Strength of Materials

, Volume 50, Issue 5, pp 724–734 | Cite as

Elastoplastic Damage Model for Concrete Under Triaxial Compression and Reversed Cyclic Loading

  • J. ZhangEmail author
  • L. Ma
  • Z. X. Zhang

The elastoplastic damage model for concrete is elaborated that can be applied to various stress states. In the previous study (2016) the 3D elastoplastic damage model, based on the Lubliner yield criterion and Drucker–Prager flow rule, was constructed. The simplified forms of the two functions set certain limitations on the calculations in true triaxial compression and high confining pressure. Improved accuracy of yield surface and potential plastic surface is required. The Menétrey–Willam yield criterion is adopted and analyzed in the effective stress space. The methods that define the hardening and softening functions through the volume plastic strain are no longer used in some successful 3D models since they employ double hardening and two-scalar damage to describe an increase in effective yield stress and degradation of stiffness. The suppression of damage evolution in triaxial compression is taken into account through the confining net decomposition of stress. The validation of specific parameters in the potential plastic function of the novel model is verified. The iteration return mapping algorithm is worked out and implemented. The reliability of the proposed model is corroborated by numerical simulation results compared with existing experimental data.


elastoplastic damage effective stress hardening law confining net decomposition return mapping algorithm 



Financial support by the National Science Foundation of China (NSFC) (Grant No. 51378377) and Fundamental Research Funds for the Central Universities (Grant No. 2016YXMS094) is much appreciated.


  1. 1.
    J. Q. Bao, X. Long, K. H. Tan, and C. K. Lee, “A new generalized Drucker–Prager flow rule for concrete under compression,” Eng. Struct., 56, 2076–2082 (2013).CrossRefGoogle Scholar
  2. 2.
    R. Carrazedo, A. Mirmiran, and J. B. de Hanai, “Plasticity based stress-strain model for concrete confinement,” Eng. Struct., 48, No. 48, 645–657 (2013).CrossRefGoogle Scholar
  3. 3.
    P. Grassl, K. Lundgren, and K. Gylltoft, “Concrete in compression: a plasticity theory with a novel hardening law,” Int. J. Solids Struct., 39, No. 20, 5205–5223 (2002).CrossRefGoogle Scholar
  4. 4.
    V. K. Papanikolaou, and A. J. Kappos, “Confinement-sensitive plasticity constitutive model for concrete in triaxial compression,” Int. J. Solids Struct., 44, No. 21, 7021– 7048 (2007).CrossRefGoogle Scholar
  5. 5.
    R. K. Abu Al-Rub and S. M. Kim, “Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture,” Eng. Fract. Mech., 77, No. 10, 1577–1603 (2010).CrossRefGoogle Scholar
  6. 6.
    J. Èervenka and V. K. Papanikolaou, “Three dimensional combined fracture-plastic material model for concrete,” Int. J. Plasticity, 24, No. 12, 2192–2220 (2008).CrossRefGoogle Scholar
  7. 7.
    U. Cicekli, G. Z. Voyiadjis, and R. K. Abu Al-Rub, “A plasticity and anisotropic damage model for plain concrete,” Int. J. Plasticity, 23, Nos. 10–11, 1874–1900 (2007).CrossRefGoogle Scholar
  8. 8.
    P. Grassl and M. Jirásek, “Damage-plastic model for concrete failure,” Int. J. Solids Struct., 43, Nos. 22–23, 7166–7196 (2006).CrossRefGoogle Scholar
  9. 9.
    L. Jason, A. Huerta, G. Pijaudier-Cabot, and S. Ghavamian, “An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model,” Comput. Method. Appl. M., 195, No. 52, 7077– 7092 (2006).CrossRefGoogle Scholar
  10. 10.
    O. Omidi and V. Lotfi, “Finite element analysis of concrete structures using plastic-damage model in 3-D implementation,” Int. J. Civil Eng., 8, No. 3, 187–203 (2010).Google Scholar
  11. 11.
    P. J. Sánchez, A. E. Huespe, J. Oliver, et al., “A macroscopic damage-plastic constitutive law for modeling quasi-brittle fracture and ductile behavior of concrete,” Int. J. Numer. Anal. Met., 36, No. 5, 546–573 (2012).CrossRefGoogle Scholar
  12. 12.
    G. Z. Voyiadjis, Z. N. Taqieddin, and P. I. Kattan, “Anisotropic damage–plasticity model for concrete,” Int. J. Plasticity, 24, No. 10, 1946–1965 (2008).CrossRefGoogle Scholar
  13. 13.
    J. Y. Wu, J. Li, and R. Faria, “An energy release rate-based plastic-damage model for concrete,” Int. J. Solids Struct., 43, Nos. 3–4, 583–612 (2006).CrossRefGoogle Scholar
  14. 14.
    J. Zhang and J. Li, “Elastoplastic damage model for concrete based on consistent free energy potential,” Sci. China Tech. Sci., 57, No. 11, 2278–2286 (2014).CrossRefGoogle Scholar
  15. 15.
    J. Zhang, J. Li, and J. W. Ju, “3D elastoplastic damage model for concrete based on novel decomposition of stress,” Int. J. Solids Struct., 94–95, 125–137 (2016).CrossRefGoogle Scholar
  16. 16.
    P. Menetrey and K. J. Willam, “Triaxial failure criterion for concrete and its generalization,” ACI Struct. J., 92, No. 3, 311–318 (1995).Google Scholar
  17. 17.
    J. Li and X. D. Ren, “Stochastic damage model for concrete based on energy equivalent strain,” Int. J. Solids Struct., 46, No. 11, 2407–2419 (2009).CrossRefGoogle Scholar
  18. 18.
    J. Zhang and J. Li, “Microelement formulation of free energy for quasi-brittle materials,” J. Eng. Mech., 140, No. 8, 06014008 (2014).CrossRefGoogle Scholar
  19. 19.
    J. W. Ju, “On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects,” Int. J. Solids Struct., 25, No. 7, 803–833 (1989).CrossRefGoogle Scholar
  20. 20.
    J. Zhang and J. Li, “Semi-implicit algorithm for elastoplastic damage models involving energy integration,” Adv. Mater. Sci. Eng., 2016, Article ID 5289642 (2016), DOI: Scholar
  21. 21.
    CEB-FIP Model Code 90, No. 213/214, Bulletin d’Information CEB, Lausanne (1993).Google Scholar
  22. 22.
    High Performance Concrete: Recommended Extensions to the Model Code 90, Research Needs, CEB-FIP Working Group on High Strength/High Performance Concrete, CEB (1995).Google Scholar
  23. 23.
    A. I. Karsan and J. O. Jirsa, “Behavior of concrete under compressive loadings,” J. Struct. Div. - ASCE, 95, 2535–2563 (1969).Google Scholar
  24. 24.
    H. B. Kupfer, H. K. Hilsdorf, and H. Rusch, “Behavior of concrete under biaxial stresses,” ACI Struct. J., 66, No. 8, 656–666 (1969).Google Scholar
  25. 25.
    D. C. Candappa, J. G. Sanjayan, and S. Setunge, “Complete triaxial stress–strain curves of high-strength concrete,” J. Mater. Civil Eng., 13, No. 3, 209–215 (2001).CrossRefGoogle Scholar
  26. 26.
    J. G. M. van Mier, Strain-Softening of Concrete under Multiaxial Loading Conditions, Technische Hogeschool Eindhoven, Eindhoven (1984), DOI: 734Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Civil Engineering and MechanicsHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations