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Elastoplastic damage model for concrete based on consistent free energy potential

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Abstract

The aim of this study is to formulate an appropriate free energy potential for inelastic behavior of concrete and construct an elastoplastic damage model on a more rational basis. The concept of effective plastic energy storage rates is proposed, which are conjugate forces of hardening variables in an undamaged configuration. Then an analogy between the evolution of hardening variables and that of a plastic strain is used to postulate the formulation of plastic free energy. This formulation reflects the specific characteristics of a certain plasticity model, so it can serve well as a thermodynamic link between plasticity and damage. By combination of the general formulation of free energy with the double hardening plasticity theory and two-parameter damage expression, a thermodynamically well-founded elastoplastic damage model for concrete is constructed. The operator split algorithm is employed, and the numerical simulations agree well with a series of material tests.

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References

  1. Chen A C T, Chen W F. Constitutive relations for concrete. J Eng Mech-ASCE, 1975, 101: 465–481

    Google Scholar 

  2. Lubliner J, Oliver J, Oller S, et al. A plastic-damage model for concrete. Int J Solids Struct, 1989, 25: 299–326

    Article  Google Scholar 

  3. Lee J, Fenves G L. Plastic-damage model for cyclic loading of concrete structures. J Eng Mech-ASCE, 1998, 124: 892–900

    Article  Google Scholar 

  4. Imran I, Pantazopoulou S J. Plasticity model for concrete under triaxial compression. J Eng Mech-ASCE, 2001, 127: 281–290

    Article  Google Scholar 

  5. Grassl P, Jirasek M. Damage-plastic model for concrete failure. Int J Solids Struct, 2006, 43: 7166–7196

    Article  MATH  Google Scholar 

  6. Papanikolaou V K, Kappos A J. Confinement-sensitive plasticity constitutive model for concrete in triaxial compression. Int J Solids Struct, 2007, 44: 7021–7048

    Article  MATH  Google Scholar 

  7. Zheng F G, Wu Z R, Gu C S, et al. A plastic damage model for concrete structure cracks with two damage variables. Sci China Tech Sci, 2012, 55: 2971–2980

    Article  Google Scholar 

  8. Ladeveze P. Sur une theorie de l’endommagement anisotrope (in French). Dissertation for the Doctoral Degree. Cachan, France: Laboratoire de Mecanique et Technologie, 1983

    Google Scholar 

  9. Mazars J. A description of micro- and macro-scale damage of concrete structures. Eng Fract Mech, 1986, 25: 729–737

    Article  Google Scholar 

  10. Simo J C, Ju J W. Strain- and stress-based continuum damage models -I. Formulation. Int J Solids Struct, 1987, 23: 821–840

    Article  MATH  Google Scholar 

  11. Ju JW. On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects. Int J Solids Struct, 1989, 25: 803–833.

    Article  MATH  Google Scholar 

  12. Faria R, Oliver J, Cervera M. A strain-based plastic viscous-damage model for massive concrete structures. Int J Solids Struct, 1998, 35: 1533–1558

    Article  MATH  Google Scholar 

  13. Comi C, Perego U. Fracture energy based bi-dissipative damage model for concrete. Int J Solids Struct, 2001, 38 (36-37): 6427–6454

    Article  Google Scholar 

  14. Wu J Y, Li J, Faria R. An energy release rate-based plastic-damage model for concrete. Int J Solids Struct, 2006, 43: 583–612

    Article  MATH  Google Scholar 

  15. Cicekli U, Voyiadjis G Z, Abu Al-Rub R K. A plasticity and anisotropic damage model for plain concrete. Int J Plast, 2007, 23: 1874–1900

    Article  MATH  Google Scholar 

  16. Li J, Ren X D. Stochastic damage model for concrete based on energy equivalent strain. Int J Solids Struct, 2009, 46: 2407–2419

    Article  MATH  Google Scholar 

  17. Zhu Q Z, Shao J F, Kondo D. A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction effects. Eur J Mech A-Solids, 2011, 30: 316–325

    Article  MATH  MathSciNet  Google Scholar 

  18. Lemaitre J. A continuous damage mechanics model for ductile fracture. J Eng Mater-T ASME, 1985, 107: 83–89

    Article  Google Scholar 

  19. Lemaitre J, Desmorat R. Engineering damage mechanics, ductile, creep, fatigue and brittle failures. Berlin: Springer, 2005

    Google Scholar 

  20. Gurtin M E, Fried E, Anand L. The mechanics and thermodynamics of continua. New York: Cambridge University Press, 2010

    Book  Google Scholar 

  21. Li J, Ren X D. Homogenization-based multi-scale damage theory. Sci China-Phys Mech Astron, 2010, 53: 690–698

    Article  Google Scholar 

  22. Ren X D, Chen J S, Li J, et al. Micro-cracks informed damage models for brittle solids. Int J Solids Struct, 2011, 48: 1560–1571

    Article  MATH  Google Scholar 

  23. Ren X D, Li J. A unified dynamic model for concrete considering viscoplasticity and rate-dependent damage. Int J Damage Mech, 2012, 22: 530–555

    Article  Google Scholar 

  24. Voyiadjis G Z, Abu Al-Rub K R, Palazotto A N. Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory. Int J Plast, 2004, 20: 981–1038

    Article  MATH  Google Scholar 

  25. Abu Al-Rub R K, Kim S M. Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture. Eng Fract Mech, 2010, 77: 1577–1603

    Article  Google Scholar 

  26. Kim S M, Abu Al-Rub R K. Meso-scale computational modeling of the plastic-damage response of cementitious composites. Cement Concrete Res, 2011, 41: 339–358

    Article  Google Scholar 

  27. Gurtin M E, Anand L, Lele S P. Gradient single-crystal plasticity with free energy dependent on dislocation densities. J Mech Phys Solids, 2007, 55: 1853–1878

    Article  MATH  MathSciNet  Google Scholar 

  28. Sumarac D, Krajcinovic D, Mallick K. Elastic parameters of brittle, elastic solids containing slits-mean field theory. Int J Damage Mech, 1992, 1: 320–346

    Article  Google Scholar 

  29. Zhang J, Li J. Microelement formulation of free energy for quasi-brittle materials. J Eng Mech-ASCE, 2014, 140: 06014008

    Article  Google Scholar 

  30. Lubliner J. On the thermodynamic foundations of nonlinear solid mechanics. Int J Nonlin Mech, 1972, 7: 237–254

    Article  MATH  Google Scholar 

  31. Coleman B D, Gurtin M. Thermodynamics with internal state variables. J Chem Phys, 1967, 47: 597–613

    Article  Google Scholar 

  32. Chaboche J L. Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int J Plast, 1989, 5: 247–302

    Article  MATH  Google Scholar 

  33. Ortiz M A. Constitutive theory for inelastic behavior of concrete. Mech Mater, 1985, 4: 67–93.

    Article  Google Scholar 

  34. Oliver J, Cervera M, Oller S, et al. Isotropic damage models and smeared crack analysis of concrete. In: Proceedings of 2nd International Conference on Computer Aided Analysis and Design of Concrete Structures, Zell am See, Austria, 1990

    Google Scholar 

  35. Zhang J, Zhang Z X, Chen C Y. Yield criterion in plastic-damage models for concrete. Acta Mech Solida Sin, 2010, 23: 220–230

    Article  Google Scholar 

  36. Zhang J, Li J. Investigation into Lubliner yield criterion of concrete for 3D simulation. Eng Struct, 2012, 44: 122–127

    Article  Google Scholar 

  37. Zhang J, Li J. Construction of homogeneous loading functions for elastoplastic damage models for concrete. Sci China Phys Mech Astron, 2014, 57: 490–500

    Article  Google Scholar 

  38. Simo J C, Hughes T J R. Computational Inelasticity. New York: Springer-Verlag, 1998

    MATH  Google Scholar 

  39. Kupfer H, Hilsdorf H K, Rusch H. Behavior of concrete under biaxial stresses. ACI J Proc, 1969, 66: 656–666

    Google Scholar 

  40. Geopalaeratnam V S, Shah S P. Softening response of plain concrete in direct tension. ACI J Proc, 1985, 82: 310–323

    Google Scholar 

  41. Karson I D, Jirsa J O. Behaviour of concrete under compressive loadings. J Struct Div-ASCE, 1969, 95: 2535–2563

    Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, China

    Ji Zhang & Jie Li

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  1. Ji Zhang
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  2. Jie Li
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Correspondence to Jie Li.

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Zhang, J., Li, J. Elastoplastic damage model for concrete based on consistent free energy potential. Sci. China Technol. Sci. 57, 2278–2286 (2014). https://doi.org/10.1007/s11431-014-5677-z

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