基于粘结裂缝模型的非均匀准脆性材料断裂模拟研究
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摘要
作为准脆性材料,混凝土的抗拉能力低、失效预警时间短,且在多级尺度上表现出非均匀性。对混凝土断裂过程的模拟研究,有助于掌握准脆性材料的裂缝起裂和开展机制。论文先对国内外非均匀准脆性材料的断裂模拟研究历史进行全面的文献回顾,重点研究各种裂缝模型的本构关系和非均匀场的模拟算法,并比较现有模拟方法的优缺点。在此基础上提出基于粘结裂缝模型的模拟方法。该方法采用具有自相关性的随机场间接表征材料属性的空间分布,在通用有限元软件Abaqus平台上,通过若干前后处理程序,进行非均匀准脆性材料的断裂模拟。
采用该方法,先对二维平面内一个轴心受拉试块进行单元类型、网格依赖性,裂缝面特征及数值算法等方面的研究,再进行二维断裂的蒙特卡罗模拟。在论证蒙特卡罗模拟结果已收敛的前提下,分析随机场方差和特征长度对极限荷载的影响,并利用模拟结果进行初步的可靠度设计及材料强度评估。将二维模拟方法扩展至三维,对一系列静态和动态断裂过程进行三维模拟,将模拟结果与其它文献或实验数据进行比较,以验证算法的可行性。在三维空间内,对上述轴心受拉试块进行蒙特卡罗模拟,从多角度分析模拟结果,并与二维模拟结果进行比较。最后,在上述混凝土断裂模型基础上,提出基于纤维拉拔实验曲线的纤维混凝土模型,并对近年来受到广泛关注的纤维混凝土加固效果进行初步模拟和参数分析。
研究表明,论文提出的模拟方法能够准确模拟混凝土破坏时,裂缝面形态粗糙、位置随机的特性；同样的平均强度下,混凝土的极限荷载随着抗拉强度随机场方差的增大而减小,随着骨料粒径的增大而减小；三维模拟方法考虑了厚度方向上材料的牵制作用,得到的极限荷载比二维模拟结果高；该方法适用于复杂多裂缝结构的静态或动态过程模拟,模拟所得荷载-位移曲线与实验方法所得曲线基本吻合,且网格敏感性较小。该方法依托于通用有限元软件,简单有效,可用于结构的可靠度设计及材料强度的评估。论文提出的纤维混凝土模型模拟结果与实验吻合,参数分析结果可为提高纤维混凝土性能提供理论参考。
As a typical kind of quasi-brittle material, the concrete has relatively low tensile strength and instant softening response as well as random strength distribution due to the multi-scaled heterogeneity. The research on its fracture modeling is necessary for understanding the mechanism of crack initiation and propagation in quasi-brittle materials. The fracture modeling in heterogeneous materials was thoroughly reviewed, focused on the constitution of crack model and the algorithm of random fields. After an overall comparison among the present numerical models, a new method based on the cohesive zone model was proposed. In the proposed method, an auto-correlated random field was adopted to represent the spatial distribution of mechanical properties with an in-house algorithm to insert the cohesive elements into the boundaries of solid elements and another one to map the samples of random properties, i.e. the tensile strength, to cohesive elements.
A two-dimensional concrete specimen under uni-axial tensile was firstly modeled with attentions on the effects of element type, mesh-dependence, crack surface characteristics and solvers of nonlinear equation. A few series of Monte Carlo Simulations (MCSs) of two-dimensional fracture modeling were then conducted. After verification of the convergence of the MCSs'results, the effects of variance and characteristic length in the random field on the structure's carrying capacity were analyzed and the applications of the MCSs'results on reliability design and calculation of characteristic material strength were introduced. The method was then extended to three-dimension. Some static and dynamic fracture examples with deterministic material properties were carried on. Their numerical results were compared with experimental data or those from other numerical models. The same concrete specimen was modeled again in the context of three-dimensional methods and compared to the two-dimensional results. Finally, a Fiber Reinforced Concrete (FRC) model was introduced based on the proposed concrete model and adopted to simulate the fracture of FRC as well as some parametric study.
The study shows that, the proposed method predicted the tortuous cracks with random spatial location in concrete; the carrying capacity decreases as the variance or characteristic length of random field of tensile strength increases; the three-dimensional model predicts higher carrying capacity than the two-dimensional model due to the interaction between the materials in thickness direction; the proposed method was proven to suit for static and dynamic modeling in complex structure as the numerical results agreed well with the experimental or numerical results in other references with little mesh-dependence; the proposed method, fulfilled in the context of a general-purposed finite element analysis package, provides a simple but effective tool for assessment of structural reliability and calculation of characteristic material strength; the proposed FRC model predicts good loading-displacement curves compared to experimental data, and the comprehensive parametric study provides theoretical guide for improvement on FRC performance.
采用该方法,先对二维平面内一个轴心受拉试块进行单元类型、网格依赖性,裂缝面特征及数值算法等方面的研究,再进行二维断裂的蒙特卡罗模拟。在论证蒙特卡罗模拟结果已收敛的前提下,分析随机场方差和特征长度对极限荷载的影响,并利用模拟结果进行初步的可靠度设计及材料强度评估。将二维模拟方法扩展至三维,对一系列静态和动态断裂过程进行三维模拟,将模拟结果与其它文献或实验数据进行比较,以验证算法的可行性。在三维空间内,对上述轴心受拉试块进行蒙特卡罗模拟,从多角度分析模拟结果,并与二维模拟结果进行比较。最后,在上述混凝土断裂模型基础上,提出基于纤维拉拔实验曲线的纤维混凝土模型,并对近年来受到广泛关注的纤维混凝土加固效果进行初步模拟和参数分析。
研究表明,论文提出的模拟方法能够准确模拟混凝土破坏时,裂缝面形态粗糙、位置随机的特性；同样的平均强度下,混凝土的极限荷载随着抗拉强度随机场方差的增大而减小,随着骨料粒径的增大而减小；三维模拟方法考虑了厚度方向上材料的牵制作用,得到的极限荷载比二维模拟结果高；该方法适用于复杂多裂缝结构的静态或动态过程模拟,模拟所得荷载-位移曲线与实验方法所得曲线基本吻合,且网格敏感性较小。该方法依托于通用有限元软件,简单有效,可用于结构的可靠度设计及材料强度的评估。论文提出的纤维混凝土模型模拟结果与实验吻合,参数分析结果可为提高纤维混凝土性能提供理论参考。
As a typical kind of quasi-brittle material, the concrete has relatively low tensile strength and instant softening response as well as random strength distribution due to the multi-scaled heterogeneity. The research on its fracture modeling is necessary for understanding the mechanism of crack initiation and propagation in quasi-brittle materials. The fracture modeling in heterogeneous materials was thoroughly reviewed, focused on the constitution of crack model and the algorithm of random fields. After an overall comparison among the present numerical models, a new method based on the cohesive zone model was proposed. In the proposed method, an auto-correlated random field was adopted to represent the spatial distribution of mechanical properties with an in-house algorithm to insert the cohesive elements into the boundaries of solid elements and another one to map the samples of random properties, i.e. the tensile strength, to cohesive elements.
A two-dimensional concrete specimen under uni-axial tensile was firstly modeled with attentions on the effects of element type, mesh-dependence, crack surface characteristics and solvers of nonlinear equation. A few series of Monte Carlo Simulations (MCSs) of two-dimensional fracture modeling were then conducted. After verification of the convergence of the MCSs'results, the effects of variance and characteristic length in the random field on the structure's carrying capacity were analyzed and the applications of the MCSs'results on reliability design and calculation of characteristic material strength were introduced. The method was then extended to three-dimension. Some static and dynamic fracture examples with deterministic material properties were carried on. Their numerical results were compared with experimental data or those from other numerical models. The same concrete specimen was modeled again in the context of three-dimensional methods and compared to the two-dimensional results. Finally, a Fiber Reinforced Concrete (FRC) model was introduced based on the proposed concrete model and adopted to simulate the fracture of FRC as well as some parametric study.
The study shows that, the proposed method predicted the tortuous cracks with random spatial location in concrete; the carrying capacity decreases as the variance or characteristic length of random field of tensile strength increases; the three-dimensional model predicts higher carrying capacity than the two-dimensional model due to the interaction between the materials in thickness direction; the proposed method was proven to suit for static and dynamic modeling in complex structure as the numerical results agreed well with the experimental or numerical results in other references with little mesh-dependence; the proposed method, fulfilled in the context of a general-purposed finite element analysis package, provides a simple but effective tool for assessment of structural reliability and calculation of characteristic material strength; the proposed FRC model predicts good loading-displacement curves compared to experimental data, and the comprehensive parametric study provides theoretical guide for improvement on FRC performance.
引文
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