摘要
空心颗粒复合材料是一种具有轻质、高强、高吸能、多功能特性的复合材料，在工程实际中被广泛应用。对于空心颗粒复合材料，根据空心颗粒体积填充比的大小以及颗粒的分布状态，可将空心颗粒复合材料分为填充型和胶结型两种类型。针对这两种类型的空心颗粒复合材料，分别建立了各自的力学模型，并基于细观力学的分析方法分析了空心颗粒复合材料的宏细观力学性能。
针对填充型空心颗粒复合材料，利用RSA（Random Sequential Adsortion）方法建立了不同特质参数下（主要指空心颗粒体积填充比和壁厚）的空心颗粒复合材料的周期性代表体积单元模型，通过合理设置空心颗粒及基体的材料属性以及边界条件，计算得出了不同特质参数下复合材料的本构关系。将材料的本构曲线拟合为双线性特征，得出了材料的有效弹性模量、泊松比、屈服极限以及热膨胀系数等弹性常数，并分析了各特质参数与材料的弹性常数之间的相互关系。将各特质参数与材料的弹性常数之间的相互关系拟合为指数函数，然后分析了各特质参数对材料力学性能影响的灵敏度，以此来评价材料的稳定性。
通过实验结果与数值模拟结果的对比发现，材料内部的初始缺陷对计算结果影响很大。将初始缺陷以球形孔洞的形式加入到材料的代表体积单元模型中去，利用有限元分析了初始缺陷程度对材料各弹性常数的影响规律。通过与实验结果的对比分析估计出了实验中材料的缺陷程度。还将Differential scheme方法做了改进，将缺陷因素考虑到其中去，作为有限元计算结果的比照。将材料的缺陷程度与材料各弹性常数之间的相互关系拟合为指数函数，分析了缺陷程度对材料弹性模量及屈服极限影响的灵敏度。
针对胶结型颗粒复合材料，提出了计算材料宏细观力学性能的组合球单元方法：将胶结型颗粒复合材料中的一对颗粒及其胶结基体视为一个组合球单元，分别得出了组合球单元在轴向、切向及其弯曲三个方向的刚度，利用直接法构建了组合球单元的单元刚度矩阵，并将材料细观结构等效为刚性梁-弹簧网络模型。以平面六边形排列方式组合的颗粒复合材料为例，计算得出了基体中的应力分布函数、三个方向的刚度，以及弹性常数和细观应力集中系数。
最后，将组合球单元方法推广到胶结型空心颗粒复合材料中去。其中的关键步骤是当球壳顶部受法向集中载荷时，将球壳的受力变形区域简化成了扁壳；当球壳顶部受切向集中载荷时，将球壳的受力变形区域简化成了平面问题。通过计算空心颗粒组合球单元的各向刚度，将胶结型空心颗粒复合材料等效为刚性梁-弹簧网络模型，然后计算出材料的有效弹性性能，并制定组合球单元的失效准则，模拟材料损伤演化的过程。
Hollow particulate composites is a kind of composite with light weight, high strength,high energy absorption capacity and multifunction characteristic, and is widely used inengineering practice. According to the volume fraction and the distribution state of thehollow particle, the composites is divided into two types: one type is called hollowparticle filled composite(with low volume fraction); another one is called cementedhollow particulate composite(with high volume fraction). The simulation calculationmodel which aim at the characters of each type of composite is established, respectively.At last, the mechanical property of the composite can be obtained based on themesoscopic mechanics analysis method.
For the hollow particle filled composite, RSA (Random Sequential Adsorption)method was adopted to generate the periodic representative volume element models whichcontain the special parameters such as the volume fraction and the wall-thickness of thehollow particle. The reasonable material attributes and boundary conditions are set inorder to obtaining the constitutive relation of the composite material with different specialparameters. Material properties of the composite were simplified to bilinear kinematichardening model, and then the effective elasticity modulus, Poisson's ratio, yield strengthand coefficient of thermal expansion are obtained. The relationships of the specialparameters and these elastic constants are analyzed. The relationships are fitted toexponential function respectively, with the purpose of analyzing the sensitivity of theinfluence of the special parameters to the elastic constants. The stability of the compositemechanical properties can be represented.
Experimental results are compared with the numerical results. It shows that thereexisted a huge error. The reason of the error is the initial defect causing a great influenceto the mechanical properties of the composite. In order to improve the numerical method,the initial defects are considered into the model in the form of spherical voids. Theinfluence rules of the defect degree to the elastic constants of composite can be obtainedthrough the FEM analysis. The defect degree of the experimental material specimen can be estimate also. Differential scheme is also improved by considering the initial defect. Atlast, the relationships of the defect degree and the elastic constants are fitted to exponentialfunction respectively to analyze the sensitivity of the defect degree influence to the elasticconstants.
For the cemented particulate composite, combinational sphere element method isintroduce to solve its mechanical problem. A pair of particles and the cement separatedfrom the composite constitute a combinational sphere element. The stiffness of acombinational sphere element on axial direction, tangential direction and bendingdirection are derived based on the elastic theory. The element stiffness matrix ofcombinational sphere element is obtained through the direct method. According to theelement stiffness matrix, the combinational sphere element can be described by anequivalent rigid beam-spring combinational model, so the composite can be described byan equivalent rigid beam-spring lattice. Finally, an example is taken out to show theapplication of the new method. Stress distribution function, stiffness on three directionsand macro effective elastic constants of composite are obtained.
Finally, the combinational sphere element method is extended into the cementedhollow particulate composite. The critical process is how to simplify the spherical shell. Ifthe shell loads a normal concentrated force, the shell can be simplified to a shallowspherical shell; if the load is a tangential concentrated force, the shell can be simplified toa flat plate. And the stiffness of a combinational hollow sphere element on the threedirections can be obtained. The cemented hollow particulate composite can be alsodescribed by an equivalent rigid beam-spring lattice model. At last, the elastic propertycan be obtained. According to the failure criterion of the combinational sphere elementmethod established, the damage evolution of the material is described.
引文
[1] Holdren J P. Materials genome initiative for global competitiveness[R], Washington D C:National Science and Technology Council,2011:1-18.
[2]万勇,黄健,冯瑞华等.浅析美国"材料基因组计划"[J].新材料产业,2012,(7):62-64.
[3]秦高梧.《美国材料基因组计划》简介[EB/OL].(2012-11-01). http://www.ral.neu.edu.cn/.
[4] Gibson L, Ashby M.多孔固体结构与性能[M].刘培生,译.北京:清华大学出版社,2003:1-6.
[5]余为.金属空心球材料组元力学性能及结构设计[D].秦皇岛:燕山大学学位论文,2011:6-12.
[6] Xue Z Y, Hutchinson J W. Crush dynamics of square honeycomb sandwich cores[J].International Journal for Numerical Methods in Engineering,2006,65(13):2221-2245.
[7] Rathbun H J, Radford D D, Xue Z, et al. Performance of metallic honeycomb-core sandwichbeams under shock loading[J]. International Journal of Solids and Structures,2006,43:1746-1763.
[8] Vaidya U K, Pillay S, Bartus S, et al. Impact and post-impact vibration response of protectivemetal foam composite sandwich plates[J]. Materials Science and Engineering A,2006,428:59-66.
[9] Zhu F, Zhao L M, Lu G X, et al. A numerical simulation of the blast impact of square metallicsandwich panels[J]. International Journal of Impact Engineering,2009,36:1-13.
[10]赵桂平,卢天健.多孔金属夹层板载冲击载荷作用下的动态响应[J].力学学报,2008,40(2):194-206.
[11]李斌潮,张钱城,卢天健.基于实验模态分析的点阵夹层结构动态性能预测[J].固体力学学报,2008,29(4):373-378.
[12]田培培,赵桂平,卢天健.具有填充材料的金属格栅夹层板在高速冲击下动态响应的数值模拟[J].应用力学学报,2009,26(4):788-792.
[13]黄桥平,赵桂平,卢天健.考虑应变率效应的复合材料层合板冲击动态响应[J].西安交通大学学报,2009,43(1):72-76.
[14]倪长也,金峰,卢天健.超轻金属点阵三明治板结构抗侵彻性能分析[J].兵工学报,2009,30(增刊2):94-97.
[15]刘培生.泡沫材料在多向拉伸载荷作用下的力学模型[J].稀有金属材料与工程,2008,37(12):2009-2103.
[16]刘培生.泡沫金属在单双向拉压载荷作用下的表征分析[J].中国有色金属学报,2008,18(11):2062-2067.
[17]王展光,陈选,李书琴,等.球形孔泡沫铝及其合金的拉伸性能[J].机械工程材料,2009,33(10):75-77.
[18] Kou D P, Li J R, Yu J L, et al. Mechanical behavior of open-cell metallic foams with dual-sizecellular structure[J]. Scripta Materialia,2008,59:483-486.
[19] Rabiei A, Vendra L J. A comparison of composite metal foam's properties and other comparablemetal foams[J]. Materials Letters,2009,63:533-536.
[20] Albanakis C, Missirlis D, Michailidis N, et al. Experimental analysis of the pressure drop andheat ransfer through metal foams used as volumetric receivers under concentrated solarradiation[J]. Experimental Thermal and Fluid Science,2009,33:246-252.
[21] Nemat-Nasser S, Kang W J, Mcgee J D, et al. Experimental investigation of energy-absorptionharacteristics of components of sandwich structures[J]. International Journal of ImpactEngineering,2007,34:1119-1146.
[22]陈成军,谢若泽,张方举,等. Taylor撞击实验在泡沫铝合金力学特性研究中的应用[J].爆炸与冲击,2008,28(2):166-171.
[23] Avalle M, Belingardi G, Ibba A. Mechanical models of cellular solids: Parameters identifi-cation from experimental tests[J]. International Journal of Impact Engineering,2007,34:3-27.
[24]卢天健.超轻多孔材料和结构创新构型的多功能化基础研究[EB/OL].(2012-02-25). http://wenku.baidu. com/view/a109da906bec0975f465e254.html.
[25] Eshelby J. The Determination of the elastic field of an ellipsoidal inclusion, and relatedproblems[J]. Proceedings of the Royal Society of London,1957,(A241):376-396.
[26] Hill R. Theory of mechanical properties of fibre-strengthened materials--iii. self-consistentmodel[J]. Journal of the Mechanics and Physics of Solids,1965,13(4):189-198.
[27] Hill R. A self-consistent mechanics of composite materials[J]. Journal of the Mechanics andPhysics of Solids,1965,13(4):213-222.
[28] Hendrix B, Yu L. Self-consistent elastic properties for transversely isotropic polycry-stals[J].Acta Materialia,1998,46(1):127-135.
[29] Zeng Q H, Yu A B, Lu G Q. Multiscale modeling and simulation of polymer nanocom-posites[J]. progress in polymer science,2008,33(2):191-269.
[30] Huang Y, Hu K X, Wei X, et al. A generalized self-consistent mechanics method for compositematerials with multiphase inclusions[J]. Journal of the Mechanics and Physics of Solids,1994,42(3):491-504.
[31] Drozdov A D. Modeling viscoelastic response of particulate polymeric composites with highvolume fractions of fillers[J]. Mathematical and Computer Modelling,1999,29(4):11-25.
[32] Mura T. Micromechanics of defects in solids[M]. Dordrecht: Martinus Nijhoff Publishers,1987:390-397.
[33]黄克智,黄永刚.固体本构关系[M].北京:清华大学出版社,1999:120-172.
[34] Kiris A, Inan E. Eshelby tensors for a spherical inclusion in microelongated elastic fields[J].International Journal of Engineering Science,2005,43(1-2):49-58.
[35] Tohgo K, Masunari A, Yoshida M. Two-phase composite model taking into account thematricity of microstructure and its application to functionally graded materials[J]. CompositesPart A: Applied Science and Manufacturing,2006,37(10):1688-1695.
[36] Zhong Y, Wang J, Wu Y, et al. Effective moduli of particle-filled composite with inhomo-geneous interphase: Part I-Mapping method and evaluation[J]. Composites Science andTechnology,2004,64(9):1353-1362.
[37] Pal R. New models for effective young's modulus of particulate composites[J]. Composites PartB: Engineering,2005,36(6-7):513-523.
[38] Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behaviour ofmultiphase materials[J]. Journal of the Mechanics and Physics of Solids,1963,11:127-140.
[39] Bédoui F, Diani J, Régnier G. Micromechanical Modeling of Elastic Properties in Polyolefins[J].Polymer,2004,45(7):2433-2442.
[40]何长军. HGMs/EP复合泡沫塑料材料设计与性能研究[D].秦皇岛:燕山大学学位论文,2011:12-13.
[41]卢子兴,黄筑平,王仁.基于三相球模型确定泡沫塑料有效模量[J].固体力学学报,1996,17(2):95-102.
[42]卢子兴.复合材料的四相球模型及其应用[J].内蒙古工业大学学报,1997,16(3):104-111.
[43]邹波,卢子兴.基于五相球模型确定含涂层空心微球复合材料的有效模量[J].复合材料学报,2006,23(5):137-142.
[44]邹波,卢子兴.中空纳米微球填充复合材料的有效力学性能[J].力学学报,2009,41(2):265-273.
[45]卢子兴.球形涂层粒子增强复合材料的有效模量[J].应用数学和力学,1998,19(10):921-929.
[46]袁应龙,卢子兴.含涂层空心球复合泡沫塑料的模量预测及讨论[J].应用数学和力学,2004,25(5):481-487.
[47]严寒冰.用微分法及Mori-Tanaka法求解复合泡沫塑料的有效模量[J].北京航空航天大学学报,2000,26(06):688-690.
[48]段慧玲,王建祥,黄筑平等.具有非均匀界面相的颗粒和纤维增强复合材料弹性静力学问题的解析解[J].应用数学和力学,2005,26(3):309-315.
[49]仲政.含柔性涂层的颗粒增强复合材料弹性模量估计[J].固体力学学报,2000,21(4):350-354.
[50]余湘彬,仲政.弱界面颗粒增强复合材料的有效弹性模量[J].同济大学学报,2000,28(3):257-261.
[51] Lee K J, Westmann RA. Elastic properties of hollow-sphere-reinforced composites[J]. Journalof Composite Materials,1970,4:242-52.
[52] Torquato S. Random heterogeneous materials: microstructure and macroscopic properties[M].New York: Springer,2001.
[53] Huang J S, Gibson L J. Elastic moduli of a composite of hollow spheres in a matrix[J]. Journalof the Mechanics and Physics of Solids,1993,41(1):55-75.
[54] Pal R. Modeling viscoelastic behavior of particulate composites with high volume fraction offiller[J]. Materials Science and Engineering: A,2005,412(1–2):71-77.
[55] Pal R. Porosity-dependence of effective mechanical properties of pore–solid compositematerials [J]. Journal of Materials Science,2005,39:1147-1158.
[56] Pal R. New models for effective Young’s modulus of particulate composites[J]. Composites PartB: Engineering,2005,36(6-7):513-523.
[57] Porfiri M, Gupta N. Effect of volume fraction and wall thickness on the elastic properties ofhollow particle filled composites[J]. Composites Part B: Engineering,2009,40(2):166-173.
[58] Tohgo K, Chou T W. Incremental theory of particulate-reinforced composites includingdebonding damage[J]. JSME International Journal,1996,39:389-397.
[59] Tohg K O, Weng G J. A progressive damage mechanics in particle-reinforced metal-matrixcomposites under high triaxial tension[J]. ASME Journal of Engineering Material Technology,1994,116:414-420.
[60] Cho Y T, Tohgo K, Ishii H. Load carrying capacity of a broken ellipsoidal inhomogeneity[J].Acta Materialia,1997,45:4787-4795.
[61] Tohgo K, Cho Y T. Theory of reinforcement damage in discontinuously reinforced compositesand its application[J]. JSME International Journal,1999,42:521-529.
[62]王晴.颗粒复合材料细微观组织结构破坏及本构方程理论研究[D].秦皇岛:燕山大学学位论文,2011:1-3.
[63]金泉,覃继宁,张荻,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.
[64]李晓军,柴东朗,郝雨林. SiCp增强镁基复合材料微区应力场的仿真模拟[J].金属学报,2004,40(9):927-929.
[65]于敬宇,李玉龙,周宏霞,等.颗粒尺寸对颗粒增强型金属基复合材料动态特性的影响[J].复合材料学报,2005,22(5):31-38.
[66]柴东朗,曹利强,李晓军,等.镁基复合材料微区力学状态的有限元分析[J].稀有金属材料与工程,2005,34(1):60-63.
[67]张芮,卢锡年.球形颗粒填充复合材料微观应力场的有限元分析[J].复合材料学报,1995,12(4):90-96.
[68]吴国民,殷雅俊.颗粒增强复合材料刚塑性细观损伤本构模型的验证[J].复合材料学报,2005,22(5):16-24.
[69]邵军超,刘越.颗粒增强金属基复合材料力学行为有限元模拟研究现状[J].材料导报,2007,21(9):111-115.
[70] Rintoul M D, Torquato S. Reconstruction of the structure of dispersions[J]. Journal of Colloidand Interface Science.1997,186,467-476.
[71] Segurado J, Llorca J. A numerical approximation to the elastic properties of sphere-reinforcedcomposites[J]. Journal of the Mechanics and Physics of Solids.2002,(50):2107-2121.
[72] Llorca J, Segurado J. Three-dimensional multiparticle cell simulations of deformation anddamage in sphere-reinforced composites[J]. Materials Science and Engineering A,2004,365(1-2):267-274.
[73] Sreedhar K, Harald B, Reinaldo R, et al. Computational evaluation of effective materialproperties of composites reinforced by randomly distributed spherical particles[J]. CompositeStructures,2007,77(2):223-231.
[74] Pierard O, Llorca J, Segurado J. Micromechanics of particle-reinforced elasto-viscoplasticcomposites: Finite element simulations versus affine homogenization[J]. International Journal ofPlasticity.2007,(23):1041-1060.
[75] Han W, Eckschlager A, Bo¨hm H J. The effects of three-dimensional multi-particlearrangements on the mechanical behavior and damage initiation of particle-reinforced MMCs[J].Composites Science and Technology,2001(61):1581-1590.
[76] Kari S, Berger H, Ramos R R. Computational evaluation of effective material properties ofcomposites reinforced by randomly distributed spherical particles[J]. Composite Structures,2007(77):223-231.
[77] Bardella L, Sfreddo A, Ventura C. A critical evaluation of micromechanical models for syntacticfoams[J]. Mechanics of Materials.2012,(50):53-69.
[78] Nguyena N Q, Gupta N. Analyzing the effect of fiber reinforcement on properties of syntacticfoams[J]. Materials Science and Engineering A,2010,(527):6422-6428.
[79] Tagliavia G, Porfiri M, Gupta N. Analysis of particle-to-particle elastic interactions in syntacticfoams[J]. Mechanics of Materials.2011,(43):952-968.
[80] Chawla N, Sidhu R S, Ganesh V V. Three-dimensional visualization and microstructure-basedmodeling of deformation in particle-reinforced composites[J]. Acta Materialia,2006(54):1541-1548.
[81] Shen H, Lissenden C J.3D finite element analysis of particle-reinforced aluminum[J]. MaterialsScience and Engineering A,2002(338):271-281.
[82]卢子兴,朱汪鲲,寇长河等.聚氨酯泡沫塑料的强度与断裂韧性[J].力学学报,2000,32(5):527-632.
[83]卢子兴,邹波,李忠明,等.空心微珠填充聚氨酯泡沫塑料的力学性能复合材料学报[J],2008,25(6):175-180.
[84]卢子兴,王嵩,李忠明等.空心微珠填充聚氨酯复合泡沫塑料的宏、细观力学性能[J].航空学报,2006,27(5):799-804.
[85]卢子兴,石上路,邹波,等.环氧树脂复合泡沫材料的压缩力学性能[J].复合材料学报,2005,22(4):17-22.
[86]杨青海,王钧,杨小利,等.空心玻璃微珠填充环氧树脂的性能与结构研究[J].云南大学学报(自然科学版),2007,29(S1):194-199.
[87]胡传群,曾黎明,周建刚.改性空心玻璃微珠/环氧树脂复合材料力学性能研究[J].热固性树脂,2008,23(06):21-23.
[88]白战争,赵秀丽,罗雪方,等.空心玻璃微珠/环氧复合材料的制备及性能研究[J].热固性树脂,2009,24(02):32-35.
[89]何长军,李慧剑,余为等.基于均匀设计的空心玻璃微珠改性环氧树脂配方研究[J].中国塑料,2009,23(12):48-51.
[90]宋美慧,武高辉,王宁等. Cf/Mg复合材料热膨胀系数及其计算[J].稀有金属材料与工程,2009,39(6):1043-1047.
[91]修子扬,宋美慧,孙东立等.增强体含量对Sip/LD11复合材料热物理性能影响[J].材料科学与工艺,2005,13(2):171-174.
[92]朱德智,李凤珍,陈国钦等. SiCp/Cu复合材料热膨胀性能研究[J].哈尔滨理工大学学报,2005,10(2):125-128.
[93]费铸铭,李贤淦,王惠.颗粒增强金属基复合材料的热导率[J].复合材料学报,1990,3:27-33.
[94]陈云,于艳.颗粒随机分布复合材料的细观构造对有效热传导系数的影响[J].复合材料学报,2012,29(2):145-149.
[95]郑晶,马光,吴澎,等. Al/Si复合材料的制备及热力学特性的研究[J].稀有金属,2006,30:5-8.
[96]谢贤清,张荻,蔡建国等. TiCp/ZA43复合材料的热膨胀行为研究[J].材料工程,2001,(8):3-6.
[97] Gupta N, Ye R, Porfiri M. Comparison of tensile and compressive characteristics of vinylester/glass micro-balloon syntactic foams[J]. Composites Part B: Engineering,2010,41(3):236-245.
[98] Gupta N, Shunmugasamy V C. High strain rate compressive response of syntactic foams:Trends in mechanical properties and failure mechanisms[J]. Materials Science and EngineeringA,2011,(528):7596-7605.
[99] Caeti R, Gupta N, Porfiri M. Processing and compressive response of functionally gradedcomposites[J]. Materials Letters,2009,(63):1964-1967.
[100] Gupta N, Gupta S K, Mueller B J. Analysis of a functionally graded particulate composite underflexural loading conditions[J]. Materials Science and Engineering A,2008,(485):439-447.
[101] Gupta N. A functionally graded syntactic foam material for high energy absorption undercompression[J]. Materials Letters,2007,(61):979-982.
[102] Gupta N, Karthikeyan C S, Sankaran S. Correlation of processing methodology to the physicaland mechanical properties of syntactic foams with and without fibers[J]. MaterialsCharacterization,1999,43(4):271-277.
[103] Canal L P, González C, Segurado J. Intraply fracture of fiber-reinforced composites: Microscopicmechanisms and modeling[J]. Composites Science and Technology,2012,72(11):1223-1232.
[104] Totry E, Aldareguía J, González C, et al. Effect of fiber, matrix and interface properties on thein-plane shear deformation of carbon-fiber reinforced composites[J]. Composites Science andTechnology,2010,70(6):970-980.
[105] González C, LLorca J. Multiscale modeling of fracture in fiber-reinforced composites[J]. ActaMaterialia,2006,54(16):4171-4181.
[106] Moraleda J, Segurado J, LLorca J. Finite deformation of incompressible fiber-reinforcedelastomers: A computational micromechanics approach[J]. Journal of the Mechanics andPhysics of Solids,2009,57(9):1596-1613.
[107] González C, Llorca J. Virtual fracture testing of composites: A computational micromechanicsapproach[J]. Engineering Fracture Mechanics,2007,74(7):1126-1138.
[108] Cundall P A. A computer model for simulating progressive large scale movements in blocky rocksystems[A]. Proceedings of the international symposium rock fracture,1971, ISRM(s1):1-8.
[109]李锡夔,万柯.颗粒材料多尺度分析的连接尺度方法[J].力学学报,2010:42(5):889-900.
[110] Schlangen E, Van M. Simple lattice model for numerical simulation of fracture of concretematerials and structure[J]. Materials and structures,1992,(25):534-542.
[111]邢纪波,俞良群.颗粒复合材料破坏行为的梁-颗粒模型研究[J].应用基础与工程科学学报,1997,5(2):193-198.
[112]王泳嘉,邢纪波.离散单元法的改进和应用.岩土力学数值方法的工程应用[M].上海:同济大学出版社,1990:245-250.
[113]邢纪波,俞良群.颗粒复合材料破坏行为的梁-颗粒模型研究[J].应用基础与工程科学学报,1997,5(2):193-198.
[114]邢纪波,俞良群,王泳嘉.三维梁-颗粒模型与岩石材料细观力学行为模拟[J].岩石力学与工程学报,1999,18(6):627-630.
[115]张德海,朱浮声,邢纪波.岩石单轴拉伸破坏过程的数值模拟[J].岩土工程学报,2005,27(8):1008-1011.
[116]张德海,邢纪波,朱浮声.三维梁-颗粒模型在岩石材料破坏模拟中的应用[J].岩土力学,2004,25(s):33-36.
[117]张德海,朱浮声,邢纪波,等.岩石类非均质脆性材料破坏过程的数值模拟[J].岩石力学与工程学报,2005,24(4):570-574.
[118]赵吉坤,张子明,刘仲秋.大理岩破坏过程的三维细观弹塑性损伤模拟研究[J].2008,30(9):1309-1315.
[119]刘金兴,邓守春,梁乃刚,等.颗粒复合材料断裂的梁网格模型[J].工程力学,2008,25(10):33-37.
[120] Dvorkin J. Large strains in cemented granular aggregates: Elastic-plastic cement[J]. Mechanicsof Materials,1996,(23):29-44.
[121]周储伟,王鑫伟.基于细观方法的颗粒增强复合材料弹塑性分析[J].南京航空航天大学学报,2001,33(6):512-515.
[122]周储伟.高体积含量颗粒增强复合材料的一个细观力学模型Ⅰ:弹性分析与等效模量[J].复合材料学报,2005,22(4):125-130.
[123]周储伟.高体积含量颗粒增强复合材料的一个细观力学模型Ⅱ:弹塑性与损伤分析[J].复合材料学报,2005,22(4):131-135.
[124]中国环氧树脂网.固化剂(一)[EB/OL].2008-07-02: http://www.cn-epoxy.com/ziliao_view.asp? id=786.
[125]余为,李慧剑,何长军,等.空心玻璃微珠填充环氧树脂复合材料力学性能研究[J].复合材料学报,2010,27(4):189-194.
[126] He C J, Li H J, Yu W, et al. Prediction of density and mechanical properties in syntacticfoamusing artificial neural network[J]. ICIC Express Letters,2010,4(6):2383-2388.
[127] He C J, Li H J, Yu W, et al. Prediction of compressive yield load for metal hollow sphere withcrack based on artificial neural network[J]. ICIC Express Letters,2009,3(4B):1263-1268.
[128]余为,辛美娟,李慧剑,等.薄壁金属空心球结构压缩力学性能研究[J].实验力学,2012,27(3):377-384.
[129] Yu W, J Li H, Liang X, et al. Experimental and theoretical studies on buckling of thin-walledMHS compressed between two rigid plates[J]. Archive of Applied Mechanics,2011,81(12):1827-1832.
[130] Yu W, Xin M J, Liang X, et al. Numerical investigation into effective elastic constants ofMHS/EP composite[J]. Journal of Materials Engineering and Performance,2012,21(10):2038-2043.