80 (5): 431–438. https://doi.org/10.14359/10867.
Simo, J. C., and T. J. Hughes. 1999. Vol. 37 of Computational inelasticity. New York: Springer.
Simo, J. C., and J. W. Ju. 1987. “Strain- and stress-based continuum damage models—I. Formulation.” Int. J. Solids Struct. 23 (7): 821–840. https://doi.org/10.1016/0020-7683(87)90083-7.
Slowik, V., G. A. Plizzari, and V. E. Saouma. 1996. “Fracture of concrete under variable amplitude fatigue loading.” ACI Mater. J. 93 (3): 272–283. https://doi.org/10.14359/9812.
Tepfers, R., and T. Kutti. 1979. “Fatigue strength of plain, ordinary, and lightweight concrete.” J. Am. Concr. Inst. 76 (5): 635–652. https://doi.org/10.14359/6962.
Toumi, A., and A. Bascoul. 2002. “Mode I crack propagation in concrete under fatigue: Microscopic observations and modelling.” Int. J. Numer. Anal. Methods Geomech. 26 (13): 1299–1312. https://doi.org/10.1002/nag.245.
Wu, J., J. Li, and R. Faria. 2006. “An energy release rate-based plastic-damage model for concrete.” Int. J. Solids Struct. 43 (3–4): 583–612. https://doi.org/10.1016/j.ijsolstr.2005.05.038.
Yankelevsky, D. Z., and H. W. Reinhardt. 1989. “Uniaxial behavior of concrete in cyclic tension.” J. Struct. Eng. 115 (1): 182. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:1(166).
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 3 • March 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Aug 17, 2021
Accepted: Nov 3, 2021
Published online: Dec 24, 2021
Published in print: Mar 1, 2022
Discussion open until: May 24, 2022
ASCE Technical Topics:
- Concrete
- Damage (material)
- Damage (structural)
- Design (by type)
- Dynamic models
- Engineering fundamentals
- Engineering materials (by type)
- Fatigue (material)
- Finite element method
- Forensic engineering
- Material mechanics
- Material properties
- Materials characterization
- Materials engineering
- Methodology (by type)
- Models (by type)
- Multiscale methods
- Numerical methods
- Structural design
- Structural engineering
- Structural models
Authors
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Cited by
- Xiaoli Wei, D. A. Makhloof, Xiaodan Ren, Analytical Models of Concrete Fatigue: A State-of-the-Art Review, Computer Modeling in Engineering & Sciences, 10.32604/cmes.2022.020160, 134, 1, (9-34), (2023).
- Moussa Leblouba, Mohamad Tarabin, Mostafa Zahri, Probabilistic analysis and simulation of crack propagation in concrete pavements and surfaces, Scientific Reports, 10.1038/s41598-022-18060-8, 12, 1, (2022).