沥青混凝土的细观力学模型及数值模拟
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摘要
沥青混凝土是一种典型的多相复合材料,在低温或荷载速率较高的状态下呈现弹性特征,而在高温及高应力等环境下显现出明显的粘弹性。目前,我国对沥青混凝土材料性质的研究仍旧主要采用经验与试验相结合的研究方式。而这种传统的研究方式无法反映出沥青混凝土的内部细观结构对整体宏观性能的影响,且费时费力。为了能够循序渐进地进行系统研究,本文采用由面到点的方法,即先对复合材料这一涉及范围较广的材料进行研究,然后进一步分析沥青混凝土材料,以期揭示材料的每一组成成分在整体材料中所起到的物理机制。
首先,引入快速多极边界元法(FMBEM)的概念,实现了具有多种不同类型夹杂的复合材料二维弹性问题的快速多极边界元分析。在此基础上进一步考虑弱界面的影响,利用弹簧型界面模型及中间层模型,给出了相应的FMBEM基本列式及编程方法。同时,基于广义自洽模型及多步骤方法,给出了能够预报具有多种夹杂及弱界面的复合材料有效宏观性能的细观力学预测模型。
其次,通过弹性-粘弹性对应原理及时间步长法,给出了多夹杂增强复合材料粘弹性问题的FMBEM算法。在此基础上,引入Kelvin型粘弹性界面,进一步得到了具有弱界面的粘弹性FMBEM算法。此外,基于有效夹杂性质的概念给出了具有Kelvin型粘弹性界面的粘弹性复合材料细观力学方法。
再次,将上述得到的研究复合材料弹性及粘弹性的数值及解析方法具体应用到沥青混凝土材料的研究中。通过数字图形处理技术,真实再现沥青混凝土试件的二维几何模型。利用已实现的FMBEM算法,对沥青混凝土材料的弹性模量及蠕变特性进行了数值模拟。同时,利用已建立起来的细观力学模型对其弹性模量进行预测。通过数值及解析方法的分析,探讨了沥青胶浆(细集料+沥青)、粗集料、空隙率及空隙大小、级配、最大粒径、沥青胶浆与集料的交界面等对沥青混凝土宏观性能的影响。
最后,利用傅立叶变换法给出了电磁弹平面问题的基本解,并开发了相应的FMBEM算法。通过数值算例可以看出,本方法可进一步应用于智能混凝土材料的数值模拟。
研究表明,本文给出的FMBEM法建模简单、存储量低、计算效率高,且无须采用数值积分的方法,因此不存在奇异积分的问题。所以,非常适合处理具有不同尺寸、形状、性质、空间分布的多夹杂复合材料问题(如沥青混凝土)。此外,本文给出的细观力学模型形式简单,易于编程计算,因此,在工程实际中也有一定的应用前景。
Asphalt concrete (AC) is a typical complex multi-phase material. When loading rate is very high and the temperature is low, it can be approximated as an equivalent elastic body in engineering application, while at high temperature and high pressure, it shows apparent viscoelasticity characteristics. To date, the prediction and determination of the bulk behavior of AC is largely based on experiments as well as experience, and it is often time-consuming and can not reflect the influence of the microstructure of AC. To this end, a systematical study will be conducted in this dissertation, to investigate the elastic and viscoelastic properties of the composite and the mechanical behavior of AC.
First of all, the basic concept of the fast multipole boundary element method (FMBEM) will be introduced, and the corresponding algorithm for 2D multi-inclusion elastic problems will be reviewed. The influence of the interfacial zone on the overall mechanical properties of the composites is investigated, where two different models, the spring layer model and the interphase model, are used to simulate the imperfect interface. Based on these models, the corresponding FMBEM formulations have been developed. A two-layer built-in micromechanical model and a stepping scheme are proposed to predict the effective properties of the multi-inclusion composite with interface imperfection.
Secondly, a new FMBEM algorithm for 2D viscoelastic problems is formulated by virtue of the elastic-viscoelastic correspondence principle and is solved by the time stepping scheme. The FMBEM formulations are derived by assuming a Kelvin type viscoelastic model, which is adopted to simulate the interface bonding imperfection. Besides, a micromechanical approach is also obtained by introducing the idea of effective properties of inclusions to estimate the creep behavior of the viscoelastic solids, which contain elastic particles but with in-between viscoelastic interfaces.
Thirdly, the obtained numerical and analytical methods are applied to investigating the mechanical behavior of AC. By means of digital image processing, the cross-sectional digital images of asphalt concrete samples are created for numerical modeling. Then the elastic modulus and creep compliance of AC are predicted by the developed FMBEM arithmetic and micromechanical models. The influence of some factors on the behaviour of AC is investigated, including the asphalt matrix, coarse aggregate, air void, aggregate gradations, the largest aggregate and interface between asphalt matrix and coarse aggregates. It has shown that all of these factors may have significant effects on the mechanical properties of AC.
Finally, a 2D FMBEM analysis of magneto-electro-elastic media has been developed. Fourier transformation is employed to derive the fundamental solution for the generalized plane-strain magneto-electro-elasticity. The numerical examples of multi-inclusion magneto-electro-elastic composites illustrate the validity and advantages of the proposed approach in the smart structure applications.
The present study indicates that the developed FMBEM is not only easy in the meshing of complicated geometries, accurate for solving singular fields, but also practical and often superior in solving large class problems, such as AC. It is also shown that the developed micromechanical method is very comprehensive and efficient for fast prediction of effective properties of composites, which makes it possible to be applied in the engineering practice.
首先,引入快速多极边界元法(FMBEM)的概念,实现了具有多种不同类型夹杂的复合材料二维弹性问题的快速多极边界元分析。在此基础上进一步考虑弱界面的影响,利用弹簧型界面模型及中间层模型,给出了相应的FMBEM基本列式及编程方法。同时,基于广义自洽模型及多步骤方法,给出了能够预报具有多种夹杂及弱界面的复合材料有效宏观性能的细观力学预测模型。
其次,通过弹性-粘弹性对应原理及时间步长法,给出了多夹杂增强复合材料粘弹性问题的FMBEM算法。在此基础上,引入Kelvin型粘弹性界面,进一步得到了具有弱界面的粘弹性FMBEM算法。此外,基于有效夹杂性质的概念给出了具有Kelvin型粘弹性界面的粘弹性复合材料细观力学方法。
再次,将上述得到的研究复合材料弹性及粘弹性的数值及解析方法具体应用到沥青混凝土材料的研究中。通过数字图形处理技术,真实再现沥青混凝土试件的二维几何模型。利用已实现的FMBEM算法,对沥青混凝土材料的弹性模量及蠕变特性进行了数值模拟。同时,利用已建立起来的细观力学模型对其弹性模量进行预测。通过数值及解析方法的分析,探讨了沥青胶浆(细集料+沥青)、粗集料、空隙率及空隙大小、级配、最大粒径、沥青胶浆与集料的交界面等对沥青混凝土宏观性能的影响。
最后,利用傅立叶变换法给出了电磁弹平面问题的基本解,并开发了相应的FMBEM算法。通过数值算例可以看出,本方法可进一步应用于智能混凝土材料的数值模拟。
研究表明,本文给出的FMBEM法建模简单、存储量低、计算效率高,且无须采用数值积分的方法,因此不存在奇异积分的问题。所以,非常适合处理具有不同尺寸、形状、性质、空间分布的多夹杂复合材料问题(如沥青混凝土)。此外,本文给出的细观力学模型形式简单,易于编程计算,因此,在工程实际中也有一定的应用前景。
Asphalt concrete (AC) is a typical complex multi-phase material. When loading rate is very high and the temperature is low, it can be approximated as an equivalent elastic body in engineering application, while at high temperature and high pressure, it shows apparent viscoelasticity characteristics. To date, the prediction and determination of the bulk behavior of AC is largely based on experiments as well as experience, and it is often time-consuming and can not reflect the influence of the microstructure of AC. To this end, a systematical study will be conducted in this dissertation, to investigate the elastic and viscoelastic properties of the composite and the mechanical behavior of AC.
First of all, the basic concept of the fast multipole boundary element method (FMBEM) will be introduced, and the corresponding algorithm for 2D multi-inclusion elastic problems will be reviewed. The influence of the interfacial zone on the overall mechanical properties of the composites is investigated, where two different models, the spring layer model and the interphase model, are used to simulate the imperfect interface. Based on these models, the corresponding FMBEM formulations have been developed. A two-layer built-in micromechanical model and a stepping scheme are proposed to predict the effective properties of the multi-inclusion composite with interface imperfection.
Secondly, a new FMBEM algorithm for 2D viscoelastic problems is formulated by virtue of the elastic-viscoelastic correspondence principle and is solved by the time stepping scheme. The FMBEM formulations are derived by assuming a Kelvin type viscoelastic model, which is adopted to simulate the interface bonding imperfection. Besides, a micromechanical approach is also obtained by introducing the idea of effective properties of inclusions to estimate the creep behavior of the viscoelastic solids, which contain elastic particles but with in-between viscoelastic interfaces.
Thirdly, the obtained numerical and analytical methods are applied to investigating the mechanical behavior of AC. By means of digital image processing, the cross-sectional digital images of asphalt concrete samples are created for numerical modeling. Then the elastic modulus and creep compliance of AC are predicted by the developed FMBEM arithmetic and micromechanical models. The influence of some factors on the behaviour of AC is investigated, including the asphalt matrix, coarse aggregate, air void, aggregate gradations, the largest aggregate and interface between asphalt matrix and coarse aggregates. It has shown that all of these factors may have significant effects on the mechanical properties of AC.
Finally, a 2D FMBEM analysis of magneto-electro-elastic media has been developed. Fourier transformation is employed to derive the fundamental solution for the generalized plane-strain magneto-electro-elasticity. The numerical examples of multi-inclusion magneto-electro-elastic composites illustrate the validity and advantages of the proposed approach in the smart structure applications.
The present study indicates that the developed FMBEM is not only easy in the meshing of complicated geometries, accurate for solving singular fields, but also practical and often superior in solving large class problems, such as AC. It is also shown that the developed micromechanical method is very comprehensive and efficient for fast prediction of effective properties of composites, which makes it possible to be applied in the engineering practice.
引文
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