Abstract
Based on the concepts of continuum damage theory, a new plastic damage model for concrete crack failure is developed through studying the basic damage mechanics. Two damage variables, tensile damage variable for tensile damage and shear damage variable for compressive damage, are adopted to represent the influence of microscopic damage on material macro-mechanics properties under tensile and compressive loadings. The yield criteria and flow rule determining the plasticity of concrete are established in the effective stress space, which is convenient to decouple the damage process from the plastic process and calibrate material parameters with experimental results. Meanwhile, the plastic part of the proposed model can be implemented by back-Euler implicit algorithm, and the damage part is explicit. Consequently, there exist robust algorithms for integrating the constitutive relations using finite element method. Comparison with several experimental results shows that the model is capable of simulating the nonlinear performance of concrete under multiaxial stress state and can be applied to practical concrete structures.
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Wu Z R, Li J, Gu C S, et al. Review on hidden trouble detection and health diagnosis of hydraulic structures. Sci China Ser E-Tech Sci, 2007, 50: 34–50
Wang S S, Ren Q W. Dynamic response of gravity dam model with crack and damage detection. Sci China Tech Sci, 2011, 54: 541–546
WU Z R, Gu C S. Trouble Detection and Health Diagnosis of Large Hydraulic Concrete Structure (in Chinese). Beijing: Higher Education Press, 2005
Wang W M, Ding J X, Wang G J, et al. Stability analysis of the temperature cracks in Xiaowan arch dam. Sci China Tech Sci, 2011, 54: 547–555
Chen A C, Chen W F. Constitutive relations for concrete. J Eng Mech-ASCE, 1975, 101: 465–481
Pramono E, Willam K. Fracture energy-based plasticity formulation of plain concrete. J Eng Mech-ASCE, 1989, 115: 1183–1203
Wu Z R, Peng Y, Li Z C, et al. Commentary of research situation and innovation frontier in hydro-structure engineering science. Sci China Tech Sci, 2011, 54: 767–780
Etse G, Willam K. Fracture energy formulation for inelastic behavior of plain concrete. J Eng Mech-ASCE, 1994, 120: 1983–2011
Menétrey Ph, Willam K J. Triaxial failure criterion for concrete and its generalization. ACI Struct J, 1995, 92: 311–318
Grassl P, Lundgren K, Gylltoft K, et al. Concrete in compression: A plasticity theory with a novel hardening law. Int J Solids Struct, 2002, 39: 5205–5223
Bao T F, Peng Y, Cong P J, et al. Analysis of crack propagation in concrete structures with structural information entropy. Sci China Tech Sci, 2010, 53: 1943–1948
Bao T F, Qin D, Zhou X W, et al. Abnormality monitoring model of cracks in concrete dams. Sci China Tech Sci, 2011, 54: 1914–1922
Gopalaratnam V S, Shah S P. Softening response of plain concrete in direct tension. ACI J Proc, 1985, 82: 310–323
Karsan I D, Jirsa J O. Behavior of concrete under compressive loadings. J Struct Div, 1969, 95: 2543–2563
Mazars J. A model of unilateral elastic damageable material and its application to concrete. Wittmann F H, ed. Fracture Toughness and Fracture Energy of Concrete, Amsterdam, Elsevier, 1986. 61–71
Xu S L, Zhao G F. Research on the Fracture Mechanics of Concrete (in Chinese). Dalian: The Press of Dalian University of Technology, 1991
Gu C S, Li Z C, Xu B, et al. Abnormality diagnosis of cracks in the concrete dam based on dynamical structure mutation. Sci China Tech Sci, 2011, 54: 1930–1939
Liu Y R, Chang Q, Yang Q, et al. Fracture analysis of rock mass based on 3-D nonlinear Finite Element Method. Sci China Tech Sci, 2011, 54: 556–564
Yu T Q, Qian J C. Damage Theory and its Application (in Chinese). Beijing: National defense Industry Press, 1993
Zhou H, Zhang K, Feng X T. A coupled elasto-plastic-damage mechanical model for marble. Sci China Tech Sci, 2011, 54: 228–234
Kachanov L M. Time of the rapture process under creep conditions. Izv Akad Nauk SSR Otd Tech Nauk, 1958, 8: 26–31
Yazdani S, Schreyer H L. Combined plasticity and damage mechanics model for plain concrete. J Eng Mech-ASCE, 1990, 116: 1435–1450
Loland K E. Continuous damage model for load-response estimation of concrete. Cement Concrete Res, 1980, 10: 395–402
Mazars J. Continuous damage theory-application to concrete. J Eng Mech-ASCE, 1980, 115: 345–365
Krajcinovic D, Fonseka G U. The continuous damage theory of brittle materials, part 1: general theory. J Appl Mech-T ASME, 1981, 48: 809–815
Voyiadijs G Z, Taqieddin Z N, Kattan P I, et al. Anisotropic damage-plasticity model for concrete. Int J Plasticity, 2008, 24: 1946–1965
Du R Q, Zhang Q, Chen S H, et al. Safety evaluation of Dagangshan arch dam resisting strong earthquakes with a rate-dependency anisotropic damage model. Sci China Tech Sci, 2011, 54: 531–540
Lubliner J, Oliver J, Oller S, et al. A plastic-damage model for concrete. Int J Solids Struct, 1989, 25: 299–326
Imran I, Pantazopoulou S J. Plasticity model for concrete under triaxial conpressions. J Eng Mech-ASCE, 2001, 127: 281–290
Krätzig W B, Pölling R. An elasto-plastic damage model for reinforced concrete with minimum number of material parameters. Comput Struct, 2004, 82: 1201–1215
Ju J W. On energy-based coupled elastoplastic damage theories. Constitutive modeling and computational aspects. Int J Solids Struct, 1989, 25: 803–833
Lee J, Fenves G V. Plastic-damage model for cyclic loading of concrete structures. J Eng Mech-ASCE, 1998, 124: 892–900
Grassl P, Jirásek M. Damage-plastic model for concrete failure. Int J Solids Struct, 2006, 43: 7166–7196
Mazars J, Pijaudier-Cabot G. Continuum damage theory-application to concrete. J Eng Mech-ASCE, 1989, 115: 345–365
Kupfer H, Hilsdorf H K, Rusch H, et al. Behavior of concrete under biaxial stresses. ACI J Proc, 1969, 66: 656–666
Imran I, Pantazopoulou S J. Experimental study of plain concrete under triaxial stress. ACI Mater J, 1996, 93: 589–601
Reinhardt H W. Fracture mechanics of an elastic softening material like concrete. Heron, 1984, 29: 1–42
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Zheng, F., Wu, Z., Gu, C. et al. A plastic damage model for concrete structure cracks with two damage variables. Sci. China Technol. Sci. 55, 2971–2980 (2012). https://doi.org/10.1007/s11431-012-4983-6
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DOI: https://doi.org/10.1007/s11431-012-4983-6