混凝土破坏过程细观数值模拟与动态力学特性机理研究
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摘要
混凝土在细观层次上由骨料、砂浆及其之间的界面过渡区组成,各细观组分对其宏观力学性能均有直接影响。采用宏观与细／微观相结合的研究方法,可以在物理机制上给予混凝土宏观力学行为合理的解释,细观数值技术已成为该领域重要的发展方向之一。有鉴于此,本文基于材料细观物理特征的考察,开展混凝土破坏过程的细观数值模拟研究以及混凝土动态力学特性的机理研究。
1.采用一维统计细观损伤力学模型,考虑损伤耗能与应变能释放之间的平衡,对混凝土材料的静态轴拉破坏过程进行了稳定性分析,解析表达了材料由均匀损伤过渡到局部损伤的临界状态、失稳破坏导致的应力跌落现象和临界状态的尺寸效应律,为混凝土破坏过程细观数值模型研究提供了参考。
2.从概率体元建模和界面过渡区模拟两方面对细观数值模型展开研究。在更低的尺度上,分属于骨料、砂浆和界面过渡区的细观单元本身也是由复合材料组成,应用复合材料力学中的Voigt近似和Reuss近似,讨论了细观单元弹性模量和抗拉强度的分布特征；与可靠度理论中抗力考虑成多个随机变量的乘积类似,以强度和弹性模量的乘积作为细观单元的一种综合性能参数,提出了基于综合性能参数的概率体元建模方法,且该方法可以反映前述弹性模量与抗拉强度的分布特征。对细观单元材质组成的单一化假定进行改进,视内嵌界面过渡区的细观单元为一种广义复合材料单元,将修正的Vogit-Reuss模型运用到复合材料单元并形成等效均质单元,单元的损伤通过各组成材料的损伤体现,建立了复合型界面损伤模型。
3.应用上述细观数值模型,仅考虑细观介质的惯性效应,对混凝土材料的动态破坏过程进行了数值模拟研究,表明材料非均质性和应力波传播是与混凝土动态力学特性有关的两个基本要素。以一维非均质杆的动态破坏为原型对此进行了理论论证,进一步探讨了混凝土动态力学特性的物理机理：应力波传播的时空性使材料中的应力非均匀性异于静态加载时仅由材料非均匀性决定的应力非均匀性,故动态加载混凝土的破坏形态及其演化过程不同于静态加载；在动态加载情形下,大多数材料单元的应力水平比静态加载高,材料单元发生破坏的概率更大,以致混凝土的动态破坏形成更多的裂纹；应力波传播引起的应力非均匀性和材料性能的非均匀性,造成了动力强度与静力强度的不同,推导了动力增强系数关于应变率的表达式,该式给出的动力增强系数表现形式及其特征规律与试验资料和相关经验公式符合。
At mesoscale, concrete may be regarded as a three-phase composite consisting of mortar matrix, coarse aggregate and interfacial transition zone (ITZ) between them. The macroscopic mechanical behaviour of the concrete depended on the properties of its components. It has been noted that the physical explanation of concrete macroscopic mechanical behaviour could be given by adopting a multi-scale analysis approach. In view of this, the mesoscale mechanical model for fracture simulation and the dynamic behavior of concrete were thoroughly studied in this paper base on the mesoscale physics of concrete. The major contributions are summarized as follows:
1. A one-dimensional stochastic micromechanical damage model was adopted to study the failure process of concrete specimen subjected to uniaxial tension. A balance was taken into account between the dissipated energy in damage evolution and the released elastic strain energy of the specimen during the loading process. Within the frame of energy principle, the stability analysis of the failure process was conducted and a stability criterion was derived. The critical state that's a transition from uniform damage to local damage, the stress drop phenomena caused by instable failure and the size effect law of critical state were analyzed. These investigations provide useful information and suggestion for the mesoscale mechanical model research.
2. A mesoscale numerical model for concrete was developed by incorporating into the model framework two key components:1) an improved modeling of probability volume element and2) the composite interface damage model.
The mesoscale element that belongs to aggregate, matrix or interfacial transition zone can be considered as a composite at lower length scale. By exploiting this observation, the distribution difference between elastic modulus and tensile strength of mesoscale element was studied based on Voigt and Reuss prediction. Structural resistance could be considered as the product of all random variables in structural reliability theory. Accordingly, the product of strength and elastic modulus was assumed to be a comprehensive property parameter for mesoscale element, and an improved modeling of probability volume element was proposed. Moreover, the distribution difference derived ahead can be reflected in the improved modeling.
A composite interface damage model was developed for the element including the interfacial transition zone but not located in a single material phase, which was considered as a composite element in a broader sense. Using the modified Voigt-Reuss averaging scheme, the influence of the interfacial transition zone was smeared into the composite element. The elastic constants of the composite element were defined in terms of the constitutive properties of both the adjacent materials and the interfacial transition zone, as well as the geometry of the homogenized element. The damage of the composite element was felt in the damage of its each component.
3. Numerical analyses of direct dynamic tensile test and direct dynamic compressive test were performed by employing the mesoscale mechanical model developed above without considering the strain-rate effects of material properties. But the effect of inertia, which is essentially a structural feature of the response, was included in the mesoscale numerical simulations. It was found that the predicted results from these tests show correctly strain-rate dependence of tensile and compressive strength and correctly strain-rate effects on concrete fracturing behaviour, which indicates that the observed dynamic properties of concrete can be attributed to two elementary factors:the heterogeneity of concrete and stress wave propagation.
The two elementary factors were further investigated with reference to the dynamic failure process of a one-dimensional heterogeneous bar. The physical explanations on mechanisms of concrete dynamic properties described below may be drawn from the study. Because of the spatio-temporal characteristics of stress wave propagation, the stress heterogeneity in a dynamically loaded specimen was different from a static loaded specimen, which leads to the difference of failure modes and evolutions between the dynamically loaded specimen and the static loaded specimen. Furthermore, the local stresses in a dynamically loaded specimen are higher, than a static loaded specimen for most materials. Thus, more materials are damaged so as to form more fractures in the dynamically loaded concrete specimen. The increase of strength with strain rate can also be largely attributed to the stress heterogeneity cause by stress wave propagation and the heterogeneity of concrete, and a formula of strength dynamic increase factor was derived.
1.采用一维统计细观损伤力学模型,考虑损伤耗能与应变能释放之间的平衡,对混凝土材料的静态轴拉破坏过程进行了稳定性分析,解析表达了材料由均匀损伤过渡到局部损伤的临界状态、失稳破坏导致的应力跌落现象和临界状态的尺寸效应律,为混凝土破坏过程细观数值模型研究提供了参考。
2.从概率体元建模和界面过渡区模拟两方面对细观数值模型展开研究。在更低的尺度上,分属于骨料、砂浆和界面过渡区的细观单元本身也是由复合材料组成,应用复合材料力学中的Voigt近似和Reuss近似,讨论了细观单元弹性模量和抗拉强度的分布特征；与可靠度理论中抗力考虑成多个随机变量的乘积类似,以强度和弹性模量的乘积作为细观单元的一种综合性能参数,提出了基于综合性能参数的概率体元建模方法,且该方法可以反映前述弹性模量与抗拉强度的分布特征。对细观单元材质组成的单一化假定进行改进,视内嵌界面过渡区的细观单元为一种广义复合材料单元,将修正的Vogit-Reuss模型运用到复合材料单元并形成等效均质单元,单元的损伤通过各组成材料的损伤体现,建立了复合型界面损伤模型。
3.应用上述细观数值模型,仅考虑细观介质的惯性效应,对混凝土材料的动态破坏过程进行了数值模拟研究,表明材料非均质性和应力波传播是与混凝土动态力学特性有关的两个基本要素。以一维非均质杆的动态破坏为原型对此进行了理论论证,进一步探讨了混凝土动态力学特性的物理机理：应力波传播的时空性使材料中的应力非均匀性异于静态加载时仅由材料非均匀性决定的应力非均匀性,故动态加载混凝土的破坏形态及其演化过程不同于静态加载；在动态加载情形下,大多数材料单元的应力水平比静态加载高,材料单元发生破坏的概率更大,以致混凝土的动态破坏形成更多的裂纹；应力波传播引起的应力非均匀性和材料性能的非均匀性,造成了动力强度与静力强度的不同,推导了动力增强系数关于应变率的表达式,该式给出的动力增强系数表现形式及其特征规律与试验资料和相关经验公式符合。
At mesoscale, concrete may be regarded as a three-phase composite consisting of mortar matrix, coarse aggregate and interfacial transition zone (ITZ) between them. The macroscopic mechanical behaviour of the concrete depended on the properties of its components. It has been noted that the physical explanation of concrete macroscopic mechanical behaviour could be given by adopting a multi-scale analysis approach. In view of this, the mesoscale mechanical model for fracture simulation and the dynamic behavior of concrete were thoroughly studied in this paper base on the mesoscale physics of concrete. The major contributions are summarized as follows:
1. A one-dimensional stochastic micromechanical damage model was adopted to study the failure process of concrete specimen subjected to uniaxial tension. A balance was taken into account between the dissipated energy in damage evolution and the released elastic strain energy of the specimen during the loading process. Within the frame of energy principle, the stability analysis of the failure process was conducted and a stability criterion was derived. The critical state that's a transition from uniform damage to local damage, the stress drop phenomena caused by instable failure and the size effect law of critical state were analyzed. These investigations provide useful information and suggestion for the mesoscale mechanical model research.
2. A mesoscale numerical model for concrete was developed by incorporating into the model framework two key components:1) an improved modeling of probability volume element and2) the composite interface damage model.
The mesoscale element that belongs to aggregate, matrix or interfacial transition zone can be considered as a composite at lower length scale. By exploiting this observation, the distribution difference between elastic modulus and tensile strength of mesoscale element was studied based on Voigt and Reuss prediction. Structural resistance could be considered as the product of all random variables in structural reliability theory. Accordingly, the product of strength and elastic modulus was assumed to be a comprehensive property parameter for mesoscale element, and an improved modeling of probability volume element was proposed. Moreover, the distribution difference derived ahead can be reflected in the improved modeling.
A composite interface damage model was developed for the element including the interfacial transition zone but not located in a single material phase, which was considered as a composite element in a broader sense. Using the modified Voigt-Reuss averaging scheme, the influence of the interfacial transition zone was smeared into the composite element. The elastic constants of the composite element were defined in terms of the constitutive properties of both the adjacent materials and the interfacial transition zone, as well as the geometry of the homogenized element. The damage of the composite element was felt in the damage of its each component.
3. Numerical analyses of direct dynamic tensile test and direct dynamic compressive test were performed by employing the mesoscale mechanical model developed above without considering the strain-rate effects of material properties. But the effect of inertia, which is essentially a structural feature of the response, was included in the mesoscale numerical simulations. It was found that the predicted results from these tests show correctly strain-rate dependence of tensile and compressive strength and correctly strain-rate effects on concrete fracturing behaviour, which indicates that the observed dynamic properties of concrete can be attributed to two elementary factors:the heterogeneity of concrete and stress wave propagation.
The two elementary factors were further investigated with reference to the dynamic failure process of a one-dimensional heterogeneous bar. The physical explanations on mechanisms of concrete dynamic properties described below may be drawn from the study. Because of the spatio-temporal characteristics of stress wave propagation, the stress heterogeneity in a dynamically loaded specimen was different from a static loaded specimen, which leads to the difference of failure modes and evolutions between the dynamically loaded specimen and the static loaded specimen. Furthermore, the local stresses in a dynamically loaded specimen are higher, than a static loaded specimen for most materials. Thus, more materials are damaged so as to form more fractures in the dynamically loaded concrete specimen. The increase of strength with strain rate can also be largely attributed to the stress heterogeneity cause by stress wave propagation and the heterogeneity of concrete, and a formula of strength dynamic increase factor was derived.
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