Journal of Concrete Structures and Materials

Journal of Concrete Structures and Materials

Elasto-plastic-damage-Fracture Constitutive Model of Concrete

Document Type : Original Article

Authors
Amanallah Kordi 1
seyed hossein hosseini lavassani 2
Peyman Homami 3
1 Faculty of Engineering, Civil Engineering Department, Kharazmi University, Iran, Tehran Civil Engineering Department, Faculty of Maritime Engineering, Chabahar Maritime University, Chabahar, Iran
2 kharazmi university
3 Kharazmi University
10.30478/jcsm.2024.453237.1369
Abstract
Abstract: It is very important to define a constitutive model in order to describe mechanical behaviors of concrete material under multiaxial forces. This paper proposes a novel potential function which can be used in constitutive law for a wide category of ductile and brittle and pressure-sensitive materials. This novel potential function permits the possibility of transition between most forms of existing associated yield surface of quasi-brittle materials (concrete) and ductile materials (steel). In this research, the potential function is generalized to several associated functions with failure criteria, such as Drucker-Prager, Tresca, Modified Tresca, Mohr-coulomb, Von-Mises, Rankin, and others. Also, the convexity and smoothness of plasticity surface of this function are investigated. Then a tri-axial elasto-plasto-fracture-damage constitutive law for the modeling of concrete is presented.
Keywords
Constitutive Law
Potential Function
Elasto-Plastic-Damage-Fracture
Plastic theory
Fracture mechanics
Damage theory

Subjects

[1]      Z.P. Bažant, S.-S. Kim, Nonlinear Creep of Concrete—Adaptation and Flow, J. Eng. Mech. Div. 105 (1979) 429–446. https://doi.org/10.1061/JMCEA3.0002483.
[2]      S.S. Hsieh, E.C. Ting, W.F. Chen, A plastic-fracture model for concrete, Int. J. Solids Struct. 18 (1982) 181–197. https://doi.org/10.1016/0020-7683(82)90001-4.
[3]      Y. Yao, H. Guo, K. Tan, An elastoplastic damage constitutive model of concrete considering the effects of dehydration and pore pressure at high temperatures, Mater. Struct. 2020 531. 53 (2020) 1–18. https://doi.org/10.1617/S11527-020-1450-X.
[4]      W.L. Qiu, F. Teng, S.S. Pan, Damage constitutive model of concrete under repeated load after seawater freeze-thaw cycles, Constr. Build. Mater. 236 (2020) 117560. https://doi.org/10.1016/J.CONBUILDMAT.2019.117560.
[5]      H. Zhen-jun, M. Yan-ni, W. Zhen-wei, Z. Xiao-jie, Z. Xue-sheng, D. Meng-jia, F. Chuan, Triaxial strength and deformation characteristics and its constitutive model of high-strength concrete before and after high temperatures, Structures. 30 (2021) 1127–1138. https://doi.org/10.1016/J.ISTRUC.2020.11.078.
[6]      G. Frantziskonis, C.S. Desai, Constitutive model with strain softening, Int. J. Solids Struct. 23 (1987) 733–750. https://doi.org/10.1016/0020-7683(87)90076-X.
[7]      J.W. Ju, On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects, Int. J. Solids Struct. 25 (1989) 803–833. https://doi.org/10.1016/0020-7683(89)90015-2.
[8]      Z.P. Bažant, Concrete fracture models: Testing and practice, Eng. Fract. Mech. 69 (2001) 165–205. https://doi.org/10.1016/S0013-7944(01)00084-4.
[9]      J. Planas, M. Elices, G. V. Guinea, F.J. Gómez, D.A. Cendón, I. Arbilla, Generalizations and specializations of cohesive crack models, Eng. Fract. Mech. 70 (2003) 1759–1776. https://doi.org/10.1016/S0013-7944(03)00123-1.
[10]    L. Contrafatto, M. Cuomo, A framework of elastic–plastic damaging model for concrete under multiaxial stress states, Int. J. Plast. 22 (2006) 2272–2300. https://doi.org/10.1016/J.IJPLAS.2006.03.011.
[11]    A.A. Lukyanov, Constitutive behaviour of anisotropic materials under shock loading, Int. J. Plast. 24 (2008) 140–167. https://doi.org/10.1016/J.IJPLAS.2007.02.009.
[12]    Z. Wang, X. Jin, N. Jin, A.A. Shah, B. Li, Damage based constitutive model for predicting the performance degradation of concrete, Lat. Am. J. Solids Struct. 11 (2014) 907–924. https://doi.org/10.1590/S1679-78252014000600001.
[13]    D. Lu, X. Zhou, X. Du, G. Wang, 3D Dynamic Elastoplastic Constitutive Model of Concrete within the Framework of Rate-Dependent Consistency Condition, J. Eng. Mech. 146 (2020) 04020124. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001854.
[14]    W.B. Krätzig, R. Pölling, Elasto-plastic damage-theories and elasto-plastic fracturing-theories – a comparison, Comput. Mater. Sci. 13 (1998) 117–131. https://doi.org/10.1016/S0927-0256(98)00052-4.
[15]    Z. Zhang, F. Ansari, Fracture mechanics of air-entrained concrete subjected to compression, Eng. Fract. Mech. 73 (2006) 1913–1924. https://doi.org/10.1016/J.ENGFRACMECH.2006.01.039.
[16]    R.A. Einsfeld, M.S.L. Velasco, Fracture parameters for high-performance concrete, Cem. Concr. Res. 36 (2006) 576–583. https://doi.org/10.1016/J.CEMCONRES.2005.09.004.
[17]    C.S. Chang, T.K. Wang, L.J. Sluys, J.G.M. Van Mier, Fracture modeling using a micro-structural mechanics approach––I. Theory and formulation, Eng. Fract. Mech. 69 (2002) 1941–1958. https://doi.org/10.1016/S0013-7944(02)00070-X.
[18]    W.-F. Chen, D.J. Han, Plasticity for structural engineers, Springer New York, NY, 1998.
[19]    R. Hill, On constitutive inequalities for simple materials—I, J. Mech. Phys. Solids. 16 (1968) 229–242. https://doi.org/10.1016/0022-5096(68)90031-8.
[20]    R. De Borst, Fracture in quasi-brittle materials: a review of continuum damage-based approaches, Eng. Fract. Mech. 69 (2002) 95–112. https://doi.org/10.1016/S0013-7944(01)00082-0.
[21]    X. Zhang, H. Wu, J. Li, A. Pi, F. Huang, A constitutive model of concrete based on Ottosen yield criterion, Int. J. Solids Struct. 193–194 (2020) 79–89. https://doi.org/10.1016/J.IJSOLSTR.2020.02.013.
[22]    W.B. Krätzig, R. Pölling, An elasto-plastic damage model for reinforced concrete with minimum number of material parameters, Comput. Struct. 82 (2004) 1201–1215. https://doi.org/10.1016/J.COMPSTRUC.2004.03.002.
[23]    X. Tao, D. V. Phillips, A simplified isotropic damage model for concrete under bi-axial stress states, Cem. Concr. Compos. 27 (2005) 716–726. https://doi.org/10.1016/J.CEMCONCOMP.2004.09.017.
[24]    S.H.H. Lavasani, A.A. Tasnimi, M. Mohamadi Soltani, A Complete Hysterical Constitutive Law for Reinforced Concrete Under Earthquake Loading, 11 (2009) 17–30. https://www.sid.ir/en/journal/ViewPaper.aspx?ID=173167.
[25]    A.A. Tasnimi, H.H. Lavasani, Uniaxial Constitutive Law for structural concrete members under monotonic and cyclic loads, Sci. Iran. 18 (2011) 150–162. https://doi.org/10.1016/J.SCIENT.2011.03.025.
[26]    L. Jason, A. Huerta, G. Pijaudier-Cabot, S. Ghavamian, An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model, Comput. Methods Appl. Mech. Eng. 195 (2006) 7077–7092. https://doi.org/10.1016/J.CMA.2005.04.017.
[27]    C. Zhang, Z. Zhu, S. Zhu, Z. He, D. Zhu, J. Liu, S. Meng, Nonlinear Creep Damage Constitutive Model of Concrete Based on Fractional Calculus Theory, Mater. 2019, Vol. 12, Page 1505. 12 (2019) 1505. https://doi.org/10.3390/MA12091505.
[28]    J.G. Yue, Y.N. Wang, D.E. Beskos, Uniaxial tension damage mechanics of steel fiber reinforced concrete using acoustic emission and machine learning crack mode classification, Cem. Concr. Compos. 123 (2021) 104205. https://doi.org/10.1016/J.CEMCONCOMP.2021.104205.
[29]    G.-J. Yin, X.-B. Zuo, X.-D. Wen, Y.-J. Tang, G.-J. Yin, X.-B. Zuo, X.-D. Wen, Y.-J. Tang, Experimental study and modeling on stress-strain curve of sulfate-corroded concrete, Comput. Concr. 28 (2021) 1. https://doi.org/10.12989/CAC.2021.28.1.001.
[30]    A.H.M.A. Gafoor, D. Dinkler, Modeling damage behavior of concrete subjected to cyclic and multiaxial loading conditions, Struct. Concr. (2021). https://doi.org/10.1002/SUCO.202100109.
[31]    G.T. Houlsby, A.M. Puzrin, A thermomechanical framework for constitutive models for rate-independent dissipative materials, Int. J. Plast. 16 (2000) 1017–1047. https://doi.org/10.1016/S0749-6419(99)00073-X.
[32]    N. Ottosen, M. Ristinmaa, The Mechanics of Constitutive Modeling, Mech. Const. Model. (2005). https://doi.org/10.1016/B978-0-08-044606-6.X5000-0.
[33]    H.C. Wu, C.K. Nanakorn, A constitutive framework of plastically deformed damaged continuum and a formulation using theendochronic concept, Int. J. Solids Struct. 36 (1999) 5057–5087. https://doi.org/10.1016/S0020-7683(98)00230-3.
[34]    L. Resende, A Damage mechanics constitutive theory for the inelastic behaviour of concrete, Comput. Methods Appl. Mech. Eng. 60 (1987) 57–93. https://doi.org/10.1016/0045-7825(87)90130-7.
[35]    L. Song, S.M. Huang, S.C. Yang, Experimental investigation on criterion of three-dimensional mixed-mode fracture for concrete, Cem. Concr. Res. 34 (2004) 913–916. https://doi.org/10.1016/J.CEMCONRES.2003.10.013.
[36]    E.E. Gdoutos, Fracture mechanics : an introduction, Springer Netherlands, 2005. https://doi.org/10.1007/1-4020-3153-X.
[37]    J.H. Argyris, G. Faust, J. Szimmat, E.P. Warnke, K.J. Willam, Recent developments in the finite element analysis of prestressed concrete reactor vessels, Nucl. Eng. Des. 28 (1974) 42–75. https://doi.org/10.1016/0029-5493(74)90088-0.
[38]    W.H. Yang, A Useful Theorem for Constructing Convex Yield Functions, J. Appl. Mech. 47 (1980) 301–303. https://doi.org/10.1115/1.3153659.
[39]    R. Widmann, Fracture mechanics and its limits of application in the field of dam construction, Eng. Fract. Mech. 35 (1990) 531–539. https://doi.org/10.1016/0013-7944(90)90228-9.
[40]    I. Ekeland, R. Témam, Convex Analysis and Variational Problems, Society for Industrial and Applied Mathematics, 1999. https://doi.org/10.1137/1.9781611971088.
[41]    D. Bigoni, A. Piccolroaz, Yield criteria for quasibrittle and frictional materials, Int. J. Solids Struct. 41 (2004) 2855–2878. https://doi.org/10.1016/J.IJSOLSTR.2003.12.024.
[42]    Y. Tanigawa, Y. and Uchida, Hysteretic characteristics of concrete in the domain of high compressive strain, in: Proc. Annu. Conv. AIJ, 1979: pp. 449–450.
[43]    H.B. Kupfer, K.H. Gerstle, Behavior of Concrete under Biaxial Stresses, J. Eng. Mech. Div. 99 (1973) 853–866. https://doi.org/10.1061/JMCEA3.0001789.
[44]    S.R. Green, S.J., Swanson, Static constitutive relations for concrete, 1973.
[45]    I. Imran, S.J. Pantazopoulou, Experimental study of plain concrete under tri- axial stress, ACI Mater. Journa. 93 (1996) 589–601. https://doi.org/10.14359/9865.
[46]    I. Imran, S.J. Pantazopoulou, Plasticity Model for Concrete under Triaxial Compression, J. Eng. Mech. 127 (2001) 281–290. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:3(281).

  • Receive Date 19 April 2024
  • Revise Date 27 June 2024
  • Accept Date 06 July 2024