Engineering Mechanics ›› 2018, Vol. 35 ›› Issue (8): 1-8,13.doi: 10.6052/j.issn.1000-4750.2017.05.ST13

    Next Articles

ADVANCES IN RESEARCHES ON STOCHASTIC DAMAGE MODELS OF CONCRETE

YU Zhi-wu1,2, SHAN Zhi1,2   

  1. 1. School of Civil Engineering, Central South University, 68 South Shaoshan Road, Changsha, Hunan 410004, China;
    2. National Engineering Laboratory for High-Speed Railway Construction, Central South University, Changsha, Hunan 410004, China
  • Received:2017-05-24 Revised:2018-04-22 Online:2018-08-29 Published:2018-08-29

Abstract: The studies on the micro damage mechanism and stochastic damage model are reviewed. Furthermore, the advances in researches on the stochastic damage model of concrete by the team of authors are introduced as well. The micro damage mechanism analysis was obtained by taking into account mode-Ⅱ microcracks, the stochastic damage model (the fiber bundle-irreversible chain model) was proposed and verified by experiments, and an X-ray computed tomography method for the damage quantification of concrete under compression was developed. Additionally, some related conclusions are drawn.

Key words: concrete, constitutive relationship model, stochastic, damage, fiber bundle-irreversible chain model

CLC Number: 

  • 039
[1] Gurson A L. Continuum theory of ductile rupture by void nucleation and growth. Part I:Yield criteria and flow rules for porous ductile media[J]. Journal of Engineering Materials and Technology, 1977, 99:2-15.
[2] Tvergaard V, Needleman A. Analysis of cup-cone fracture in a round tensile bar[J]. ACTA Metallurgica, 1984, 32:57-169.
[3] Zhan S, Wang T C, Han X. A micromechanical damage theory for brittle materials with small cracks[J]. Fatigue & Fracture of Engineering Materials & Structures, 1998, 21:1337-1349.
[4] Caballero A, Carol I, Lopez C M. A meso-level approach to the 3D numerical analysis of cracking and fracture of concrete materials[J]. Fatigue & Fracture of Engineering Materials & Structures, 2006, 29:979-991.
[5] Aliha M M, Ayatollahi M R. Brittle fracture evaluation of a fine grain cement mortar in combined tensile-shear deformation[J]. Fatigue & Fracture of Engineering Materials & Structures, 2009, 32:987-994.
[6] Kim S M, Abu AL-RUB R K. Meso-scale computational modeling of the plastic-damage response of cementitious composites[J]. Cement and Concrete Research, 2011, 41:339-358.
[7] Trivedi N, Singh R K, Chattopadhyay J. Size independent fracture energy evaluation for plain cement concrete[J]. Fatigue & Fracture of Engineering Materials & Structures, 2015, 38:789-798.
[8] Kosteski L E, Riera J D, Iturrioz I, et al. Assessment of empirical formulas for prediction of the effects of projectile impact on concrete structures[J]. Fatigue & Fracture of Engineering Materials & Structures, 2015, 38:948-959.
[9] Yan Y, Ren Q, Xia N, et al. Artificial neural network approach to predict the fracture parameters of the size effect model for concrete[J]. Fatigue & Fracture of Engineering Materials & Structures, 2015, 38(11):1347-1358.
[10] Katcoff, Z C, Graham-Brady G, et al. Modeling dynamic brittle behavior of materials with circular flaws or pores[J]. International Journal of Solids and Structures, 2014, 51:754-766.
[11] Nguyen D G. A thermodynamic approach to constitution modeling of concrete using damage mechanics and plasticity theory[D]. Oxford:University of Oxford, 2005.
[12] Lee J, Fenves G L. Plastic-damage model for cyclic loading of concrete structures[J]. Journal of Engineering Mechanics, 1998, 124(8):892-900.
[13] Faria R, Oliver J, Cervera M. A strain-based plastic viscous-damage model for massive concrete structures[J]. International Journal of Solids and Structures, 1998, 35(14):1533-1558.
[14] Wu J Y, Li J, Faria R. An energy release rate-based plastic-damage model for concrete[J]. International Journal of Solids and Structures, 2006, 43(3/4):583-612.
[15] Grassl P, Jirasek M. Damage-plastic model for concrete failure[J]. International Journal of Solids and Structures, 2006, 43:7166-7196.
[16] Grassl P, Xenos D, Nyström U, et al. CDPM2:A damage-plasticity approach to modelling the failure of concrete[J]. International Journal of Solids and Structures, 2013, 50:3805-3816.
[17] Slate F O, Olsefski S. X-Rays for study of internal structure and microcracking of concrete[J]. Journal of the American Concrete Institute, 1963, 60(5):575-588.
[18] ABU AL-Rub R K, Voyiadjis G Z. On the coupling of anisotropic damage and plasticity models for ductile Materials[J]. International Journal of Solids and Structures, 2003, 40:2611-2643.
[19] Paskin A, Massoumzadeh B, Shukla K, et al. Effect of atomic crack tip geometry on local stresses[J]. ACTA Metall, 1985, 33(11):1987-1996.
[20] Dienes J G, Paskin A. Molecular dynamic simulations of crack propagation[J]. Journal of Physics and Chemistry of Solids, 1987, 48(11):1015-1033.
[21] Gumbsch P. An atomistic study of brittle fracture:toward explicit failure criteria from atomistic modeling[J]. J. Mater. Res., 1995, 10(11):2897-2907.
[22] Gumbsch P, Beltz G E. On the continuum versus atomistic descriptions of dislocation nucleation and cleavage in Nickel[J]. Modelling and Simulation in Materials Science and Engineering, 1995, 3(5):597-613.
[23] Zhou Z L, Gu J L, Chen N P, et al. Comparison of finite element calculation and experimental study of elastic-plastic deformation at crack tip[J]. ACTA Mechnica Sinica, 1995, 27:51-57.
[24] Fischer L L, Beltz G E. The effect of crack blunting on the competition between dislocation nucleation and Cleavage[J]. Journal of the Mechanics and Physics of Solids, 2001, 49:635-654.
[25] Hajlaoui K, Yavari A R, Doisneau B, et al. Shear delocalization and crack blunting of a metallic glass containing nanoparticles:In situ deformation in TEM analysis[J]. Scripta Materialia, 2006, 54:1829-1834.
[26] Mazars J, Pijaudier-Cabot G. Continuum damage theory:Application to concrete[J]. ASCE Journal of Engineering Mechanics, 1989, 115(2):345-365.
[27] Hu G, Liu J, Graham-Brady L, et al. A 3D mechanistic model for brittle materials containing evolving flaw distributions under dynamic multiaxial loading[J]. Journal of the Mechanics and Physics of Solids, 2015, 78:269-297.
[28] Burr A, Hild F, Leckie F A. Micro-mechanics and continuum damage mechanics[J]. Archive of Applied Mechanics, 1995, 65:437-456.
[29] Halm D, Dragon A. An anisotropic model of damage and frictional sliding for brittle materials[J]. European Journal of Mechanics-A/Solids, 1998, 17(3):439-460.
[30] Dragon A, Halm D, Desoyer T. Anisotropic damage in quasi-brittle solids:modelling, computational issues and applications[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 183:331-352.
[31] Le J, Bazant Z P, Bazant M Z. Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures:I. Strength, static crack growth, lifetime and scaling[J]. Journal of the Mechanics and Physics of Solids, 2011, 59:1291-21.
[32] Le J L, Bazant Z P. Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures:Ⅱ. Fatigue crack growth, lifetime and scaling[J]. Journal of the Mechanics and Physics of Solids, 2011, 59:1322-1337.
[33] Najar J. Brittle residual strain and continuum damage at variable uniaxial loading[J]. International Journal of Damage Mechanics, 1994, 3:260-276.
[34] Feng X Q, Gross D. Three-dimensional micromechanical model for quasi-brittle solids with residual strains under tension[J]. International Journal of Damage Mechanics, 2000, 9:79-110.
[35] Peirce F T. Tensile test for cotton yarns-the weakest Link[J]. Journal of the Textile Institute Transactions, 1926, 17:355-370.
[36] Daniels H E. The statistic theory of the strength of bundles of threads:I[J]. Proceedings of the Royal Society A:Mathematical, Physical & Engineering Sciences, 1945, 183:405-35.
[37] Li J, Ren X D. Stochastic damage model for concrete based on energy equivalent strain[J]. International Journal of Solids and Structures, 2009, 46:2407-2419.
[38] Krajcinovic D, Rinaldi A. Thermodynamics and statistical physics of damage processes in quasiductile solids[J]. Mechanics of Materials, 2005, 37:299-315.
[39] Kandarpa S, Kirkner D J, Spencer B F. Stochastic damage model for brittle material subjected to monotonic loading[J]. Journal of Engineering Mechanics, 1996, 126:788-95.
[40] Krajcinovic D. Damage mechanics[M]. 2nd ed. Amsterdam:Elsevier, 1996.
[41] Phoenix S L, smith R L. A comparison of probabilistic techniques for the strength of fibrous materials under local load-sharing among fibers[J]. International Journal of Solids and Structures, 1983, 19:479-496.
[42] Krajcinovic D, Silva M G. Statistical aspects of the continuous damage theory[J]. International Journal of Solids and Structures, 1982, 18:551-562.
[43] Harlow D G, Phoenix S L. The chain-of-bundles probability model for the strength of fibrous materials:I. Analysis and conjectures[J]. Journal of Composite Materials, 1978:195-214.
[44] Coleman B D. Time dependence of mechanical breakdown in bundles of fibers:I. Constant total load[J]. Journal of Applied Physics, 1957, 28:1058-1064.
[45] Mishnaevsky L, Brøndsted P. Micromechanical modeling of damage and fracture of unidirectional fiber Reinforced composites:a review[J]. Computational Materials Science, 2009, 44:1351-1359.
[46] Hidalgo R C, Zapperi S, Herrmann H J. Discrete fracture model with anisotropic load sharing[J]. Journal of Statistical Mechanics:Theory and Experiment, 2008(1):P01004.
[47] Pradhan S, Bhattacharyya P, Chakrabarti B K. Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model[J]. Physical Review E, 2002, 66:1-12.
[48] Hidalgo R C, Kun F, Herrmann H J. Fracture model with variable range of interaction[J]. Physical Review E, 2002, 65:046148.
[49] Hidalgo R C, Kun F, Herrmann H J. Bursts in a fiber bundle model with continuous damage[J]. Physical Review E, 2001, 64:066122.
[50] Sornette D. Critical phenomena in natural sciences[M]. Berlin:Springer, 2000.
[51] Kun F, Zapperi S, Herrmann H J. Damage in fiber bundle models[J]. The European Physical Journal B, 2000, 17:269-279.
[52] Hemmer P C, Hansen A. The distribution of simultaneous fiber failures in fiber bundles[J]. Journal of Applied Mechanics, 1992, 59:909-914.
[53] Newman W I, Gabrielov A M. Failure of hierarchical distributions of fibre bundles:I[J]. International Journal of Fracture, 1991, 50:1-14.
[54] Pradhan S, Hansen A, Chakrabarti B K. Failure processes in elastic fiber bundles[J]. Reviews of Modern Physics, 2010, 82:499-555.
[55] Raischel F, Kun F, Herrmann H J. Failure process of a bundle of plastic fibers[J]. Physical Review E, 2006, 73:066101.
[56] Kun F, Raischel F, Hidalgo R C, et al. Extensions of fiber bundle models, modelling critical and catastrophic phenomena in Geo-Science:a statistical approach (lecture notes in physics)[M]. Berlin:Springer, 2006:57-92.
[57] Kun F, Raischel F, Hidalgo R C, et al. Extension of fiber bundle models for creep rupture and interface failure[J]. International Journal of Fracture, 2013, 140(1):255-265.
[58] Chen J Y, Bai W F, Fan S L, et al. Statistical damage model for quasi-brittle materials under uniaxial tension[J]. Journal of Central South University, 2009, 16:669-676.
[59] Ren X D, Li J. Hysteretic deteriorating model for quasi-brittle materials based on micromechanical damage approach[J]. International Journal of Non-Linear Mechanics, 2011, 46(1):321-329.
[60] Vincent M, Guy B. A Gurson-type model accounting for VOID size effects[J]. International Journal of Solids and Structures, 2013, 50:320-327.
[61] Yu Z, Shan Z, Ouyang Z, et al. A simple damage model for concrete considering irreversible mode-Ⅱ microcracks[J]. Fatigue Fract Engng Mater Struct, 2016, 39:1419-1432.
[62] Yu Z W, Tan S, Shan Z, et al. X-ray computed tomography quantification of damage in concrete under compression considering irreversible mode-Ⅱ microcracks[J]. Fatigue & Fracture of Engineering Materials & Structures, 2017, 40(12):1960-1972.
[63] 单智. 混凝土随机损伤本构模型及其应用[D].长沙:中南大学, 2017. Shan Zhi. Stochastic damage model of concrete and its application[D]. Changsha:Central South University, 2017. (in Chinese)
[64] Shan Z, Yu Z W. A fiber bundle-plastic chain model for quasi-brittle materials under uniaxial loading[J]. Journal of Statistical Mechanics:Theory and Experiment, 2015(11):P11010.
[65] 李杰, 吴建营, 陈建兵. 混凝土随机损伤力学[M]. 北京:科学出版社, 2014:95-98. Li Jie, Wu Jianying, Chen Jianbing. Stochastic damage mechanics of concrete structures[M]. Beijing:Science Press, 2014:95-98. (in Chinese)
[66] Li J, Ren X. Stochastic damage model for concrete based on energy equivalent strain[J]. International Journal of Solids and Structures, 2009, 46(11/12):2407-2419.
[67] Buyukozturk O. Imaging of concrete structures[J]. Ndt&E International, 1998, 31(4):233-243.
[68] Wang H, Sun X. Quantification of compressioninduced damage and its effect on the chloride transport in structural concrete[C]. International Conference on Performance-based and Life-cycle Structural Engineering, 2015:911-919.
[69] Song H, Zhang H, Fu D, et al. Experimental study on damage evolution of rock under uniform and concentrated loading conditions using digital image correlation[J]. Fatigue Fract Engng Mater Struct, 2013, 36:760-768.
[70] Bayraktar E, Isac N, Bessri K, et al. Damage mechanisms in natural (NR) and synthetic rubber (SBR):nucleation, growth and instability of the cavitation[J]. Fatigue Fract Engng Mater Struct, 2008, 31:184-196.
[71] Guvenilir, STOCK. High resolution computed tomography and implication for fatigue crack closure modeling[J]. Fatigue Fract Engng Mater Struct, 1998, 21:439-450.
[72] Wang L B, Frost J D, Voyiadjis G Z, et al. Quantification of damage parameters using X-ray tomography images[J]. Mechanics of Materials, 2003, 35:777-790.
[73] Wan K, Xue X. In situ compressive damage of cement paste characterized by Lab source X-ray computer tomography[J]. Materials Characterization, 2013, 82:32-40.
[74] 田威. 混凝土损伤演化的CT研究及其在细观数值模拟中的应用[D]. 西安:西安理工大学, 2009. Tian Wei. CT study on the concrete-damage evolution and its application in numerical stimulation[D]. Xi'an:Xi'an University of Technology, 2009. (in Chinese)
[75] Ge X, Ren J, Pu Y, et al. Real-in time CT test of the rock meso-damage propagation law[J]. Science in China (Series E), 2001, 44(3):328-336.
[76] 党发宁, 尹小涛, 丁卫华, 等. 基于CT试验的岩体分区破损本构模型[J]. 岩石力学与工程学报, 2005, 24(22):4003-4009. Dang Faning, Yin Xiaotao, Ding Weihua, et al. Subarea breakage constitutive model of rock mass based on CT test[J]. Chinese Journal of Rock Mechanics and Engineering, 24(22):4003-4009. (in Chinese)
[77] 陈四利, 宁宝宽, 鲍文博, 等. 水泥土细观破裂过程的损伤本构模型[J]. 岩土力学, 2007, 28(1):93-96. Chen Siliang, Ning Baokuan, Bao Wenbo. et al. A damage constitutive model of cemented soil on meso-fracture process testing[J]. Rock and Soil Mechanics, 2007, 28(1):93-96. (in Chinese)
[78] 张全胜, 杨更社, 任建喜. 岩石损伤变量及本构方程的新探讨[J]. 岩石力学与工程学报, 2003, 22(1):30-34. Zhang Quanshen, Yang Gengshe, Ren Jianxi. New study of damage variable and constitutive equation of rock. Chin[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22(1):30-34. (in Chinese)
[79] 杨更社, 谢定义, 张长庆. 岩石损伤CT数分布规律的定量分析[J]. 岩石力学与工程学报, 1998, 17(3):279-285. Yang Gengshe, Xie Dingyi, Zhang Changqing. The quantitative analysis of distribution regulation of CT values of rock damage[J]. Chinese Journal of Rock Mechanics and Engineering, 1998, 17(3):279-285. (in Chinese)
[80] Ma T, Yang C, Chen P, et al. On the damage constitutive model for hydrated shale using CT scanning technology[J]. Journal of Natural Gas Science and Engineering, 2016, 28:204-214.
[81] Eberhardt E, Stead D, Stimpson B. Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences, 1999, 36(3):361-380.
[82] Lemaitre J, Lippmann H. A course on damage mechanics[M]. Berlin:Springer, 1996.
[83] Budiansky B, O'connell R J. Elastic moduli of a cracked solid[J]. International Journal of Solids and Structures, 1976, 12(2):81-97.
[1] DING Jie, ZOU Yun, CAI Xin, LI Tian-qi, ZHENG Li-jun, ZHAO Tao-gan. Experimental study on exterior joint of damage control steel frame [J]. Engineering Mechanics, 2018, 35(S1): 107-112.
[2] CHEN Rong, LEI Jun-qing. Study on the seismic behavior of RC bridge piers under variable axial load [J]. Engineering Mechanics, 2018, 35(S1): 239-245.
[3] XU Chun-yi, LU Biao, YU Xi. Experimental study on the seismic behavior of masonry wall with fiberglass geogrid [J]. Engineering Mechanics, 2018, 35(S1): 126-133.
[4] ZHENG Wen-bin, ZHANG Jian-wei, CAO Wan-lin. Shaking table test study on L-shaped shear walls with single layer of web reinforcement [J]. Engineering Mechanics, 2018, 35(S1): 134-139.
[5] WANG Jian-qun, LÜ Peng, XU Qiao, LUO Xu-guo, ZHU Ming-qiao. Calculation model for concrete creep and its practical application [J]. Engineering Mechanics, 2018, 35(S1): 156-160.
[6] WANG Bing, YOU Hong-xu, LIU Xiao. Working mechanism analysis of steel reinforced recycled aggregate concrete beams after high temperature [J]. Engineering Mechanics, 2018, 35(S1): 161-165,180.
[7] TANG Qiong, LI Yi, LU Xin-zheng, YAN Wei-ming. Study on axial compression capacity of multi-spiral hoops confined concrete columns [J]. Engineering Mechanics, 2018, 35(S1): 166-171.
[8] ZHU Ming-qiao, ZHANG Zi-wei, JIANG Qiao, SHI Wei-hua. Experimental analysis on the force transmission path of a double-deck traffic concrete box girder [J]. Engineering Mechanics, 2018, 35(S1): 181-187.
[9] ZHONG Ming. An in-situ evaluation method for cumulative damage of structural concrete [J]. Engineering Mechanics, 2018, 35(S1): 278-286.
[10] ZHENG Fu-cong, GUO Zong-ming, ZHANG Yao-ting. Seismic behavior analysis of prestressed concrete frame structure under near-fault pulsed ground motions [J]. Engineering Mechanics, 2018, 35(S1): 330-337.
[11] YANG Chao, YANG Shu-tong, QI De-hai. Experimental study on the bond performance between BFRP bars and coral concrete [J]. Engineering Mechanics, 2018, 35(S1): 172-180.
[12] ZHUO Wei-dong, HUANG Lu, CHEN Zhen, YE Gao-ming, HUANG Xin-yi. EXPERIMENTAL AND NUMERICAL ANALYSIS ON MECHANICAL BEHAVIOR OF ECCENTRICALLY LOADED SELF-COMPACTING CONCRETE SHORT COLUMNS WITH 500 MPa STEEL BARS [J]. Engineering Mechanics, 2018, 35(9): 197-206.
[13] YU Bo, TAO Bo-xiong, LIU Sheng-bin. A PROBABILISTIC MODEL FOR PEAK STRESS OF CONCRETE CONFINED BY TIES [J]. Engineering Mechanics, 2018, 35(9): 135-144.
[14] ZHANG Zhen-yu, WAN Lu, FENG Ji-li. CHARACTERISTICS OF DIRECT SHEAR TEST FOR PLAIN CONCRETE JOINT WITH RUBBER AND ITS COHESIVE ZONE MODEL [J]. Engineering Mechanics, 2018, 35(8): 55-66.
[15] WU Zhi-jun, ZHANG Peng-lin, LIU Quan-sheng, LI Wan-feng, JIANG Wei-zhong. DYNAMIC FAILURE ANALYSIS OF REINFORCED CONCRETE SLAB BASED ON COHESIVE ELEMENT UNDER EXPLOSIVE LOAD [J]. Engineering Mechanics, 2018, 35(8): 79-90,110.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] ZHANG Dong-juan;CUI Zhen-shan;LI Yu-qiang;RUAN Xue-yu. SPRINGBACK OF SHEET METAL AFTER PLANE STRAIN STRETCH-BENDING[J]. Engineering Mechanics, 2007, 24(7): 0 -071 .
[2] LI Zhong-xian,HUANG Xin. INFLUENCE OF TRAVELING WAVE EFFECT ON SEISMIC RESPONSES OF CONTINUOUS RIGID-FRAMED BRIDGE IN DEEP WATER[J]. Engineering Mechanics, 2013, 30(3): 120 -125 .
[3] HU Xiao-rong;YU Mao-hong. RESEARCH ON TRIPLE-SHEAR YIELD CRITERION FOR MATERIALS[J]. Engineering Mechanics, 2006, 23(4): 6 -11 .
[4] XIONG Tie-hua;CHANG Xiao-lin. APPLICATION OF RESPONSE SURFACE METHOD IN SYSTEM RELIABILITY ANALYSIS[J]. Engineering Mechanics, 2006, 23(4): 58 -61 .
[5] GE Xin-sheng;CHEN Li-qun;LIU Yan-zhu. OPTIMAL CONTROL OF A NONHOLONOMIC MOTION PLANNING FOR MUTILBODY SYSTEMS[J]. Engineering Mechanics, 2006, 23(3): 63 -68 .
[6] GU Zhi-ping;HE Xing-suo;FANG Tong. EFFECT OF THE DIFFERENTIAL LINKING CONDITION ON SUB-HARMONIC RESONANCE[J]. Engineering Mechanics, 2006, 23(4): 62 -66 .
[7] LIU Yao-ru;ZHOU Wei-yuan;YANG Qiang. PARALLEL 3-D FINITE ELEMENT ANALYSIS BASED ON EBE METHOD[J]. Engineering Mechanics, 2006, 23(3): 27 -31 .
[8] WU Chen;ZHOU Rui-zhong. ELEMENT-FREE GALERKIN METHOD WITH WAVELET BASIS AND ITS COMPARISON WITH FINITE ELEMENT METHOD[J]. Engineering Mechanics, 2006, 23(4): 28 -32 .
[9] LUO Guan-wei;ZHANG Yan-long;XIE Jian-hua. DOUBLE HOPF BIFURCATION OF PERIODIC MOTION OF THE MULTI-DEGREE-OF-FREEDOM VIBRATORY SYSTEM WITH A CLEARANCE[J]. Engineering Mechanics, 2006, 23(3): 37 -43,6 .
[10] LI Qing-xiang;SUN Bing-nan;. AERODYNAMIC STABILITY ANALYSIS OF SMALL CURVED MEM- BRANE IN UNIFORM FLOW[J]. Engineering Mechanics, 2006, 23(4): 39 -44,5 .