Advertisement

Acta Mechanica Solida Sinica

, Volume 32, Issue 1, pp 69–80 | Cite as

Rate-Dependent Characteristic of Relaxation Time of Concrete

  • Hui Song
  • Jiankang ChenEmail author
  • Cheng Qian
  • Yunfeng Lv
  • Yonghui Cao
Article
  • 58 Downloads

Abstract

This study focused on the rate-dependent relaxation time of concrete using the split Hopkinson pressure bar test and the ultrasonic technique. Based on the experimental results, and considering the viscous effect in concrete, the viscoelastic stress–strain relationship was established in terms of the principles of irreversible thermodynamics and the generalized Onsager’s principle, providing the convergence of an iterative scheme in terms of the Lipschitz’s condition. It was found that the relaxation time of concrete depends on the strain rate. Furthermore, considering the state equations and damage evolution, a nonlinear viscoelastic constitutive model of concrete coupling damage was proposed. Compared with the experimental results, this model could better characterize the strengthening and softening characteristics of concrete prior to and beyond the strength limit. Further analysis indicated that the viscous effect is dominantly caused by the C–S–H in concrete.

Keywords

Concrete Constitutive relation Viscoelasticity Relaxation time Damage evolution 

Notes

Acknowledgements

The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (NSFC #11832013, #11772164, #11572163), the National Basic Research Program of China (973 Program, 2009CB623203), the Key Research Program of Society Development of Ningbo (2013C51007) and the K.C. Wong Magna Fund in Ningbo University.

References

  1. 1.
    Mazars J, Pijaudier-Cabot G. Continuum damage theory-application to concrete. J Eng Mech. 1989;115(2):345–65.Google Scholar
  2. 2.
    Mazars J. A description of micro- and macroscale damage of concrete structures. Eng Fract Mech. 1986;25(5):729–37.Google Scholar
  3. 3.
    Supartono F, Sidoroff F. Anisotropic damage modeling for brittle elastic materials. In: Symposium of France–Poland; 1984.Google Scholar
  4. 4.
    Zhou YW, Wu YF. General model for constitutive relationships of concrete and its composite structures. Compos Struct. 2012;94(2):580–92.Google Scholar
  5. 5.
    Hsieh SS, Ting EC, Chen WF. A plastic-fracture model for concrete. Int J Solids Struct. 1982;18(3):181–97.zbMATHGoogle Scholar
  6. 6.
    Dimaggio FL, Sandler IS. Material model for granular soils. J Eng Mech. 1970;97(3):935–50.Google Scholar
  7. 7.
    Sandler IS, Dimaggio FL, Baladi GY. Generalized cap model for geologic materials. J Geotech Geoenviron. 1974;102n(12):683–99.Google Scholar
  8. 8.
    Grote DL, Park SW, Zhou M. Dynamic behavior of concrete at high strain rates and pressures: I. experimental characterization. Int J Impact Eng. 2001;25(9):869–86.Google Scholar
  9. 9.
    Park SW, Xia Q, Zhou M. Dynamic behavior of concrete at high strain rates and pressures: II. numerical simulation. Int J Impact Eng. 2001;25(9):887–910.Google Scholar
  10. 10.
    Zhang J, Li J. Elastoplastic damage model for concrete based on consistent free energy potential. Sci China Technol Sci. 2014;57(11):2278–86.Google Scholar
  11. 11.
    Zhang J, Li J. Construction of homogeneous loading functions for elastoplastic damage models for concrete. Sci China Phys Mech. 2014;57(3):490–500.Google Scholar
  12. 12.
    Marzec I, Tejchman J, Winnicki A. Computational simulations of concrete behavior under dynamic conditions using elasto-visco-plastic model with non-local softening. Comput Concrete. 2015;15(4):515–45.Google Scholar
  13. 13.
    Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures. In: Proceedings of the 7th intern symposium on ballistics. Netherlands: Am. Def. Orp. (ADPA); 1983. pp. 541–47.Google Scholar
  14. 14.
    Forrestal MJ, Luk VK, Watts HA. Penetration of reinforced concrete with ogive-nose penetrators. Int J Solids Struct. 1988;24(1):77–87.Google Scholar
  15. 15.
    Holmquist TJ, John GR. A computational constitutive model for concrete subjected large strain, high strain rates and high pressure. In: 14th international symposium on ballistics Québec; 1993. pp. 591–600.Google Scholar
  16. 16.
    Polanco-Loria M, Hopperstad OS, Børvik T, et al. Numerical predictions of ballistic limits for concrete slabs using a modified version of the HJC concrete model. Int J Impact Eng. 2008;35(5):290–303.Google Scholar
  17. 17.
    Polanco-Loria, M. Improvements to the HJC concrete model in LSDYNA SINTEF Report STF24 F01286. Trondheim; 2002.Google Scholar
  18. 18.
    Riedel W. Beton unter dynamischen Lasten Meso-und makro mechanische Modelle und ihre Parameter. Freiburg, Ph.d thesis, Ermst-Mach-Institut; 2000.Google Scholar
  19. 19.
    Riedel W, Thoma K, Hiermaier S. Penetration of reinforced concrete by BETA-B-500d numerical analysis using a new macroscopic concrete model for hydrocodes. In: Proceedings of 9th international symposium interaction of the effect of munitions with structures. Berlin-Strausberg; 1999. pp. 315–22.Google Scholar
  20. 20.
    Heider N, Hiermaier S. Numerical simulation the performance of tandem warheads[A]. In: 19th international symposium ballistics. Interlaken: Thun: IBS2001 Symposium office; 2001. pp. 1493–99.Google Scholar
  21. 21.
    Lu Y, Tu ZG, Tan SC, Lim HS. A comparative numerical simulation study of concrete debris of clamped slabs under internal blast. In: Proceedings of the 32nd DOD explosives safety seminar. Philadelphia; 2006. pp. 24–6.Google Scholar
  22. 22.
    Tu ZG, Lu Y. Modifications of RHT material model for improved numerical simulation of dynamic response of concrete. Int J Impact Eng. 2010;37(10):1072–82.Google Scholar
  23. 23.
    Bazant ZP, Prasannan S. Solidification theory for concrete creep. I: formulation. J Eng Mech. 1989;115(8):1691–703.Google Scholar
  24. 24.
    Bazant ZP, Prasannan S. Solidification theory for concrete creep. II: verification and application. J Eng Mech. 1989;115(8):1704–25.Google Scholar
  25. 25.
    Tehrania FF, Absia JF, Allou F, Petitb C. Heterogeneous numerical modeling of asphalt concrete through use of a biphasic approach: porous matrix/inclusions. Comp Mater Sci. 2013;69(1):186–96.Google Scholar
  26. 26.
    Choi S, Cha SW, Oh BH. Identification of viscoelastic behavior for early-age concrete based on measured strain and stress histories. Mater Struct. 2010;43(8):1161–75.Google Scholar
  27. 27.
    Zhu H, Sun L. A viscoelastic–viscoplastic damage constitutive model for asphalt mixtures based on thermodynamics. Int J Plast. 2013;40(1):81–100.Google Scholar
  28. 28.
    Subramanian V, Guddati MN, Kim YR. A viscoplastic model for rate-dependent hardening for asphalt concrete in compression. Mech Mater. 2013;59(3):142–59.Google Scholar
  29. 29.
    Sun L, Zhu Y. A serial two-stage viscoelastic–viscoplastic constitutive model with thermodynamical consistency for characterizing time-dependent deformation behavior of asphalt concrete mixtures. Constr Build Mater. 2013;40(7):584–95.Google Scholar
  30. 30.
    Zeng G, Yang X, Chen L, Bai F. Damage evolution and crack propagation in Semicircular sending asphalt mixture specimens. Acta Mech Solida Sin. 2016;29(6):596–609.Google Scholar
  31. 31.
    Chen JK, Qian C. Loading history dependence of retardation time of calcium–silicate–hydrate. Constr Build Mater. 2017;147:558–65.Google Scholar
  32. 32.
    Huang ZP. Fundamentals of continuum mechanics. Beijing: Higher Education Press; 2003 (in Chinese).Google Scholar
  33. 33.
    Chen JK, Huang ZP, Chu HJ, Bai SL. Nonlinear viscoelastic constitutive relations based on the rate sensitive relaxation time under the condition of uniaxial stress. Acta Polym Sin. 2003;138(3):414–9 (in Chinese).Google Scholar
  34. 34.
    Riedel W, Kawai N, Kondo KI. Numerical assessment for impact strength measurements in concrete materials. Int J Impact Eng. 2009;36(2):283–93.Google Scholar
  35. 35.
    Lu CS, Danzer R, Fischer FD. Fracture statistics of brittle materials: Weibull or normal distribution. Phys Rev E. 2002;65(6Pt2):067102.Google Scholar
  36. 36.
    Song SC, Wang TH, Cai HN, Wang FC. Numerical calculations of adiabatic shearing localization of steel projectile impacting concrete. Explos Shock Waves. 2007;27(3):246–50 (in Chinese).Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2018

Authors and Affiliations

  • Hui Song
    • 1
    • 3
  • Jiankang Chen
    • 1
    • 2
    Email author
  • Cheng Qian
    • 1
  • Yunfeng Lv
    • 1
  • Yonghui Cao
    • 1
  1. 1.The Faculty of Mechanical Engineering and MechanicsNingbo UniversityNingboChina
  2. 2.State Key Laboratory of Turbulence and Complex SystemsPeking UniversityBeijingChina
  3. 3.The Faculty of Civil Engineering and ArchitectureNanchang Institute of TechnologyNanchangChina

Personalised recommendations