复合材料微结构仿真与性能预测一体化研究
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摘要
复合材料作为一种新型材料,以其优良的特殊性能和可设计性,在众多领域都有着广泛应用。随着复合材料应用的不断深入,对复合材料的性能要求也愈来愈来高,设计并研究高性能、特殊性能的新型先进复合材料有着重要意义。随着计算机可视化技术和数值计算方法的发展,复合材料的微观组织结构可视化演示得以实现,复合材料的有限元细观力学分析能够研究复合材料细观应力场和定量描述细观结构与性能的关系,阐明复合材料性能变化的规律,指导复合材料的设计,极大地推动了复合材料的发展。目前复合材料结构—性能研究的发展趋势是采用数字化、数值化、虚拟化、可视化技术,建立复合材料微观组织结构可视化仿真、性能预测、性能导向型设计一体化的模拟平台。
基于复合材料结构-性能研究的发展现状,本文以数字材料技术为先导,对复合材料的微观组织结构进行计算机设计与构筑,以可视化技术为手段,对复合材料的微观组织结构进行可视化演示,以数值材料技术为核心,计算并预测复合材料微观组织结构的细观结果与有效性能。
本文采用Laguerre图对多晶体基体材料的微结构进行仿真。讨论Laguerre图的构造算法,依次研究带权点集Regular三角化的逐点插入增量算法和Regular三角化与Laguerre图的对偶转换实现流程。阐述了通过控制带权点集来完成多晶体材料微结构设计的方法。结合球填充带权点集的设计不仅实现多晶体微结构的模型拟合,还可以完成对具有特殊晶粒分布的多晶体微结构的仿真。同时还讨论了多晶体微结构的空间变换设计,将其用于生成定向凝固的多晶体微结构、构造纳米晶的晶界。在完成几何形貌设计的同时,本文还对晶粒晶体学取向的模拟和设计的方法进行阐述
增强相微观组织结构的计算机表征也是本文研究的重点。本文设计了基于Monto-Carlo方法模拟增强相微观组织结构的技术流程。以[0,1]区间的均匀分布随机数发生器为基础,编写了任意区间均匀分布、正态分布和指数概率分布的随机数发生器,用于生成各种几何形貌增强体的几何特征、取向分布、空间分布的信息数据。同时利用基于方向包围盒的空间几何相交检测算法,不仅可以定量澄清增强体之间相互位置关系,还可以实现增强体之间位置关系的控制与设计。本文对增强相微观组织结构的设计有三种方式：(1)针对增强相组成物几何形状的组合设计；(2)对增强相组成物几何特征和取向牲的随机数参数设计,(3)基于空间划分子区域的组合设计。单独使用或组合使用这三种方式能够仿真得到多种增强相的微观组织结构。
完成复合材料基体相和增强相微观组织结构的仿真后,还从几何角度讨论了界面相的表征方法。将界面相近似为包覆在增强体上的具有相同厚度的壳体结构,依次对界面相的各亚层区域进行处理,构造出具有分层特征的壳体结构,用于表征界面相的微结构。本文还研究的复合材料中气孔与夹杂缺陷的表征,讨论了这两种缺陷分布在界面上或随机部位的模拟方法。结合基体相的构造、增强相的设计和界面相的构造,给出了颗粒增强、纤维增强及织物增强复合材料微观组织结构的仿真示例。
对复合材料细观有限元力学分析的基础是建立可用于数值计算的复合材料微结构代表性体积单元的几何模型。因此对ABAQUS前处理进行二次开发,分别编写了适用于多晶体结构和增强体的几何建模和网格划分程序,实现了复合材料微观组织结构的自动化建模。利用单胞自动识别技术与均匀化处理方法对颗粒增强多晶体复合材料微观组织结构的细观应力场进行了计算。采用基于定义的有限元方法,对复合材料的代表性体积单元施加六组周期性均匀应变边界条件,求得复合材料的刚度矩阵,给出了织物增强复合材料工程弹性常数的预测实例实例。最后对复合材料的等效热膨胀系数进行了预测。采用有限元方法预测的结果与实验测量值吻合较好,验证了预测方法的有效性。
最后,对复合材料微观组织结构仿真与性能预测一体化技术进行了研究。将复合材料各组成物微观组织结构的仿真过程进行模块化处理,并设计各仿真模块的接口程序。对基于ABAQUS二次开发的脚本程序如自动化几何建模、网格划分、各向异性材料赋予、边界条件与载荷施加、结果提取与计算等过程进行集成,达到复合材料微结构代表性体积单元性能预测的自动化实现。此外,采用Python语言进行图形用户界面开发,设计各仿真模块的参数输入对话框,同时结合PyOpenGL编程,编写了三维可视化程序,用于演示复合材料组成物的微观组织结构。软件中采用外部数据文件间接传递仿真参数,实现了图形用户主界面、三维可视化视窗、自主开发的程序、ABAQUS脚本调用之间的无缝衔接。开发了复合材料微结构数值仿真的软件VirtualTPS,为复合材料结构-性能研究提供了基础性的工具
As a new type of material, composite materials have a wide range of applications due to its excellent performance and the designability in a number of areas. With the development of composite applications, the performance requirements of composite materials also become higher and higher, and it has an important significance in the design of high-performance, special performance new advanced composite materials. With the development of computer visualization techniques and numerical calculation method, the microstructure of the composite in visual presentation can be achieved. The composite micromechanics employed by finite element analysis can study mesoscopic stress field and quantitative description of the relationship of composite mesostructure and performance, clarify the law of composite material properties, and guide the design of composite materials. This will greatly promote the development of composite materials. The trends of composite structure performance research is the use of digital, numerical, virtualization, visualization techniques to establish the microstructure of the composite structure visualization simulation, performance prediction, performance-oriented design integrated simulation platform.
Based on the current development of the composite structure performance, this paper tried to use the digital materials technology as the pilot to design and build a composite microstructure. As a means of visualization technology, visual presentation was demonstrated the composite microstructure. As the core of the numerical material technology, the composite material microstructure the meso-results effective performance can be calculated and predicted.
Laguerre diagram can be used for simulation polycrystalline materials microstructure. This paper discussed the algorithm of Laguerre diagram construction, and researched the point-by-point with the weight point set regular triangulation insert incremental algorithm and regular triangulation and Laguerre map to achieve dual conversion process to complete structure Laguerre diagram. This paper discussed the polycrystalline material microstructure by control the weight point set. By design of weight point set with sphere packing algorithm, it will not only achieve the model fitting of polycrystal microstructure, but can also complete the simulation polycrystal microstructure having particular grain size distribution. This paper also discussed the method of spatial transformation, which can be used as generate directional solidification of a polycrystalline microstructure, and can also be used to construct nano-crystalline grain boundary. After Completed design geometric morphology, the paper also described simulation and design method of grain crystallographic orientation.
Another research point in this study is the enhanced phase characterization of microstructure by computer. This paper described the technical processes which enhanced the simulation phase microstructure by Monto-Carlo methods. Based on the interval [0,1] of the uniformly distributed random number generator, the random number generator with any uniform distribution, normal distribution and the exponential probability distribution was given to generate a variety of geometric morphology enhancers with geometric characteristics of orientation distribution, the spatial distribution of information and data. Based on the direction of the bounding box, geometric intersection detection algorithm was used at the same time, this not only can be quantitatively clarified to enhance the mutual positional relationship between the control and design of the positional relationship between the bodies, can also implement enhanced. There are three way to enhance the design of phase microstructure structure in this paper:(1) the combination of object geometry design for enhanced;(2) the design of enhanced random number parameter phase composed of animal characteristics and orientation of the object geometry (3) the design of the divided space based on the combination. Employed one method alone or in combination of these three methods, it can be obtain a variety of enhanced phase microstructure based on simulation.
After finishing the simulation of composite matrix phase and the reinforcing phase, this study described the interface simulation from the geometric point. The interface phase was seen as shell structure had the same thickness which coated on the reinforcing body, then processed sequentially sub-layer region on the interface phase and constructed the hierarchical structure which can be used for represent the characterization of interface phase micro structure. Pores and inclusions of composite material also studied in this paper, the simulation method of two defect characterization distributed at the interface and at the random parts was also discussed. Combined with the matrix phase of construct, the design of reinforcing phase and interface phase of construct, the paper gave the simulation example of the particle reinforced, fiber reinforced and fabric reinforced composite material microstructure.
The finite element mechanical analysis of composite material microstructure is based on the establishment of the composite microstructure with the numerical calculation of the geometric model of the representative volume element. Therefore, after secondary development of the pre-treatment of the ABAQUS, the geometric modeling and meshing program applies to polycrystalline structure and enhance phase was written, respectively, in order to achieve the automated modeling of composite material microstructure. Particle reinforced polycrystalline composite microstructure mesoscopic stress field was calculated by using the cell automatic identification technology and the homogenization processing method. Based on the definition of finite element method, six groups of the periodic boundary conditions of uniform strain is applied on representative volume element of the composite material, and obtained the stiffness of the matrix of the composite material. And then, engineering elastic constants of fabric reinforced composites was predicted. In this paper, the equivalent thermal expansion coefficient of the composite was predicted. The forecast result was in good agreement with the predictions of the finite element results and the experimental data. This indicated that the finite element analysis model was accuracy to verify the validity of the prediction method.
After the above work has been completed, this paper researched the composite microstructure simulation and performance prediction integration technology. The simulation module interface program was taken on the microstructure of composites materials and designed the software for simulation module. Based on ABAQUS secondary development of the script, such as automated geometric modeling, meshing, anisotropic material given boundary conditions and load application, the results of extraction and calculation process, it could automate the simulation and prediction the integration representative volume element of the composite microstructure. In addition, the Python language was employed to development of graphical user interface, then designed input dialog of simulation module parameter. Simultaneously, software was combined with PyOpenGL programming, the preparation of a three-dimensional visualization program demonstrated demo composite composition microstructure. The software uses an external data file transfer simulation parameters indirectly, this could achieve the main graphical user interface, three-dimensional visualization window, a seamless transition between the self-development programs, and ABAQUS script calls. Furthermore, the numerical simulation software VirtualTPS of the composite microstructure was developed in this study, and provided the basic tools for composite structure-performance.
基于复合材料结构-性能研究的发展现状,本文以数字材料技术为先导,对复合材料的微观组织结构进行计算机设计与构筑,以可视化技术为手段,对复合材料的微观组织结构进行可视化演示,以数值材料技术为核心,计算并预测复合材料微观组织结构的细观结果与有效性能。
本文采用Laguerre图对多晶体基体材料的微结构进行仿真。讨论Laguerre图的构造算法,依次研究带权点集Regular三角化的逐点插入增量算法和Regular三角化与Laguerre图的对偶转换实现流程。阐述了通过控制带权点集来完成多晶体材料微结构设计的方法。结合球填充带权点集的设计不仅实现多晶体微结构的模型拟合,还可以完成对具有特殊晶粒分布的多晶体微结构的仿真。同时还讨论了多晶体微结构的空间变换设计,将其用于生成定向凝固的多晶体微结构、构造纳米晶的晶界。在完成几何形貌设计的同时,本文还对晶粒晶体学取向的模拟和设计的方法进行阐述
增强相微观组织结构的计算机表征也是本文研究的重点。本文设计了基于Monto-Carlo方法模拟增强相微观组织结构的技术流程。以[0,1]区间的均匀分布随机数发生器为基础,编写了任意区间均匀分布、正态分布和指数概率分布的随机数发生器,用于生成各种几何形貌增强体的几何特征、取向分布、空间分布的信息数据。同时利用基于方向包围盒的空间几何相交检测算法,不仅可以定量澄清增强体之间相互位置关系,还可以实现增强体之间位置关系的控制与设计。本文对增强相微观组织结构的设计有三种方式：(1)针对增强相组成物几何形状的组合设计；(2)对增强相组成物几何特征和取向牲的随机数参数设计,(3)基于空间划分子区域的组合设计。单独使用或组合使用这三种方式能够仿真得到多种增强相的微观组织结构。
完成复合材料基体相和增强相微观组织结构的仿真后,还从几何角度讨论了界面相的表征方法。将界面相近似为包覆在增强体上的具有相同厚度的壳体结构,依次对界面相的各亚层区域进行处理,构造出具有分层特征的壳体结构,用于表征界面相的微结构。本文还研究的复合材料中气孔与夹杂缺陷的表征,讨论了这两种缺陷分布在界面上或随机部位的模拟方法。结合基体相的构造、增强相的设计和界面相的构造,给出了颗粒增强、纤维增强及织物增强复合材料微观组织结构的仿真示例。
对复合材料细观有限元力学分析的基础是建立可用于数值计算的复合材料微结构代表性体积单元的几何模型。因此对ABAQUS前处理进行二次开发,分别编写了适用于多晶体结构和增强体的几何建模和网格划分程序,实现了复合材料微观组织结构的自动化建模。利用单胞自动识别技术与均匀化处理方法对颗粒增强多晶体复合材料微观组织结构的细观应力场进行了计算。采用基于定义的有限元方法,对复合材料的代表性体积单元施加六组周期性均匀应变边界条件,求得复合材料的刚度矩阵,给出了织物增强复合材料工程弹性常数的预测实例实例。最后对复合材料的等效热膨胀系数进行了预测。采用有限元方法预测的结果与实验测量值吻合较好,验证了预测方法的有效性。
最后,对复合材料微观组织结构仿真与性能预测一体化技术进行了研究。将复合材料各组成物微观组织结构的仿真过程进行模块化处理,并设计各仿真模块的接口程序。对基于ABAQUS二次开发的脚本程序如自动化几何建模、网格划分、各向异性材料赋予、边界条件与载荷施加、结果提取与计算等过程进行集成,达到复合材料微结构代表性体积单元性能预测的自动化实现。此外,采用Python语言进行图形用户界面开发,设计各仿真模块的参数输入对话框,同时结合PyOpenGL编程,编写了三维可视化程序,用于演示复合材料组成物的微观组织结构。软件中采用外部数据文件间接传递仿真参数,实现了图形用户主界面、三维可视化视窗、自主开发的程序、ABAQUS脚本调用之间的无缝衔接。开发了复合材料微结构数值仿真的软件VirtualTPS,为复合材料结构-性能研究提供了基础性的工具
As a new type of material, composite materials have a wide range of applications due to its excellent performance and the designability in a number of areas. With the development of composite applications, the performance requirements of composite materials also become higher and higher, and it has an important significance in the design of high-performance, special performance new advanced composite materials. With the development of computer visualization techniques and numerical calculation method, the microstructure of the composite in visual presentation can be achieved. The composite micromechanics employed by finite element analysis can study mesoscopic stress field and quantitative description of the relationship of composite mesostructure and performance, clarify the law of composite material properties, and guide the design of composite materials. This will greatly promote the development of composite materials. The trends of composite structure performance research is the use of digital, numerical, virtualization, visualization techniques to establish the microstructure of the composite structure visualization simulation, performance prediction, performance-oriented design integrated simulation platform.
Based on the current development of the composite structure performance, this paper tried to use the digital materials technology as the pilot to design and build a composite microstructure. As a means of visualization technology, visual presentation was demonstrated the composite microstructure. As the core of the numerical material technology, the composite material microstructure the meso-results effective performance can be calculated and predicted.
Laguerre diagram can be used for simulation polycrystalline materials microstructure. This paper discussed the algorithm of Laguerre diagram construction, and researched the point-by-point with the weight point set regular triangulation insert incremental algorithm and regular triangulation and Laguerre map to achieve dual conversion process to complete structure Laguerre diagram. This paper discussed the polycrystalline material microstructure by control the weight point set. By design of weight point set with sphere packing algorithm, it will not only achieve the model fitting of polycrystal microstructure, but can also complete the simulation polycrystal microstructure having particular grain size distribution. This paper also discussed the method of spatial transformation, which can be used as generate directional solidification of a polycrystalline microstructure, and can also be used to construct nano-crystalline grain boundary. After Completed design geometric morphology, the paper also described simulation and design method of grain crystallographic orientation.
Another research point in this study is the enhanced phase characterization of microstructure by computer. This paper described the technical processes which enhanced the simulation phase microstructure by Monto-Carlo methods. Based on the interval [0,1] of the uniformly distributed random number generator, the random number generator with any uniform distribution, normal distribution and the exponential probability distribution was given to generate a variety of geometric morphology enhancers with geometric characteristics of orientation distribution, the spatial distribution of information and data. Based on the direction of the bounding box, geometric intersection detection algorithm was used at the same time, this not only can be quantitatively clarified to enhance the mutual positional relationship between the control and design of the positional relationship between the bodies, can also implement enhanced. There are three way to enhance the design of phase microstructure structure in this paper:(1) the combination of object geometry design for enhanced;(2) the design of enhanced random number parameter phase composed of animal characteristics and orientation of the object geometry (3) the design of the divided space based on the combination. Employed one method alone or in combination of these three methods, it can be obtain a variety of enhanced phase microstructure based on simulation.
After finishing the simulation of composite matrix phase and the reinforcing phase, this study described the interface simulation from the geometric point. The interface phase was seen as shell structure had the same thickness which coated on the reinforcing body, then processed sequentially sub-layer region on the interface phase and constructed the hierarchical structure which can be used for represent the characterization of interface phase micro structure. Pores and inclusions of composite material also studied in this paper, the simulation method of two defect characterization distributed at the interface and at the random parts was also discussed. Combined with the matrix phase of construct, the design of reinforcing phase and interface phase of construct, the paper gave the simulation example of the particle reinforced, fiber reinforced and fabric reinforced composite material microstructure.
The finite element mechanical analysis of composite material microstructure is based on the establishment of the composite microstructure with the numerical calculation of the geometric model of the representative volume element. Therefore, after secondary development of the pre-treatment of the ABAQUS, the geometric modeling and meshing program applies to polycrystalline structure and enhance phase was written, respectively, in order to achieve the automated modeling of composite material microstructure. Particle reinforced polycrystalline composite microstructure mesoscopic stress field was calculated by using the cell automatic identification technology and the homogenization processing method. Based on the definition of finite element method, six groups of the periodic boundary conditions of uniform strain is applied on representative volume element of the composite material, and obtained the stiffness of the matrix of the composite material. And then, engineering elastic constants of fabric reinforced composites was predicted. In this paper, the equivalent thermal expansion coefficient of the composite was predicted. The forecast result was in good agreement with the predictions of the finite element results and the experimental data. This indicated that the finite element analysis model was accuracy to verify the validity of the prediction method.
After the above work has been completed, this paper researched the composite microstructure simulation and performance prediction integration technology. The simulation module interface program was taken on the microstructure of composites materials and designed the software for simulation module. Based on ABAQUS secondary development of the script, such as automated geometric modeling, meshing, anisotropic material given boundary conditions and load application, the results of extraction and calculation process, it could automate the simulation and prediction the integration representative volume element of the composite microstructure. In addition, the Python language was employed to development of graphical user interface, then designed input dialog of simulation module parameter. Simultaneously, software was combined with PyOpenGL programming, the preparation of a three-dimensional visualization program demonstrated demo composite composition microstructure. The software uses an external data file transfer simulation parameters indirectly, this could achieve the main graphical user interface, three-dimensional visualization window, a seamless transition between the self-development programs, and ABAQUS script calls. Furthermore, the numerical simulation software VirtualTPS of the composite microstructure was developed in this study, and provided the basic tools for composite structure-performance.
引文
[1]材料科学技术百科全书编辑委员会.材料科学技术百科全书[M].北京：中国大百科全书出版社,1995
[2]陈绍杰.先进复合材料的现状和趋势[J].高科技纤维与应用,2001,26(6)：1-5
[3]高树理,柴孟贤,张明习.透波复合材料的研究进展[J].工程塑性材料应用,2000,28(5)：31-35.
[4]梁军,杜善义.防热复合材料高温力学性能[J].复合材料学报,2004,21(1)：73-77
[5]陈华辉,邓海金,李明,林晓松.现代复合材料[M].北京：中国物资出版社,1998,1-11
[6]H Steven, E Troy. Advanced grid stiffened structures for the next generation of launch vehicles[C].1997 IEEE Aerospace Conference Proceeding. Kahre:IEEE Aerospace and Electronics Systems Society, 1997:263-269
[7]I M Robert. Advanced composite structures research in Australia [J].Composite Structure,2002,57:3-10
[8]董元彩,孟卫,魏欣等.环氧树脂/二氧化钛纳米复合材料的制备及性能[J].塑料工业,1999,27(6)：37-38
[9]阮圣平,吴凤清,王永为等.钡铁氧体纳米复合材料的制备及其微波吸收性能[J].物理化学学报,2003,19(3)：275-277
[10]E T Thostenson, C Li. Nanocomposites in context[J]. Composite Science and Technology,2005,65(3):491-512
[11]吕维洁.原位合成钛基复合材料的制备、微结构及力学性[D].上海：上海交通大学,2000
[12]万红,潘进,杨德明.铝基混杂增强金属基复合材料的制备[J].宇航材料工艺,1996,3：41-45
[13]马爱斌,王明,蒋建清.氧化铝纤维、石墨混杂增强ZL108复合材料的摩擦特性[J].材料工程,1993,2：20-23
[14]J Jang, S Han. Mechanical properties of glass fiber mat/PMMA functionally gradient composite[J]. Composites:Part A,1999,30A: 1045-1053
[15]党智敏,王海燕,王岚.新型高温高介无机/有机功能复合材料[J].复合材料学报,2005,22(5)：9-16
[16]S A R Hashmi. Attaining a controlled graded distribution of particles in polymerizing fluid for functionally graded materials[J]. Journal of Applied Polymer Science,2006,99(6):3009-3017
[17]谢建宏,张为公.智能材料结构的研究与发展[J].传感技术学报,2004(3)：165-167
[18]杜善义,冷劲松,王殿富.智能材料系统与结构[M].北京：科学出版社,2001
[19]陈斌.生物复合材料的细观结构和仿生复合材料的研究[J].材料导报,1998,12(5)：70-75
[20]陈平,于祺,孙明,陆春.高性能热塑性树脂基复合材料的研究进展[J].纤维复合材料,2005,2：52-57
[21]陈平,陆春,于祺,李俊燕.纤维增强热塑性树脂基复合材料界面研究进展[J].材料科学与工艺,2007,15(5)：665-669
[22]陈祥宝.先进树脂基复合材料的发展和应用[J].航空材料学报,2003,23(增刊)：198-204
[23]秦华宇,吕玲,梁国正等.闰福胜,王志强,张明习.环氧树脂改性氰酸醋树脂复合材料的研究[J].纤维复合材料,1999,4(23)：23-26
[24]包建文,陈祥宝.电子束固化树脂基复合材料进展[J].高分子通报,2002(2)：69-72
[25]李成功,傅恒志,于翘等.航空航天材料[M].北京：国防工业出版社,2002
[26]张凤翻.航空结构复合材料对碳纤维的需求[J].材料导报,2000,14(11)：5-8
[27]D Eylon, M M Keller, P E Jone. Development of permanent-mold cast TiAl automotive valves[J]. Intermetallics,1998,6(6):703-708
[28]I Weiss, S L Semiatin. Thermo mechanical processing of beta titanium alloys an overview[J]. Materials Science and Engineering,1998, 243(1):46-65.
[29]T Clyne, et al. An introduction to metal matrix composites[M] Cambridge:Cambridge University Press,1993
[30]崔岩.碳化硅颗粒增强铝基复合材料的航空航天应用[J].材料工程,2002,6：3-6
[31]张立同,成来飞,徐永东.新型碳化硅陶瓷基复合材料的研究进展[J].航空制造技术,2003(1)：24-32
[32]樊建中,姚忠凯.颗粒增强铝基复合材料研究进展[J].材料导报,1996,11(3)：35-38
[33]沈真.中国航空研究院编著.复合材料结构设计手册[M].北京：航空工业出版社,2001,1-18
[34]吴德隆,沈怀荣.纺织结构复合材料的力学性能[M].长沙：国防科技大学出版社,1998,1-7
[35]李嘉禄,孙颖.二步法方型三维编织复合材料的细观结构[J].复合材料学报,2002,19(4)：69-75
[36]Ishikawa T, Chou T W. Stiffness and strength behavior of Woven fabric composites[J]. J Materils Science,1982,17(11):3211-3220
[37]秦湘阁,刘国权.多晶体品粒尺度三维组织建模及可视化[J].北京科技大学学报,2001,23(6)：35-42
[38]李顺林,王兴业.复合材料结构设计基础[M].武汉：武汉理工大学出版社,1993
[39]尤风翔,郝庆东.复合材料层合板随机参数结构的响应分析[J].河南科技大学学报(自然科学版),2004,25(4)：14—19
[40]李旭东.材料结构弱点Ⅰ：基本概念与科学问题[J].材料研究学报,2007,21(增刊)：16-21
[41]李旭东.材料结构弱点Ⅱ：微裂纹虚拟扩展模拟[J].材料研究学报,2007,21(增刊)：22-29
[42]Li X D. On composites structure weaknesses Part I:simulation, properties and numerical approach[J]. Metallurgical and Material Transactions,2002, A33:2205-2215
[43]Li X D. On composites structure weaknesses Part II:computer experiments, identifications and correlation[J]. Metallurgical and Material Transactions,2002, A33:2217-2227
[44]H Singh, A M Gokhale. Visualization of three dimensional micro structures[J]. Mater Character,2005,54(1):21
[45]J Schwertel, H Stamm. Analysis and modeling of tessellations by means of image analysis methods[J]. Journal of Microcrocopy,1997, 11:198-209.
[46]K M Wu, M Enomoto. Three-dimensional morphology of degenerate ferrite in an Fe-C-Mo alloy[J]. Scripta Materialia,2002,46:569-574
[47]D J Derosier, A Kan. Reconstruction of three dimensional structures from electron micrographs[J]. Nature,1968,217:130
[48]S I Lieberman, A M Gokhale S Tamirisakandala. Reconstruction of three dimensional microstructures of TiB whiskers in powder processed Ti-6Al-4V-1B alloys[J]. Mater Charact,2007,58:527
[49]M Li, S Ghosh, O Richmond, et al. Three dimensional characterization and modeling of particle reinforced metal matrix composites:part I. Quantitative description of microstructural morphology[J]. Materials Science and Engineering,1999,266(1):221-224
[50]K M Wu, Y Inagawa, M Enornoto. Three-dimensional morphology of ferrite fomled in association with inclusions in low-carbon steel. Mater Charact,2004,52:121
[51]R S Sidhu, N Chawla. Three-dimensional microstructure characterization of Ag3Sn in Sn-rich solder by serial sectioning. Mater Charact,2004,52:255
[52]N C Kuijpers, J Tirel, D N Hanlon. Quantification of the evolution of the 3D intermetallic structure in a 6005A aluminum alloy during a homogenization treatment[J]. Mater Charact,2002,48:379
[53]M P Adersonv, D J Srolovitz, G S Grest. Computer simulation of grain growth I. Kinetics[J]. Acta Metall,1984,32(5):783
[54]D J Srolovitz, M P Adersonv, G S Grest. Computer simulation of grain growth Ⅱ. Grain size distribution, topology and local dynamics [J]. Acta Metall,1984,32(5):793
[55]QYu, K, Esehe. A Monte Carlo algorithm for single phase normal grain growth with improved accuracy and efficiency[J]. Comp Mater Sci,2003,27:259-270
[56]Ikare V, Cawleyj D. Numerical simulation of grain growth in liquid phase sintering materials-Ⅰ:model[J]. Actamater,1998,46(4): 1333-1342
[57]秦湘阁,刘国权.基于Monte Carlo Potts方法的三维大尺度晶粒组织仿真模型及定量表征[J].北京科技大学学报,2004,26(1)：49
[58]刘国权,张禹,秦湘阁,等.材料显微组织三维观测与基于图像的模型研究[J].中国体视学与图像分析,2001,6：46
[59]S Torquato. Random heterogeneous media:microstructure and improved bounds on effective properties. Appl Mech Rev,1991,44: 37-76
[60]康国政,高庆,刘世楷.纤维取向对短纤维复合材料中应力传递的影响[J].西南交通大学学报,1998,33(1)：7-12
[61]W J Lee, J H Son, N H Kang. Finite element analysis of deformation behaviors in random whisker-reinforced composite[J]. Scripta Materials,2009,61:580-583
[62]金泉,谭继宁,张获等.颗粒和纤维混杂增强复合材料力学性能的三维有限元模拟[J].复合材料学报,2006,23(2)：14-20
[63]T Ohya. Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms[J]. Journal of Operation & Research Sociaty,1984,27: 306-336
[64]S Forune. A sweep line algorithm for voronoi diagrams[J]. Algorithmica, New York:Springer-Verlag Inc,1987,2:153-174
[65]S Kumar. Computer simulation of 3D material microstructure and its application in the determination of mechanical behavior of polycrystalline materials and engineering structures[D]. PhD Dissertation, The Pennsylvania State University. USA,1992
[66]M W D Van der Burg, V Shulmeister. On the linear elastic properties of regular and random open-cell foams models[J]. J Cell Plast,1997, 33:31-54
[67]V Shulmeister, M W D Van der Burg. A numerical study of large deformations of low-density elastomeric open-cell foams[J]. Mech. Mater,1998,30(2):125-140.
[68]李旭东.复合材料微观组织结构的计算机可视化表征[C].2004年材料科学与工程新进展.北京：冶金工业出版社,2004：1103-1111
[69]X D Li. Visualized simulation and modularized architecture of microstructure for composite materials[J]. Composite Interfaces,2005, 12:291-309
[70]卢子兴,张家雷,王嵩.各向异性随机泡沫模型的弹性性能分析[J].北京航空航天大学学报,2006,32(12)：1468-1471
[71]F Aurenhamme. Power diagrams:Properties, algorithms and applications[J]. SIAM Journal on Computing,1987,16(1):78-96
[72]He D, Ekere N N, L. Cai. Computer simulation of random packing of unequal particles[J]. Physical review E,1999,60(6):7098-7014
[73]Nolan G T, Kavanagh P E. Computer simulation of random packings of spheres with lognormal distributions[J]. Powder Technology,1993,76 (3):309-316
[74]C Lautensack. Fitting three-dimensional Laguerre tessellations to foam structures[J]. Journal of Applied Statistics,2008,35(9): 985-995
[75]C Lautensack. Random Laguerre tessellations[D]. Weiler bei Bingen: University Karlsruhe,2007
[76]吴壮志,杨钦,怀进鹏.Power图的性质及构造算法研究[J].计算机辅助设计与图形学学报,2001,13(12)：1057-1062
[77]Fan Z, Wu Y, Zhao X, Lu Y. Simulation of polycrystalline structure with Voronoi diagram in Laguerre geometry based on random closed packing of spheres[J]. Computational Materials Science,2004,29: 301-308
[78]M Kuhn. Optimierung von Power-Diagrammen zur Modellierung keramischer Mikrostrukturen[D]. Master's thesis, Fernuniversitat Hagen, Fraunhofer EMI, Freiburg i. Br.,2005
[79]Kanaun S, Tkachenko O. Mechanical properties of open cell foams: simulations by Laguerre tessellation procedure[J]. International Journal of Fracture,2006,140:305-312
[80]C Lautensack. Fitting three-dimensional Laguerre tessellations to foam structures[J]. Journal of Applied Statistics,2008,35(9): 985-995.
[81]Y G Wu, W B Zhou, B Wang, F Yang. Modeling and characterization of two-phase composites by Voronoi diagram in the Laguerre geometry based on random close packing of spheres[J]. Computational Materials Science,2010,47:951-961
[82]杜善义,王彪.复合材料细观力学[M].北京：科学出版社,1998
[83]J D Eshelby. The determination of the elastic field of an ellipsoid al inclusion and related problems[C]. Proc. Roy. Soc., London,1957, A241:376-396
[84]J D Eshelby. The elastic field outside of an ellipsoidal inclusion[C]. Proc. Roy. Soc., London,1959, A252:561-569
[85]A V Hershey. The elasticity of an isotropic aggregate of anisotropic cubic crystals[J]. J. Appl. Mech.,1954,21:236-240
[86]E Kroner. Bereclmung der elastischen konstanten des vielkristalls aus den konstanten des einkristalIs[J]. Zeitschrift fur Physik,1958,151: 504-518
[87]R Hill. A self-consistent mechanics of composite materials[J]. J. Mech. Phys. Solids,1965,13:213-222
[88]B Budiansky. On the Elastic moduli of some heterogeneous materials[J]. J. Mech. Phys. Solids,1965,13(4):223-227
[89]R M Christensen, KHLo. Solutions for effective shear properties in three sphere and cylinder models[J]. J. Mech. Phys. Solids,1979,27: 315-330
[90]T Mori, K Tanaka. Average stress in matrix and average energy of materials with misfitting inclusions[J]. Act. Metall.,1973,21: 571-574
[91]Z Hashin, S Shtrikman. A variational approach to the theory of the elastic behaviour of multiphase materials[J]. J. Mech. Phys. Solids, 1963,11:127-140
[92]王冒成,邵敏编著.有限单元法基本原理和数值方法[M].北京：清华大学出版社,2000
[93]S S Rao. The Finite element Methods in Engineering[J]. Pergamon Press,1982,10:264-272
[94]M I Baskes, R G Hoagland, A Needleman. Summary report: computational issues in the mechanical behavior of metals and intermetallics[J]. Mater Sci Eng A,1992,159:1-34
[95]P R Dawson, A Needleman. Issues in the finite element modeling of polyphases plasticity[J]. Mater Sci Eng A,1994,175:43-48
[96]方岱宁,周储伟.有限元计算细观力学对复合材料力学行为的数值分析[J].力学进展,1998,28(2)：173-188
[97]H C Brown, H J Lee, C C Chamis. Fiber shape effects on metal matrix composite behavior, NASATM-106067, NASA Lew is Center, USA, 1992
[98]T Nakamura, S Suresh. Effects of thermal residual stresses and fiber packing on deformation of metal-matrix composites[J]. Acta Metall Mater,1993,41:1665-1681
[99]A Needleman, A S Kushner. An analysis of void distribution effects on plastic flow in porous solids[J]. Eur J Mech, A Solids,1990,9: 193-206
[100]N J Sorensen, S Suresh, V Tvergaard. Effects of reinforcement orientation on tensile response of metal-matrix composites[J]. Mater Sci Eng, A,1995,197:1-10
[101]J R Brockenborough, S Suresh, H A Wienecke. Deformation of metal-matrix composites with continuous fibers:geometrical effects of fiber distribution and shape[J]. Acta Metall Mat,1991,39(5): 735-752
[102]M S Axelsen. Quantitative description of morphology and microdamages of composite materials, PhD Thesis. Aalborg Univeristy,1995
[103]杨庆生,陈浩然.夹层问题中的自洽有限元法和复合材料的平均弹性模量性质[J].复合材料学报,1992,9：1-12
[104]方岱宁,齐航.颗粒增强复合材料有效性能的三维数值分析[J].力学学报,1996,28：475-482
[105]秦湘阁,刘国权.颗粒增强复合材料显微组织的计算机仿真[J].佳木斯大学学报,2001,19(1)：36-41
[106]李华清,成丽娟,李旭东.平面微裂纹扩展过程的计算机模拟[J].兰州理工大学学报,2004,30(3)：23-26.
[107]王瑞,王建坤,武玲.平纹织物复合材料的弹性模量预测[J].复合材料学报,2002,19(1)：90-94
[108]Edelsbrunner H, Shah N R. Incremental topological flipping works for regular triangulations[J]. Algorithmic,1996,15,223-241
[109]Bowyer A. Computing Dirichlet tessellations[J]. Computer Journal, 1981,24(2):162-166
[110]Watson D F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes[J]. Computer Journal,1981, 24(2):167-172
[111]Watson D F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes[J]. Computer Journal,1981, 24(2):167-172
[112]Chen L, Tao X M, Choy C L. On the microstructure of three dimensional braided performs[J]. Composites Science and Technology, 1999,59:391-404
[113]Holliday L, Robinson J. The thermal expansion of composites based on polymers[J]. Journal of Materials Science,1973,8(3):301-311
[2]陈绍杰.先进复合材料的现状和趋势[J].高科技纤维与应用,2001,26(6)：1-5
[3]高树理,柴孟贤,张明习.透波复合材料的研究进展[J].工程塑性材料应用,2000,28(5)：31-35.
[4]梁军,杜善义.防热复合材料高温力学性能[J].复合材料学报,2004,21(1)：73-77
[5]陈华辉,邓海金,李明,林晓松.现代复合材料[M].北京：中国物资出版社,1998,1-11
[6]H Steven, E Troy. Advanced grid stiffened structures for the next generation of launch vehicles[C].1997 IEEE Aerospace Conference Proceeding. Kahre:IEEE Aerospace and Electronics Systems Society, 1997:263-269
[7]I M Robert. Advanced composite structures research in Australia [J].Composite Structure,2002,57:3-10
[8]董元彩,孟卫,魏欣等.环氧树脂/二氧化钛纳米复合材料的制备及性能[J].塑料工业,1999,27(6)：37-38
[9]阮圣平,吴凤清,王永为等.钡铁氧体纳米复合材料的制备及其微波吸收性能[J].物理化学学报,2003,19(3)：275-277
[10]E T Thostenson, C Li. Nanocomposites in context[J]. Composite Science and Technology,2005,65(3):491-512
[11]吕维洁.原位合成钛基复合材料的制备、微结构及力学性[D].上海：上海交通大学,2000
[12]万红,潘进,杨德明.铝基混杂增强金属基复合材料的制备[J].宇航材料工艺,1996,3：41-45
[13]马爱斌,王明,蒋建清.氧化铝纤维、石墨混杂增强ZL108复合材料的摩擦特性[J].材料工程,1993,2：20-23
[14]J Jang, S Han. Mechanical properties of glass fiber mat/PMMA functionally gradient composite[J]. Composites:Part A,1999,30A: 1045-1053
[15]党智敏,王海燕,王岚.新型高温高介无机/有机功能复合材料[J].复合材料学报,2005,22(5)：9-16
[16]S A R Hashmi. Attaining a controlled graded distribution of particles in polymerizing fluid for functionally graded materials[J]. Journal of Applied Polymer Science,2006,99(6):3009-3017
[17]谢建宏,张为公.智能材料结构的研究与发展[J].传感技术学报,2004(3)：165-167
[18]杜善义,冷劲松,王殿富.智能材料系统与结构[M].北京：科学出版社,2001
[19]陈斌.生物复合材料的细观结构和仿生复合材料的研究[J].材料导报,1998,12(5)：70-75
[20]陈平,于祺,孙明,陆春.高性能热塑性树脂基复合材料的研究进展[J].纤维复合材料,2005,2：52-57
[21]陈平,陆春,于祺,李俊燕.纤维增强热塑性树脂基复合材料界面研究进展[J].材料科学与工艺,2007,15(5)：665-669
[22]陈祥宝.先进树脂基复合材料的发展和应用[J].航空材料学报,2003,23(增刊)：198-204
[23]秦华宇,吕玲,梁国正等.闰福胜,王志强,张明习.环氧树脂改性氰酸醋树脂复合材料的研究[J].纤维复合材料,1999,4(23)：23-26
[24]包建文,陈祥宝.电子束固化树脂基复合材料进展[J].高分子通报,2002(2)：69-72
[25]李成功,傅恒志,于翘等.航空航天材料[M].北京：国防工业出版社,2002
[26]张凤翻.航空结构复合材料对碳纤维的需求[J].材料导报,2000,14(11)：5-8
[27]D Eylon, M M Keller, P E Jone. Development of permanent-mold cast TiAl automotive valves[J]. Intermetallics,1998,6(6):703-708
[28]I Weiss, S L Semiatin. Thermo mechanical processing of beta titanium alloys an overview[J]. Materials Science and Engineering,1998, 243(1):46-65.
[29]T Clyne, et al. An introduction to metal matrix composites[M] Cambridge:Cambridge University Press,1993
[30]崔岩.碳化硅颗粒增强铝基复合材料的航空航天应用[J].材料工程,2002,6：3-6
[31]张立同,成来飞,徐永东.新型碳化硅陶瓷基复合材料的研究进展[J].航空制造技术,2003(1)：24-32
[32]樊建中,姚忠凯.颗粒增强铝基复合材料研究进展[J].材料导报,1996,11(3)：35-38
[33]沈真.中国航空研究院编著.复合材料结构设计手册[M].北京：航空工业出版社,2001,1-18
[34]吴德隆,沈怀荣.纺织结构复合材料的力学性能[M].长沙：国防科技大学出版社,1998,1-7
[35]李嘉禄,孙颖.二步法方型三维编织复合材料的细观结构[J].复合材料学报,2002,19(4)：69-75
[36]Ishikawa T, Chou T W. Stiffness and strength behavior of Woven fabric composites[J]. J Materils Science,1982,17(11):3211-3220
[37]秦湘阁,刘国权.多晶体品粒尺度三维组织建模及可视化[J].北京科技大学学报,2001,23(6)：35-42
[38]李顺林,王兴业.复合材料结构设计基础[M].武汉：武汉理工大学出版社,1993
[39]尤风翔,郝庆东.复合材料层合板随机参数结构的响应分析[J].河南科技大学学报(自然科学版),2004,25(4)：14—19
[40]李旭东.材料结构弱点Ⅰ：基本概念与科学问题[J].材料研究学报,2007,21(增刊)：16-21
[41]李旭东.材料结构弱点Ⅱ：微裂纹虚拟扩展模拟[J].材料研究学报,2007,21(增刊)：22-29
[42]Li X D. On composites structure weaknesses Part I:simulation, properties and numerical approach[J]. Metallurgical and Material Transactions,2002, A33:2205-2215
[43]Li X D. On composites structure weaknesses Part II:computer experiments, identifications and correlation[J]. Metallurgical and Material Transactions,2002, A33:2217-2227
[44]H Singh, A M Gokhale. Visualization of three dimensional micro structures[J]. Mater Character,2005,54(1):21
[45]J Schwertel, H Stamm. Analysis and modeling of tessellations by means of image analysis methods[J]. Journal of Microcrocopy,1997, 11:198-209.
[46]K M Wu, M Enomoto. Three-dimensional morphology of degenerate ferrite in an Fe-C-Mo alloy[J]. Scripta Materialia,2002,46:569-574
[47]D J Derosier, A Kan. Reconstruction of three dimensional structures from electron micrographs[J]. Nature,1968,217:130
[48]S I Lieberman, A M Gokhale S Tamirisakandala. Reconstruction of three dimensional microstructures of TiB whiskers in powder processed Ti-6Al-4V-1B alloys[J]. Mater Charact,2007,58:527
[49]M Li, S Ghosh, O Richmond, et al. Three dimensional characterization and modeling of particle reinforced metal matrix composites:part I. Quantitative description of microstructural morphology[J]. Materials Science and Engineering,1999,266(1):221-224
[50]K M Wu, Y Inagawa, M Enornoto. Three-dimensional morphology of ferrite fomled in association with inclusions in low-carbon steel. Mater Charact,2004,52:121
[51]R S Sidhu, N Chawla. Three-dimensional microstructure characterization of Ag3Sn in Sn-rich solder by serial sectioning. Mater Charact,2004,52:255
[52]N C Kuijpers, J Tirel, D N Hanlon. Quantification of the evolution of the 3D intermetallic structure in a 6005A aluminum alloy during a homogenization treatment[J]. Mater Charact,2002,48:379
[53]M P Adersonv, D J Srolovitz, G S Grest. Computer simulation of grain growth I. Kinetics[J]. Acta Metall,1984,32(5):783
[54]D J Srolovitz, M P Adersonv, G S Grest. Computer simulation of grain growth Ⅱ. Grain size distribution, topology and local dynamics [J]. Acta Metall,1984,32(5):793
[55]QYu, K, Esehe. A Monte Carlo algorithm for single phase normal grain growth with improved accuracy and efficiency[J]. Comp Mater Sci,2003,27:259-270
[56]Ikare V, Cawleyj D. Numerical simulation of grain growth in liquid phase sintering materials-Ⅰ:model[J]. Actamater,1998,46(4): 1333-1342
[57]秦湘阁,刘国权.基于Monte Carlo Potts方法的三维大尺度晶粒组织仿真模型及定量表征[J].北京科技大学学报,2004,26(1)：49
[58]刘国权,张禹,秦湘阁,等.材料显微组织三维观测与基于图像的模型研究[J].中国体视学与图像分析,2001,6：46
[59]S Torquato. Random heterogeneous media:microstructure and improved bounds on effective properties. Appl Mech Rev,1991,44: 37-76
[60]康国政,高庆,刘世楷.纤维取向对短纤维复合材料中应力传递的影响[J].西南交通大学学报,1998,33(1)：7-12
[61]W J Lee, J H Son, N H Kang. Finite element analysis of deformation behaviors in random whisker-reinforced composite[J]. Scripta Materials,2009,61:580-583
[62]金泉,谭继宁,张获等.颗粒和纤维混杂增强复合材料力学性能的三维有限元模拟[J].复合材料学报,2006,23(2)：14-20
[63]T Ohya. Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms[J]. Journal of Operation & Research Sociaty,1984,27: 306-336
[64]S Forune. A sweep line algorithm for voronoi diagrams[J]. Algorithmica, New York:Springer-Verlag Inc,1987,2:153-174
[65]S Kumar. Computer simulation of 3D material microstructure and its application in the determination of mechanical behavior of polycrystalline materials and engineering structures[D]. PhD Dissertation, The Pennsylvania State University. USA,1992
[66]M W D Van der Burg, V Shulmeister. On the linear elastic properties of regular and random open-cell foams models[J]. J Cell Plast,1997, 33:31-54
[67]V Shulmeister, M W D Van der Burg. A numerical study of large deformations of low-density elastomeric open-cell foams[J]. Mech. Mater,1998,30(2):125-140.
[68]李旭东.复合材料微观组织结构的计算机可视化表征[C].2004年材料科学与工程新进展.北京：冶金工业出版社,2004：1103-1111
[69]X D Li. Visualized simulation and modularized architecture of microstructure for composite materials[J]. Composite Interfaces,2005, 12:291-309
[70]卢子兴,张家雷,王嵩.各向异性随机泡沫模型的弹性性能分析[J].北京航空航天大学学报,2006,32(12)：1468-1471
[71]F Aurenhamme. Power diagrams:Properties, algorithms and applications[J]. SIAM Journal on Computing,1987,16(1):78-96
[72]He D, Ekere N N, L. Cai. Computer simulation of random packing of unequal particles[J]. Physical review E,1999,60(6):7098-7014
[73]Nolan G T, Kavanagh P E. Computer simulation of random packings of spheres with lognormal distributions[J]. Powder Technology,1993,76 (3):309-316
[74]C Lautensack. Fitting three-dimensional Laguerre tessellations to foam structures[J]. Journal of Applied Statistics,2008,35(9): 985-995
[75]C Lautensack. Random Laguerre tessellations[D]. Weiler bei Bingen: University Karlsruhe,2007
[76]吴壮志,杨钦,怀进鹏.Power图的性质及构造算法研究[J].计算机辅助设计与图形学学报,2001,13(12)：1057-1062
[77]Fan Z, Wu Y, Zhao X, Lu Y. Simulation of polycrystalline structure with Voronoi diagram in Laguerre geometry based on random closed packing of spheres[J]. Computational Materials Science,2004,29: 301-308
[78]M Kuhn. Optimierung von Power-Diagrammen zur Modellierung keramischer Mikrostrukturen[D]. Master's thesis, Fernuniversitat Hagen, Fraunhofer EMI, Freiburg i. Br.,2005
[79]Kanaun S, Tkachenko O. Mechanical properties of open cell foams: simulations by Laguerre tessellation procedure[J]. International Journal of Fracture,2006,140:305-312
[80]C Lautensack. Fitting three-dimensional Laguerre tessellations to foam structures[J]. Journal of Applied Statistics,2008,35(9): 985-995.
[81]Y G Wu, W B Zhou, B Wang, F Yang. Modeling and characterization of two-phase composites by Voronoi diagram in the Laguerre geometry based on random close packing of spheres[J]. Computational Materials Science,2010,47:951-961
[82]杜善义,王彪.复合材料细观力学[M].北京：科学出版社,1998
[83]J D Eshelby. The determination of the elastic field of an ellipsoid al inclusion and related problems[C]. Proc. Roy. Soc., London,1957, A241:376-396
[84]J D Eshelby. The elastic field outside of an ellipsoidal inclusion[C]. Proc. Roy. Soc., London,1959, A252:561-569
[85]A V Hershey. The elasticity of an isotropic aggregate of anisotropic cubic crystals[J]. J. Appl. Mech.,1954,21:236-240
[86]E Kroner. Bereclmung der elastischen konstanten des vielkristalls aus den konstanten des einkristalIs[J]. Zeitschrift fur Physik,1958,151: 504-518
[87]R Hill. A self-consistent mechanics of composite materials[J]. J. Mech. Phys. Solids,1965,13:213-222
[88]B Budiansky. On the Elastic moduli of some heterogeneous materials[J]. J. Mech. Phys. Solids,1965,13(4):223-227
[89]R M Christensen, KHLo. Solutions for effective shear properties in three sphere and cylinder models[J]. J. Mech. Phys. Solids,1979,27: 315-330
[90]T Mori, K Tanaka. Average stress in matrix and average energy of materials with misfitting inclusions[J]. Act. Metall.,1973,21: 571-574
[91]Z Hashin, S Shtrikman. A variational approach to the theory of the elastic behaviour of multiphase materials[J]. J. Mech. Phys. Solids, 1963,11:127-140
[92]王冒成,邵敏编著.有限单元法基本原理和数值方法[M].北京：清华大学出版社,2000
[93]S S Rao. The Finite element Methods in Engineering[J]. Pergamon Press,1982,10:264-272
[94]M I Baskes, R G Hoagland, A Needleman. Summary report: computational issues in the mechanical behavior of metals and intermetallics[J]. Mater Sci Eng A,1992,159:1-34
[95]P R Dawson, A Needleman. Issues in the finite element modeling of polyphases plasticity[J]. Mater Sci Eng A,1994,175:43-48
[96]方岱宁,周储伟.有限元计算细观力学对复合材料力学行为的数值分析[J].力学进展,1998,28(2)：173-188
[97]H C Brown, H J Lee, C C Chamis. Fiber shape effects on metal matrix composite behavior, NASATM-106067, NASA Lew is Center, USA, 1992
[98]T Nakamura, S Suresh. Effects of thermal residual stresses and fiber packing on deformation of metal-matrix composites[J]. Acta Metall Mater,1993,41:1665-1681
[99]A Needleman, A S Kushner. An analysis of void distribution effects on plastic flow in porous solids[J]. Eur J Mech, A Solids,1990,9: 193-206
[100]N J Sorensen, S Suresh, V Tvergaard. Effects of reinforcement orientation on tensile response of metal-matrix composites[J]. Mater Sci Eng, A,1995,197:1-10
[101]J R Brockenborough, S Suresh, H A Wienecke. Deformation of metal-matrix composites with continuous fibers:geometrical effects of fiber distribution and shape[J]. Acta Metall Mat,1991,39(5): 735-752
[102]M S Axelsen. Quantitative description of morphology and microdamages of composite materials, PhD Thesis. Aalborg Univeristy,1995
[103]杨庆生,陈浩然.夹层问题中的自洽有限元法和复合材料的平均弹性模量性质[J].复合材料学报,1992,9：1-12
[104]方岱宁,齐航.颗粒增强复合材料有效性能的三维数值分析[J].力学学报,1996,28：475-482
[105]秦湘阁,刘国权.颗粒增强复合材料显微组织的计算机仿真[J].佳木斯大学学报,2001,19(1)：36-41
[106]李华清,成丽娟,李旭东.平面微裂纹扩展过程的计算机模拟[J].兰州理工大学学报,2004,30(3)：23-26.
[107]王瑞,王建坤,武玲.平纹织物复合材料的弹性模量预测[J].复合材料学报,2002,19(1)：90-94
[108]Edelsbrunner H, Shah N R. Incremental topological flipping works for regular triangulations[J]. Algorithmic,1996,15,223-241
[109]Bowyer A. Computing Dirichlet tessellations[J]. Computer Journal, 1981,24(2):162-166
[110]Watson D F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes[J]. Computer Journal,1981, 24(2):167-172
[111]Watson D F. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes[J]. Computer Journal,1981, 24(2):167-172
[112]Chen L, Tao X M, Choy C L. On the microstructure of three dimensional braided performs[J]. Composites Science and Technology, 1999,59:391-404
[113]Holliday L, Robinson J. The thermal expansion of composites based on polymers[J]. Journal of Materials Science,1973,8(3):301-311
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