混凝土的一种标量损伤弹塑性本构模型
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摘要
荷载作用下材料性能的劣化是混凝土结构的微观损伤机理,其宏观表现为结构刚度的折减和承载力的降低。论文推导了基于不可逆热力学过程的弹塑性标量损伤本构,给出时间离散的屈服准则。采用基于向后Euler法的应力更新算法——两步图形返回的最近点投影法,推导了满足迭代结果收敛假设的塑性参数及算法刚度张量,给出了空间梁单元本构积分算法的Jacobi矩阵。将模型用于混凝土简支梁的承载力试验模拟,与计算数据对比表明了模型和算法的合理性和有效性。
Degradation of material properties could be considered as the micro damage mechanism of concrete structures,which introduces the macro behaviors of structures with stiffness delimitation and bearing loss of the system.In this essay,the authors derived one kind of scalar damage constitutive model based on the irreversible thermodynamics.The yielding criterion was expressed in time-discretization formulation.The two-step map returning method(closest point projection method) based upon implicit backward Euler scheme was obtained according to the stress upgrade algorithm.The plastic parameter and the consistent tangent stiffness tensor were deduced which meet the convergent supposition.The constitutive integral Jacobi matrix of a 3D beam element was listed at the same time.Then a simple-supported concrete beam under monotonic loading was simulated according to the previous damage model.Comparison between the experiment results and simulation solution indicates the validity and rationality of the model and framework described beforehand.
Degradation of material properties could be considered as the micro damage mechanism of concrete structures,which introduces the macro behaviors of structures with stiffness delimitation and bearing loss of the system.In this essay,the authors derived one kind of scalar damage constitutive model based on the irreversible thermodynamics.The yielding criterion was expressed in time-discretization formulation.The two-step map returning method(closest point projection method) based upon implicit backward Euler scheme was obtained according to the stress upgrade algorithm.The plastic parameter and the consistent tangent stiffness tensor were deduced which meet the convergent supposition.The constitutive integral Jacobi matrix of a 3D beam element was listed at the same time.Then a simple-supported concrete beam under monotonic loading was simulated according to the previous damage model.Comparison between the experiment results and simulation solution indicates the validity and rationality of the model and framework described beforehand.
引文
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[6]邵长江.混凝土损伤本构理论及其在大跨桥梁地震响应分析中的应用研究[D].西南交通大学,2007.(SHAO Chang-jiang.Research on damage constitu-tive theory of concrete and its application in seismic a-nalysis of long-span bridge[D].Southwest JiaotongUniversity,2007.(in Chinese))
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[10]Bresler B,Scordelies A C.Shear strength of rein-forced beams[J].ACI Materials Journal,1963,60(1):51-74.
[2]Cordier G,Dang W K.Strain hardening effects anddamage in plastic fatigue[A].Proc IUTAM,Symp onPhysical Non-Linearities in Structure Analysis,Sen-lis/France[C].Springer-Verlag,Berlin,1981:52-55.图5作用力与跨中下缘损伤变量演化关系曲线Fig.5 Loading-damage variable curve at thelower margin of the midspan
[3]Krajcinovic D.Continuous damage mechanics revisi-ted:basic concept and definitions[J].Journal of Ap-plied Mechanics,1985,52:829-834.
[4]冯西桥.脆性材料的细观损伤理论和损伤结构的安定性分析[D].清华大学,1995.(FENG Xi-qiao.ManoDamage Theory of Brittle Materials and Safety Anal-ysis on Damage Structures[D].Tsinghua Univerisy,1995.(in Chinese))
[5]Ju J W.On energy-based coupled elastoplastic dam-age theories:Constitutive modeling and computation-al aspects[J].International Journal of Solids andStructures,1989,25:803-833.
[6]邵长江.混凝土损伤本构理论及其在大跨桥梁地震响应分析中的应用研究[D].西南交通大学,2007.(SHAO Chang-jiang.Research on damage constitu-tive theory of concrete and its application in seismic a-nalysis of long-span bridge[D].Southwest JiaotongUniversity,2007.(in Chinese))
[7]Simo J C,Ju J.Strain and stress based continuumdamage models-part I:formulation[J].InternationalJournal of Solids and Structures,1987,23(7):281-290.
[8]Barbat A H,Oller S,O ate E,Hanganu A.ViscousDamage model for Timoshenko beam structures[J].International Journal of Solids and Structures,1997,34(30):3953-3976.
[9]Ngo D,Scordelies A C.Finite element anlysis of re-inforced beam[J].ACI Materials Journal,1967,64:512-163.
[10]Bresler B,Scordelies A C.Shear strength of rein-forced beams[J].ACI Materials Journal,1963,60(1):51-74.
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