双基推进剂屈服准则及粘弹塑性本构模型研究
|
摘要
双基推进剂由于其燃温低、燃速低、燃气清洁和强度高等特点已成为各类中小口径火箭、炮射火箭增程发动机及导弹燃气发生器的主要动力源之一。随着火箭武器技术不断的发展,对装药的性能要求越来越高,但是其在试验和发射过程中常会发生意想不到的问题,这样推进剂装药结构完整性问题就越来越受到各界的关注,建立起便于应用且较为准确的双基固体推进剂屈服准则、本构关系和装药结构完整性数值仿真方法已经成为目前研究的热点之一。
本文以固体火箭发动机在设计、贮存和使用过程中所常见的力学问题为研究背景,主要针对双基推进剂材料,展开了关于双基推进剂静动态力学性能、屈服准则、粘弹塑性本构模型及模型参数获取方法和子程序二次开发的研究。全文主要就以下几方面进行了较为深入地研究：
(1)对双基固体推进剂准静动态力学性能展开了系列的研究,由于双基推进剂的力学特性与其它高分子材料的力学性能有一定的差异,对推进剂材料的泊松比、表面应变测量方法、力学性能与温度及率的相关性展开了研究,提出了针对双基推进剂材料屈服点的判断方法。
(2)对双基推进剂材料的屈服准则和静水压力下的力学性能展开了研究,首先根据万能材料试验机的结构设计出了相应的围压试验装置,然后通过不同围压压力水平下的单轴压缩试验研究了该类推进剂材料的力学性能与围压压力之间的关系,利用莫尔-库伦理论首次获得了推进剂材料的粘聚力和内摩擦角,接着对多种屈服准则进行了对比分析,遴选出了能够较好反映推进剂材料在不同条件下的屈服判据。
(3)结合粘弹塑性本构模型的特点,根据不同应力水平下的蠕变回复试验和循环蠕变回复试验确定了该本构模型的参数,并对该本构模型进行了相应的试验验证,证明了本文建立的本构模型具有一定的准确性。
(4)基于Schapery的非线性粘弹性本构关系,结合粘塑性本构模型,建立了非线性粘弹塑性本构模型,运用增量方法将粘弹塑性本构方程由一维推广到三维增量形式,提出了屈服因子的概念,用来判断推进剂材料的屈服程度,并基于FORTRAN语言和有限元软件进行了二次开发,即编制了相应的UMAT子程序。
通过本文的研究,获得了双基固体推进剂材料在静动态加载条件下的力学响应特性、变化规律和力学性能的影响因素。针对双基推进剂材料建立起的本构理论、运用的有限元方法及结论,将有效地指导该类固体火箭发动机装药设计,特别是为固体推进剂自由装填装药结构完整性分析提供了理论基础和依据。
Because double-base propellant has advantages such as low combustion temperature, low burning rate, cleanly fuel gas and high strength, so it has been one of major fuels for all kinds of medium-small caliber rockets, cannon launched rocket extend-range motor and missile gas generator. With the rocket weapon technology unceasing development, the performance of the propellant grain will require more and more high, but the propellants grains also often have happened unexpected problems during test and emission process. So propellant grain structure integrity problem has been paied more and more attention to by many scholars, set up suitable for application and relatively accurate yield criterion, constitutive relation and numerical simulation method has become one of the hot topics in the study for rocket weapon.
The common mechanical problem for solid rocket motor in the design, storage and use process are considered as the research background for the double-base propellant materials. The static and dynamic mechanical properties, yield criterion, visco-elastoplastic constitutive model and model parameter acquisition method and subroutine secondary development of double-base class propellant have been carried out to study. The main contents include the following sections:
(1) The quasi-static and dynamic mechanical properties of double-base solid propellant are launched a series of research.Because the mechanical properties of double-base propellant and mechanical properties of other polymer materials have certain differences, the poisson's ratio, surface strain measurement method, mechanical property and temperature and rate correlation of propellant material are launched research, and the yield point judgment method of double-base propellant material is proposed.
(2) The yield criterion and mechanical properties under hydraulic pressure of double-base propellant material are carried out to study. First of all, according to the structure of the universal material testing machine, the corresponding confining pressure test device is designed, and then the relationship between mechanical property of propellant material and confining pressure is stuied by uniaxial compression test under the different confining pressure level. The cohesion and internal friction angle of double-base propellant by Mohr-Coulomp theory have been obtained the first, and then a variety of yield criteria are compared to analysis. And the yield criterion which is suitable for propellant material under different conditions is selected.
(3) According to the characteristics of visco-elastoplastic constitutive model, the constitutive model parameters are determine by creep recovery test and cyclic creep recovery test under different stress level, and the constitutive model is verified by the corresponding test. The results prove that the established constitutive model has certain accuracy in this paper.
(4) The nonlinear visco-elastoplastic constitutive model is established which is based on Schapery's nonlinear viscoelastic constitutive model and viscoplastic constitutive model. The three-dimensional incremental form of visco-elastoplastic constitutive equation is extended using incremental method. The concept of yield factor is proposed to judge the yield degree of propellant material. And a user subroutine is programmed with FORTRAN, which is integrated into ABAQUS for numerical simulation, namely the corresponding UMAT subroutine is programmed.
The mechanical response characteristics, the change rule and the influence factors of mechanical performance of double-base class solid propellant materials are obtained under static and dynamic loading conditions. For double-base propellant material, establishing constitutive theory, using the finite element method and conclusion will effectively guide the solid rocket motor grain design. Especially these will provide theoretical foundation for solid propellant free loading grain structural integrity analysis.
本文以固体火箭发动机在设计、贮存和使用过程中所常见的力学问题为研究背景,主要针对双基推进剂材料,展开了关于双基推进剂静动态力学性能、屈服准则、粘弹塑性本构模型及模型参数获取方法和子程序二次开发的研究。全文主要就以下几方面进行了较为深入地研究：
(1)对双基固体推进剂准静动态力学性能展开了系列的研究,由于双基推进剂的力学特性与其它高分子材料的力学性能有一定的差异,对推进剂材料的泊松比、表面应变测量方法、力学性能与温度及率的相关性展开了研究,提出了针对双基推进剂材料屈服点的判断方法。
(2)对双基推进剂材料的屈服准则和静水压力下的力学性能展开了研究,首先根据万能材料试验机的结构设计出了相应的围压试验装置,然后通过不同围压压力水平下的单轴压缩试验研究了该类推进剂材料的力学性能与围压压力之间的关系,利用莫尔-库伦理论首次获得了推进剂材料的粘聚力和内摩擦角,接着对多种屈服准则进行了对比分析,遴选出了能够较好反映推进剂材料在不同条件下的屈服判据。
(3)结合粘弹塑性本构模型的特点,根据不同应力水平下的蠕变回复试验和循环蠕变回复试验确定了该本构模型的参数,并对该本构模型进行了相应的试验验证,证明了本文建立的本构模型具有一定的准确性。
(4)基于Schapery的非线性粘弹性本构关系,结合粘塑性本构模型,建立了非线性粘弹塑性本构模型,运用增量方法将粘弹塑性本构方程由一维推广到三维增量形式,提出了屈服因子的概念,用来判断推进剂材料的屈服程度,并基于FORTRAN语言和有限元软件进行了二次开发,即编制了相应的UMAT子程序。
通过本文的研究,获得了双基固体推进剂材料在静动态加载条件下的力学响应特性、变化规律和力学性能的影响因素。针对双基推进剂材料建立起的本构理论、运用的有限元方法及结论,将有效地指导该类固体火箭发动机装药设计,特别是为固体推进剂自由装填装药结构完整性分析提供了理论基础和依据。
Because double-base propellant has advantages such as low combustion temperature, low burning rate, cleanly fuel gas and high strength, so it has been one of major fuels for all kinds of medium-small caliber rockets, cannon launched rocket extend-range motor and missile gas generator. With the rocket weapon technology unceasing development, the performance of the propellant grain will require more and more high, but the propellants grains also often have happened unexpected problems during test and emission process. So propellant grain structure integrity problem has been paied more and more attention to by many scholars, set up suitable for application and relatively accurate yield criterion, constitutive relation and numerical simulation method has become one of the hot topics in the study for rocket weapon.
The common mechanical problem for solid rocket motor in the design, storage and use process are considered as the research background for the double-base propellant materials. The static and dynamic mechanical properties, yield criterion, visco-elastoplastic constitutive model and model parameter acquisition method and subroutine secondary development of double-base class propellant have been carried out to study. The main contents include the following sections:
(1) The quasi-static and dynamic mechanical properties of double-base solid propellant are launched a series of research.Because the mechanical properties of double-base propellant and mechanical properties of other polymer materials have certain differences, the poisson's ratio, surface strain measurement method, mechanical property and temperature and rate correlation of propellant material are launched research, and the yield point judgment method of double-base propellant material is proposed.
(2) The yield criterion and mechanical properties under hydraulic pressure of double-base propellant material are carried out to study. First of all, according to the structure of the universal material testing machine, the corresponding confining pressure test device is designed, and then the relationship between mechanical property of propellant material and confining pressure is stuied by uniaxial compression test under the different confining pressure level. The cohesion and internal friction angle of double-base propellant by Mohr-Coulomp theory have been obtained the first, and then a variety of yield criteria are compared to analysis. And the yield criterion which is suitable for propellant material under different conditions is selected.
(3) According to the characteristics of visco-elastoplastic constitutive model, the constitutive model parameters are determine by creep recovery test and cyclic creep recovery test under different stress level, and the constitutive model is verified by the corresponding test. The results prove that the established constitutive model has certain accuracy in this paper.
(4) The nonlinear visco-elastoplastic constitutive model is established which is based on Schapery's nonlinear viscoelastic constitutive model and viscoplastic constitutive model. The three-dimensional incremental form of visco-elastoplastic constitutive equation is extended using incremental method. The concept of yield factor is proposed to judge the yield degree of propellant material. And a user subroutine is programmed with FORTRAN, which is integrated into ABAQUS for numerical simulation, namely the corresponding UMAT subroutine is programmed.
The mechanical response characteristics, the change rule and the influence factors of mechanical performance of double-base class solid propellant materials are obtained under static and dynamic loading conditions. For double-base propellant material, establishing constitutive theory, using the finite element method and conclusion will effectively guide the solid rocket motor grain design. Especially these will provide theoretical foundation for solid propellant free loading grain structural integrity analysis.
引文
[1]P. P. Castaneda,J. R. Willis.On the Overall Properties of Nonlinearly Viscous Composites[J].Proceedings of the Royal Society of London.Series A,1988,416:217-244.
[2]杨挺青.粘弹塑性本构理论及其应用[J].力学进展,1992,22(1)：10-19.
[3]欧阳鬯.粘弹塑性理论[M].长沙：湖南科学技术出版社,出版日期：1986.
[4]G. Herder, F. P. Weterings, W. P. C. de Klerk.Mechanical analysis on rocket propellants[J] Journal of Thermal Analysis and Calorimetry,2003,72 (3):921-929.
[5]Shiang-Woei Chyuan.Studies of poisson's ratio variation for solid propellant grain under ignition pressure loading[J].Internationan Journal of Pressure Vessels and Piping,2003,80(12):871-877.
[6]Neviere Robert.An extension of the time-temperature superposition principle to non-linear viscoelastic solids[J].International Journal of Solids and Structures, 2006,43(17):5295-5306.
[7]F. Xu,N. Aravas,P. Sofronis.Constitutive modeling of solid propellant materials with evolving microstructural damage [J] Journal of the Mechanics and Physics of Solids,2008,56(5):2050-2073.
[8]Ren Ping,Hou Xiao,He Gaorang.et al.Comparative Research of Tensile and Compressive Modulus of Composite Solid Propellant for Solid Rocket Motor[J] Journal of Astronautics,2010,31 (10):2354-2359.
[9]H. C. Yildinm,S. Ozupek.Structural assessment of a solid propellant rocket motor: Effects of aging and damage [J].Aerospace Science and Technology,2011,15(8): 635-641.
[10]杨挺青.非线性粘弹理论中的单积分型本构关系[J].力学进展,1988,1：52-60.
[11]曹树刚.煤岩的蠕变损伤、瓦斯渗流和煤与瓦斯突出关系的研究[博士学位论文][D].重庆：重庆大学,2000.
[12]W. N. Findley J. S. Lai,K. Onaran. Creep and relaxation of nonlinear viscoelastic materials:with an introduction to linear viscoelasticity[M]. Dover Publication, New York,1989.
[13]杨挺青,罗文波,徐平等.粘弹性理论与应用[M].北京：科学出版社,2004.
[14]张淳源,张为民.非线性粘弹性理论及其应用研究进展[J].湘潭大学自然科学学报,2003,25(4)：28-32.
[15]张为民.非线性粘弹性本构理论及其应用[J].湘潭大学自然科学学报,2000,22(4)：39-44.
[16]A. Hanyga,M. Seredynskab.Multiple-integral viscoelastic constitutive equations[J]. International Journal of Non-Linear Mechanics,2007,42(5):722-732.
[17]W. N. Findley,J. S. Lai,K. Onaran.Creep and relaxation of nonlinear viscoelastic materials[M], North Holland Publishing Company,1976.
[18]J. D. Ferry.Viscoelastic Propersties of Polymers[M].3rd Edition,John Wiley.New York,1980.
[19]R. A. Schapery.On a thermodynamic constitutive theory and its application to various nonlinear materials[J].Proc. IUTAM Symp.,East Kilbride,1968:259-285.
[20]R. A. Schapery.On the characterization of nonlinear viscoelastic materials [J]. Polymer Engineering and Science,1969,9(4):295-310.
[21]王礼立,施绍裘,江瑛等.ZWT非线性热粘弹性本构关系的研究与应用[J].宁波大学学报(理工版),2000,13Sup：141-149.
[22]Leaderman H.Large longitudinal retarded elastic deformation of rubber like network polymers [J].Trans.Soc Rheol,1962:361-382.
[23]J. Smart,J. G. Williams.A comparison of single integral nonlinear viscoelastic theories[J]. J Mech.Phys.Solids,1972,20:313-324.
[24]Jung Gyoo-Dong,Youn Sung-Kie,Kim Bong-Kyu.Development of a three-dimensional nonlinear viscoelastic constitutive model of solid propellant[J] Journal of the Brazilian Society of Mechanical Sciences,2000,22(3):457-476
[25]Levesque Martin,Derrien Katell,Baptiste Didier,et al.On the development and parameter identification of Schapery-type constitutive theories [J].Mechanics of time-dependent materials,2008,12(2):95-127.
[26]Jazouli Said,Luo Wenbo,Bremand Fabriceet al.Nonlinear creep behavior of viscoelastic polycarbonate[J]. Journal of Materials Science,2006,41(2):531-536.
[27]张永敬,赵光辉,阳建红等.HTPB复合固体推进剂非线性本构方程研究[J].推进技术,2000,21(4)：70-72.
[28]Luo Wen-bo,Wang Chu-hong,Zhao Rong-guo.Application of time-temperature-stress superposition principle to nonlinear creep of Poly(methyl methacrylate)[J].Key Engineering Materials,2007,340-341:1091-1096.
[29]李东.固体推进剂药柱表面裂纹动态力学特性研究[D].南京理工大学博士学位论文,2008.
[30]M. A. Burke,P. J. Woytowitz,G. Reggi.A Nonlinear Viscoelastic constitive Model for Solid Propellant, AIAA-2213,1990.
[31]强洪夫.固体火箭发动机装药结构完整性数值仿真与实验研究[D].西安交通大学博士学位论文,1998.
[32]孟红磊.改性双基推进剂装药结构完整性数值仿真方法研究[D].南京理工大学博士学位论文,2011.
[33]牛秉彝等.高聚物粘弹及断裂性能[M].北京：国防工业出版社,1991.
[34]袁军堂.高聚物及其复合材料的应用技术研究[D].南京理工大学博士论文,2001.
[35]彭网大,杨风云,廖庆惠等.HTPB复合固体推进剂粘弹特性研究——主松弛模量的时间、温度依赖性[J].推进技术,1984,(02)：6-18.
[36]余世方,赵伯华,辛振河等.固体推进剂粘弹力学特性的实验研究[J].推进技术,1985,(4)：1-8.
[37]彭网大,朱慧,张志毅等.HTPB复合固体推进剂粘弹特性研究——动态抗张模量的时间、温度依赖性[J].推进技术,1986,(4)：46-55.
[38]贾展宁.改性双基推进剂力学性能特点分析[J].兵工学报,1989,(3)：17-23.
[39]田学林,卢红斌.NEPE推进剂的动态力学分析[J].北京理工大学学报,1995,15(6)：49-51.
[40]侯竹林,韩盘铭.NEPE固体推进剂动态力学性能的研究[J].固体火箭技术,1999,22(2)：37-39,51.
[41]张伟,樊学忠,张腊莹等NEPE推进剂低温瞬态的粘弹特性[J].固体火箭技术,2009,32(3)：298-301,343.
[42]胡全星,姜豫东,李健.推进剂松弛模量主曲线及W.L.F.方程参数的拟合处理[J].固体火箭技术,2003,26(2)：46-48.
[43]曾甲牙.固体填充剂对推进剂力学性能的影响[J].固体火箭技术,2002,25(1)：46-50.
[44]蒙上阳,唐国金,雷勇军.材料性能对固体发动机结构完整性的影响[J].国防科技大学学报,2002,24(5)：10-15.
[45]高鸣,赵伯华.固体推进剂体积模量主曲线试验研究[J].推进技术,1995,(2)：67-71.
[46]高鸣,蔡体敏.固体推进剂体积模量试验研究[J].火炸药学报,1999,(2)：5-7.
[47]R. Caracciolo,M. Giovagnoni.Frequency dependence of Poisson's ratio using the method of reduced variables[J].Mechanics of Materials,1996,24(1):75-85.
[48]HARRY H. HILTON.Implications and Constraints of Time-Independent Poisson Ratios in Linear Isotropic and Anisotropic Viscoelasticity[J]. Journal of Elasticity, 2001,63(3):221-251.
[49]P. H. Mott,J. R. Dorgan,C. M. Roland.The bulk modulus and Poisson's ratio of "incompressible" materials. Journal of Sound and Vibration,2008,312(4-5):572-575.
[50]Taniguchi Yusuke,Ando Kosei.Time dependence of Poisson's effect in wood I:the lateral strain behavior. Journal of Wood Science,2009,56(2):100-106.
[51]何铁山,张劲民.环境压强对固体推进剂力学行为的影响[J].推进技术,2005,26(4)：367-370.
[52]郭翔,张小平,张炜.拉伸速率对NEPE推进剂力学性能的影响[J].固体火箭技术,2007,30(4)：321-323,327.
[53]王玉峰,李高春,刘著卿等.应变率和加载方式对HTPB推进剂力学性能及耗散特性的影响[J].含能材料,2010,18(4)：377-382.
[54]罗天元,黄文明,王艳艳等.湿度对HTPB复合推进剂力学性能的影响[J].火炸药学报,2009,32(6)：84-86.
[55]刘著卿,李高春,王玉峰等.应变加载历史对推进剂力学性能的影响[J].火炸药学报,2010,33(4)：5-9.
[56]王瑛,张晓宏,陈雪莉等.改性双基推进剂组合装药界面力学性能[J].含能材料,2011,19(3)：287-290.
[57]杨凤林,庞爱民,张小平.复合固体推进剂单向拉伸曲线分析[J].固体火箭技术,2001,24(3)：1-4.
[58]宋丹平,翟鹏程,郑剑等.一种固体推进剂本构关系的研究[J].固体力学学报,2008,29(S1)：6-8.
[59]M. S. Matecic,M. S. Suceska.Artificial ageing of double base rocket propellant[J]. Journal of Thermal Analysis and Calorimetry,2009,96(2):523-529.
[60]S. M.Walley,C. R.Siviour,D. R. Drodge.et al.High-rate mechanical properties of energetic materials[J].JOM Journal of the Minerals, Metals and Materials,2010, 62(1):31-34.
[61]Wang Ling,Song Yuming,Gyanda Reena.et al.Preparation and mechanical properties of crosslinked 1,2,3-triazole-polymers as potential propellant binders[J] Journal of Applied Polymer Science,2010,117(5):2612-2621.
[62]Sui Xin,Wang Ningfei,Wan Qian.et al.Effects of Relaxed Modulus on the Structure Integrity of NEPE Propellant Grains during High Temperature Aging[J].Propellants, Explosives, Pyrotechnics,2010,35(6):535-539.
[63]Deng Kai,Yang Jianhong,Huang Weiwei.et al.A new method to obtain shear modulus of solid propellant[J].Acta Astronautica,2011,69(7-8):440-444.
[64]C. A. Coulomb.English translation:Note on an application of the rules of maximum and minimum to some statical problems,relevant to architecture, Heyman J.,1997,41-74.
[65]Hu L. W. An experimental study of the fracture of metals under hydrostatic pressure[J]. J. Mech. Phys. Solids,1956,4(2):96-103.
[66]W. Prager.Strain hardening under combined stress[J].J. Appl.Phys.,1945,16:837-840.
[67]W. Whitney,R. D. Andres.The behaviour of polystyrene,polymrthl, methacrylate, polycarbonate,and polyvinyl formale under conplex stress state[J].J. Polym. Sci., 1967,16,2961.
[68]P. B. Bowder,J. A. Jukes.Plastic flow of polymers[J].J. Mater.Sci.,1972,7:52-63.
[69]R. Raghava,R. M. Caddell,S. Y.Yeh Gregory.The macroscopic yield behaviour of Polymers[J] Journal of Materials Science,1973,8(2):225-232.
[70]R. H. Sigley,A. S. Wronski,T. V. Parry.Three-parameter yield criterion for a brittle polyester resin[J]. Journal of Materials Science,1991,26(15):3985-3990.
[71]R. Quinson,J. Perez,M.Rink.et al.Yield criteria for amorphous glassy polymers[J]. Journal of Materials Science,1997,32(5):1371-1379.
[72]R. D. Sudduth.Development of a Simplified Relationship Between Uniaxial Creep,Stress Relaxation,and Constant Strain-Rate Results for Viscoelastic Polymeric Materials[J].Journal of Applied Polymer Science,2001,82(3):527-540.
[73]R. D. Sudduth.Indications that the yield point at constant strain rate and the inception of tertiary creep are manifestations of the same failure criterion using the universal viscoelastic model[J]. Journal of Materials Science,2003,6 (38):1123-1134.
[74]R. M. Christensen.A Comprehensive Theory of Yielding and Failure for Isotropic Materials[J] Journal of Engineering Materials and Technology,2007,129(2):173-181.
[75]沈怀荣.温度相依固体推进剂的蠕变损伤模型[J].固体推进技术,1992,11(4)：39-43.
[76]R. M.Muthiah,V. N. Krishnamurthy,B. R. Gupta.Rheology of HTPB propellant.I. Effect of solid loading, oxidizer particle size, and aluminum content[J]. Journal of Applied Polymer Science,1992,44(11):2043-2052.
[77]Yu Mao-hong.Advances in strength theories for materials under complex stress state in the 20th Century[J]. Appl Mech Rev,2002,55(3):169-218.
[78]Li Dong-wei,Fan Ju-hong,Wang Ren-he.Research on visco-elastic-plastic creep model of artificially frozen soil under high confining pressures[J].Cold Regions Science and Technology,2011,65(2):219-225.
[79]Sung Shinjang,Liu Li-wei,Hong Hongki. et al.Evolution of yield surface in the 2D and 3D stress spaces[J].International Journal of Solids and Structures,2011,48(6):1054-1069.
[80]贾乃文.粘塑性力学及工程应用[M].北京：地震出版社,2000.
[81]A. C. Lund,C. A. Schuh.The Mohr-Coulomb criterion from unit shear processes in metallic glass[J].Intermetallics,2004,12(10-11):1159-1165.
[82]杨璐,沈新普.基于Coulomb准则的混凝土塑性损伤本构模型及其数值验证[J].岩土力学,2008,29(12)：3318-3322.
[83]Zhang Lian-yang,Cao Ping,Radha K C.Evaluation of rock strength criteria for wellbore stability analysis[J].International Journal of Rock Mechanics and Mining Sciences,2010,47(8):1304-1316.
[84]常晓林,马刚,刘杏红.基于复合屈服准则的混凝土塑性损伤模型[J].四川大学学报,2011,43(1)：1-7.
[85]D. Debasis,C. D. Kamal.Modelling of fully grouted rock bolt based on enriched finite element method[J].International Journal of Rock Mechanics and Mining Sciences,2011,48(2):283-293.
[86]Rocio Seltzer,Adrian P. Cisilino,Patricia M.Frontini.et al.Determination of the Drucker-Prager parameters of polymers exhibiting pressure-sensitive plastic behaviour by depth-sensing indentation[J].International Journal of Mechanical Sciences,2011,53 (6):471-478.
[87]Rezaiee-Pajand Mohammad, Sharifian Mehrzad,Sharifian Mehrda.Accurate and approximate integrations of Drucker-Prager plasticity with linear isotropic and kinematic hardening[J].European Journal of Mechanics A:Solids,2011,30(3):345-361.
[88]Khan Akhtar,Zhang Hao-yue.Finite deformation of a polymer:Experiments and modeling[J].International Journal of Plasticity,2001,17(9):1167-1188.
[89]A. Sides,J. Uzan,Perl M.A comprehensive viscoelasto-plastic characterization of sand-asphalt compressive and tensile cyclic loading[J].Test Evaluat,1985,13(1):49-59.
[90]Y. Lu,P. J. Wright.Numerical approach of visco-elastoplastic analysis for asphalt mixtures[J]. Computers and Structures,1998,69(2):139-147.
[91]J. M. Gonzalez,C. J. Miquel,S. Oller, et al. A viscoplastic constitutive model with strain rate variables for asphalt mixtures'numerical simulation [J]. Computational Materials Science 2007,38(4):543-560.
[92]Wang Zhong-jin,Liu Jian-guang.Sectional finite element analysis of coupled deformation between elastoplastic sheet metal and visco-elastoplastic body[J]. Acta Mechanica Solida Sinica,2011,24(2):153-165.
[93]刘建光,王忠金,刘岩.VPF用粘性介质粘弹塑性本构模型及参数确定[J].材料科学与工艺,2010,18(6)：843-846.
[94]曹树刚,鲜学福.煤岩的广义弹粘塑性模型分析[J].煤炭学报,2001,26(4)：364-369.
[95]邹友平,郭军杰,邹友峰.煤岩的改进广义弹粘塑性模型分析[J].矿业研究与开 发,2004,24(6)：30-31,78.
[96]邓荣贵,周德培,张倬元等.一种新的岩石流变模型[J].岩石力学与工程学报,2001,20(6)：780-784.
[97]韦立德,徐卫亚,朱珍德等.岩石粘弹塑性模型的研究[J].岩土力学,2002,23(5)：583-586.
[98]Yoon Wonseo,Huang Xin-yu.A nonlinear viscoelastic-viscoplastic constitutive model for ionomer membranes in polymer electrolyte membrane fuel cells. Journal of Power Sources,2011,196(8):3933-3941.
[99]A. F. Epee,F. Lauro,B. Bennani.et al.Constitutive model for a semi-crystalline polymer under dynamic loading[J].International Journal of Solids and Structures,2011,48(10): 1590-1599.
[100]曹树刚,边金,李鹏.岩石蠕变本构关系及改进的西原正夫模型[J].岩石力学与工程学报,2002,21(5)：632-634.
[101]M. C. Weng,L. S. Tsai,C. Y. Liao. et al.Numerical modeling of tunnel excavation in weak sandstone using a time-dependent anisotropic degradation model [J].Tunnelling and Underground Space Technology,2010,25(4):397-406.
[102]Ye Yong,Yang Xin-hua,Chen Chuan-yao.Experimental researches on visco-elastoplastic constitutive model of asphalt mastic[J].Construction and Building Materials,2009,23(10):3161-3165.
[103]Y. C. Lou.Viscoelastic Characterization of a Nonlinear Fiber-Reinforced Plastic Journal of Composite Materials,1971,5(2):208-234.
[104]J. Lai,A. Bakker.3-D schapery representation for non-linear viscoelasticity and finite element implementation[J].Computational Mechanics,1996,18(3):182-191.
[105]G. R. Chehab.Characterization of asphalt concrete in tension using a viscoelasto-plastic model.Ph.D. dissertation, Dept.of Civil Engineering,North Carolina State Univ.,Raleigh, N.C.,2002
[106]Y. Q. Zhao.Permanent deformation characterization of asphalt concrete using a viscoelastoplastic model.Ph.D. dissertation,Dept.of Civil Engineering,North Carolina State Univ., Raleigh, N.C.,2002
[107]Abdel-Rahman Saadeh Shadi.Characterization of asphalt concrete using anisot-ropic damage iscoelastic-viscoplastic model.Ph.D. Civil Engineering. Texas A&M University,2006
[108]Ye Yong,Yang Xin-hua,Chen Chuanyao.Modified Schapery's Model for Asphalt Sand[J]. Journal of Engineering Mechanics,2010,136(4):448-454.
[109]Ye Yong,Yang Xin-hua,Chen Chuan-yao.Viscoplastic behaviour of asphalt mixture in compression[J].Materials Research Innovations,2011,15(1):s45-s48.
[110]E. Chailleux,P. Davies.Modelling the Non-Linear Viscoelastic and Viscoplastic Behaviour of Aramid Fibre Yarns[J].Mechanics of time-dependent materials, 2003,7(3):291-303.
[111]邓凯,阳建红,陈飞等HTPB复合固体推进剂本构方程[J].宇航学报,2010,31(7)：1815-1818.
[112]O. C. Zienkiewicz,M. Wattson.Some Creep Effects Stress Analysis with Particular Reference to Concrete Pressure Vessel[J].Nuclear Engineering and Design,1966,4: 406-412.
[113]O. C. Zienkiewicz,M. WattsonJ. P. King.A Numerical Method of Viscoelastic Sress Analysis[J].Int.J.Mech.Sci,1968,10:807-827.
[114]D. Touati,G. Cederbaum.On the prediction of stress relaxation from known creep of nonlinear materials [J] Journal of Engineering Materials and Technology, 1997,119(2):121-124.
[115]D. Touati,G. Cederbaum.Post buckling of non-linear viscoelastic imperfect laminated plates Part I:Material considerations[J].Composite Structures,1998,42(1):33-41.
[116]Huang Chien-Wei,Masad Eyad,Muliana Anastasia.et al.Nonlinearly viscoelastic analysis of asphalt mixes subjected to shear loading[J].Mechanics of time-dependent materials,2007,11(2):91-110.
[117]Masad Eyad,Huang Chien-Wei,Airey Gordon.et al.Nonlinear viscoelastic analysis of unaged and aged asphalt binders[J].Construction and Building Materials,2008,22(11):2170-2179.
[118]Rami. M. Haj-Ali,Aanstasia. H. Muliana.Numerical finite element formulation of the Schapery non-linear viscoelastic material model [J]. International Journal for Numerical Methods in Engineering,2004,59(1):25-45.
[119]Jung Gyoo-Dong,Youn Sung-Kie,Kim Bong-Kyu.A three-dimensional nonlinear viscoelastic constitutive model of solid propellant[J].International Journal of Solids and Structures,2000,37(34):4715-4732.
[120]潘晓明,杨钊,雷春娟等.广义西原粘弹塑流变模型在ABAQUS中开发与应用[J].建筑结构学报,2010(S2)：324-329.
[121]潘晓明,杨钊,许建聪.非定常西原黏弹塑性流变模型的应用研究[J].岩石力学与工程学报,2011,30(S1)：2640-2646.
[122]J. S. Kim,A. H. Muliana.A combined viscoelastic-viscoplastic behavior of particle reinforced composites[J].International Journal of Solids and Structures,2010,47(5):580-594.
[123]M. K. Darabi,R. K. Abu Al-Rub,E.A. Masad.et al.A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials[J].International Journal of Solids and Structures,2011,48(1):191-207.
[124]S. H. Dessouky.Multiscale approach for modeling hot mix asphalt[D].Ph.D. Texas A&M University,2005.
[125]Huang Chien-Wei,Abu Al-Rub Rashid K.,Masad Eyad A.et al.Three-Dimensional Simulations of Asphalt Pavement Permanent Deformation Using a Nonlinear Viscoelastic and Viscoplastic Model [J] Journal of Materials in Civil Engineering,2011,23(1):56-68.
[126]Huang Chien-Wei,Abu Al-Rub Rashid K.,Masad Eyad A.et al.Numerical implementation and validation of a nonlinear viscoelastic and viscoplastic model for asphalt concrete mixes[J].International Journal of Pavement Engineering,2011,12(4): 433-447.
[127]P. Tandaiya,U. Ramamurty,R. Narasimhan.On numerical implementation of an isotropic elastic-viscoplastic constitutive model for bulk metallic glasses[J]. Modelling & Simulation in Materials Science & Engineering,2011,19(1):015002-015002.
[128]钟涛.大长径比固体火箭发动机点火瞬态过程研究[D].国防科学技术大学博士论文,2005.
[129]刘中兵,利凤祥,李越森等.高过载条件下固体推进剂药柱结构完整性分析计算[J].固体火箭技术,2003,6(2)：12-16.
[130]刘中兵,利凤祥,李越森等.轴向过载下固体推进剂药柱变形研究[J].推进技术,2004,25(2)：162-164.
[131]郑颖建.高过载下固体火箭发动机药柱结构的完整性分析[D]哈尔滨工程大学,2005.
[132]利凤祥,刘中兵,李越森等.药柱结构对其抗轴向过载能力的影响[J].推进技术,2004,25(2)：165-169.
[133]田四朋.固体火箭发动机药柱三维粘弹性响应面随机有限元分析[J].固体火箭技术,2010,33(1)：17-20.
[134]Kalaycioglu Baris,Dirikolu M. Husnu,Celik Veli.An elasto-viscoplastic analysis of direct extrusion of a double base solid propellant[J].Advances in Engineering Software,2010,41(9):1110-1114.
[135]职世君,孙冰,张建伟.固体推进剂复合型裂纹扩展数值计算[J].固体火箭技术,2011, 34(1)：28-31,47.
[136]Chyuan Shiang-Woei.Dynamic analysis of solid propellant grains subjected to ignition pressurization loading[J] Journal of Sound and Vibration,2003,268(3):465-483.
[137]孟红磊,周长省,鞠玉涛等.非均布瞬态内压作用下星孔药柱应力分析[J].固体火箭技术,2010,33(3)：289-293.
[138]R. M. Hinterhoelzl,R. A. Schapery.FEM implementation of a three-demensional viscoelastic constitutive model for particulate composites with damage growth[J]. Mechanics of time-dependent materials,2004,8:65-94.
[139]Gutierrez-Lemini,Danton.Single-Specimen Technique to Establish the J-Resistance of Linear Viscoelastic Solids with Constant Poisson's Ratio [R]. Alabama:Marshall Space Flight Center,2001
[140]R. M. Pidaparti,A. Vogt.Experimental investigation of Poisson's ratio as a damage parameter for bone fatigue. Journal of Biomedical Materials Research,2002,59(2):282-287.
[141]沈庭芳,高鸣,赵伯华.固体火箭药柱泊松比的表征与诊断[J].宇航学报,1996,17(4)：86-90.
[142]郝松林.粘弹性泊松比的各种表述方法[J].国防科技大学学报,1992,14(4)：7-12.
[143]郝晓剑,靳鸿.动态测试技术及应用[M].北京：电子工业出版社,2008.
[144]尹福炎.箔式应变片结构模型与有限元分析[J].衡器,2009,38(6)：49-52.
[145]HARRY H. HILTON, SUNG YI.The significance of (an) isotropic viscoelastic Poisson ratio stressand time dependencies[J]. International Journal of Solids and Structures, 1998,35(23):3081-3095.
[146]李东,周长省,鞠玉涛等.双基固体推进剂药柱本构关系的实验研究[J].弹道学报,2009,21(2)：6-9.
[147]Jia Zhanning.The glass transition temprature measurement of nitrocellulose by torsional braid analysis[J].Propellants, Explosives, Pyrotechnics,1992,17(1):34-37.
[148]R. C. Warren.Transition and relaxation in plasticized nitrocellulose[J].Polymer,1988,29: 919-923.
[149]D. J. Townend,R. C. Warren.Relaxation in double base propellants[J].Polymer,1985, 1(26):79-83.
[150]赵伯华,辛振河.双钴-1推进剂粘弹力学性能的实验研究[J].推进技术,1989,(1)：43-46.
[151]贾展宁,周起槐.硝化纤维素、双基粘合剂和改性双基推进剂动态粘弹性分析[J].北京工业学院报,1984,(3)：72-80.
[152]周舟,贾展宁,周起槐.改性双基(CMDB)推进剂动态力学性能的研究[J].兵工学报,1985,(2)：49-58.
[153]刘子如,张腊莹,衡淑云等.双基推进剂的玻璃化温度[J].火炸药学报,2009,32(2)：56-59.
[154]赵伯华,沈庭芳,沈月萍.动态力学实验诊断应力松弛模量的研究[J].北京理工大学,1995,15(3)：339-343.
[155]Y. Traissac,J. Ninous,R. Neviere.et al.Mechanical behavior of a solid composite propellant during motor ignition[J].Rubber Chemistry and Technology,1994,68:146-157.
[156]I. Sridhar,N. A. Fleck.The multiaxial yield behaviour of an aluminium alloy foam[J]. Journal of Materials Science,2005,40(15):4005-4008.
[157]Lorenzo Peroni,Massimiliano Avalle,Marco Peroni.The mechanical behaviour of aluminium foam structures in different loading conditions[J].International Journal of Impact Engineering,2008,35(7):644-658.
[158]Voyiadjis George Z,Shojaei Amir,Li Guoqiang.A generalized coupled viscoplastic-viscodamage-viscohealing theory for glassy polymers [J].International Journal of Plasticity,2012,28(1):21-45.
[159]O. C.Zienkiewicz, R. L.Taylor.The finit element method for solid and structural mechanics[M].Elsevier (Singapore) Pte Ltd,2009.
[160]H. Poon,M. F. Ahmad.A finite element constitutive update scheme for anisotropic, viscoelastic solids exhibiting non-linearity of the Schapery type[J].International Journal for Numerical Methods in Engineering,1999,46(12):2027-2041.
[161]R. L.Taylor, K. S.Pister, G L.Goudreau.Thermomechanical Analysis of Viscoelastic Solids[J].International Journal for Numerical Methods in Engineering,1970,2(1):45-59.
[162]D.R.J. OWEN,E. HINTON.Finite elements in plasticity—theory and practice[M]. Swansea:Pineridge Press,1980.
[163]J. Varna,L. Rozite,R.Joffe. et al.Non-linear behaviour of PLA based flax composites [J]. Plastics, Rubber and Composites,2012,41(2):49-60.
[2]杨挺青.粘弹塑性本构理论及其应用[J].力学进展,1992,22(1)：10-19.
[3]欧阳鬯.粘弹塑性理论[M].长沙：湖南科学技术出版社,出版日期：1986.
[4]G. Herder, F. P. Weterings, W. P. C. de Klerk.Mechanical analysis on rocket propellants[J] Journal of Thermal Analysis and Calorimetry,2003,72 (3):921-929.
[5]Shiang-Woei Chyuan.Studies of poisson's ratio variation for solid propellant grain under ignition pressure loading[J].Internationan Journal of Pressure Vessels and Piping,2003,80(12):871-877.
[6]Neviere Robert.An extension of the time-temperature superposition principle to non-linear viscoelastic solids[J].International Journal of Solids and Structures, 2006,43(17):5295-5306.
[7]F. Xu,N. Aravas,P. Sofronis.Constitutive modeling of solid propellant materials with evolving microstructural damage [J] Journal of the Mechanics and Physics of Solids,2008,56(5):2050-2073.
[8]Ren Ping,Hou Xiao,He Gaorang.et al.Comparative Research of Tensile and Compressive Modulus of Composite Solid Propellant for Solid Rocket Motor[J] Journal of Astronautics,2010,31 (10):2354-2359.
[9]H. C. Yildinm,S. Ozupek.Structural assessment of a solid propellant rocket motor: Effects of aging and damage [J].Aerospace Science and Technology,2011,15(8): 635-641.
[10]杨挺青.非线性粘弹理论中的单积分型本构关系[J].力学进展,1988,1：52-60.
[11]曹树刚.煤岩的蠕变损伤、瓦斯渗流和煤与瓦斯突出关系的研究[博士学位论文][D].重庆：重庆大学,2000.
[12]W. N. Findley J. S. Lai,K. Onaran. Creep and relaxation of nonlinear viscoelastic materials:with an introduction to linear viscoelasticity[M]. Dover Publication, New York,1989.
[13]杨挺青,罗文波,徐平等.粘弹性理论与应用[M].北京：科学出版社,2004.
[14]张淳源,张为民.非线性粘弹性理论及其应用研究进展[J].湘潭大学自然科学学报,2003,25(4)：28-32.
[15]张为民.非线性粘弹性本构理论及其应用[J].湘潭大学自然科学学报,2000,22(4)：39-44.
[16]A. Hanyga,M. Seredynskab.Multiple-integral viscoelastic constitutive equations[J]. International Journal of Non-Linear Mechanics,2007,42(5):722-732.
[17]W. N. Findley,J. S. Lai,K. Onaran.Creep and relaxation of nonlinear viscoelastic materials[M], North Holland Publishing Company,1976.
[18]J. D. Ferry.Viscoelastic Propersties of Polymers[M].3rd Edition,John Wiley.New York,1980.
[19]R. A. Schapery.On a thermodynamic constitutive theory and its application to various nonlinear materials[J].Proc. IUTAM Symp.,East Kilbride,1968:259-285.
[20]R. A. Schapery.On the characterization of nonlinear viscoelastic materials [J]. Polymer Engineering and Science,1969,9(4):295-310.
[21]王礼立,施绍裘,江瑛等.ZWT非线性热粘弹性本构关系的研究与应用[J].宁波大学学报(理工版),2000,13Sup：141-149.
[22]Leaderman H.Large longitudinal retarded elastic deformation of rubber like network polymers [J].Trans.Soc Rheol,1962:361-382.
[23]J. Smart,J. G. Williams.A comparison of single integral nonlinear viscoelastic theories[J]. J Mech.Phys.Solids,1972,20:313-324.
[24]Jung Gyoo-Dong,Youn Sung-Kie,Kim Bong-Kyu.Development of a three-dimensional nonlinear viscoelastic constitutive model of solid propellant[J] Journal of the Brazilian Society of Mechanical Sciences,2000,22(3):457-476
[25]Levesque Martin,Derrien Katell,Baptiste Didier,et al.On the development and parameter identification of Schapery-type constitutive theories [J].Mechanics of time-dependent materials,2008,12(2):95-127.
[26]Jazouli Said,Luo Wenbo,Bremand Fabriceet al.Nonlinear creep behavior of viscoelastic polycarbonate[J]. Journal of Materials Science,2006,41(2):531-536.
[27]张永敬,赵光辉,阳建红等.HTPB复合固体推进剂非线性本构方程研究[J].推进技术,2000,21(4)：70-72.
[28]Luo Wen-bo,Wang Chu-hong,Zhao Rong-guo.Application of time-temperature-stress superposition principle to nonlinear creep of Poly(methyl methacrylate)[J].Key Engineering Materials,2007,340-341:1091-1096.
[29]李东.固体推进剂药柱表面裂纹动态力学特性研究[D].南京理工大学博士学位论文,2008.
[30]M. A. Burke,P. J. Woytowitz,G. Reggi.A Nonlinear Viscoelastic constitive Model for Solid Propellant, AIAA-2213,1990.
[31]强洪夫.固体火箭发动机装药结构完整性数值仿真与实验研究[D].西安交通大学博士学位论文,1998.
[32]孟红磊.改性双基推进剂装药结构完整性数值仿真方法研究[D].南京理工大学博士学位论文,2011.
[33]牛秉彝等.高聚物粘弹及断裂性能[M].北京：国防工业出版社,1991.
[34]袁军堂.高聚物及其复合材料的应用技术研究[D].南京理工大学博士论文,2001.
[35]彭网大,杨风云,廖庆惠等.HTPB复合固体推进剂粘弹特性研究——主松弛模量的时间、温度依赖性[J].推进技术,1984,(02)：6-18.
[36]余世方,赵伯华,辛振河等.固体推进剂粘弹力学特性的实验研究[J].推进技术,1985,(4)：1-8.
[37]彭网大,朱慧,张志毅等.HTPB复合固体推进剂粘弹特性研究——动态抗张模量的时间、温度依赖性[J].推进技术,1986,(4)：46-55.
[38]贾展宁.改性双基推进剂力学性能特点分析[J].兵工学报,1989,(3)：17-23.
[39]田学林,卢红斌.NEPE推进剂的动态力学分析[J].北京理工大学学报,1995,15(6)：49-51.
[40]侯竹林,韩盘铭.NEPE固体推进剂动态力学性能的研究[J].固体火箭技术,1999,22(2)：37-39,51.
[41]张伟,樊学忠,张腊莹等NEPE推进剂低温瞬态的粘弹特性[J].固体火箭技术,2009,32(3)：298-301,343.
[42]胡全星,姜豫东,李健.推进剂松弛模量主曲线及W.L.F.方程参数的拟合处理[J].固体火箭技术,2003,26(2)：46-48.
[43]曾甲牙.固体填充剂对推进剂力学性能的影响[J].固体火箭技术,2002,25(1)：46-50.
[44]蒙上阳,唐国金,雷勇军.材料性能对固体发动机结构完整性的影响[J].国防科技大学学报,2002,24(5)：10-15.
[45]高鸣,赵伯华.固体推进剂体积模量主曲线试验研究[J].推进技术,1995,(2)：67-71.
[46]高鸣,蔡体敏.固体推进剂体积模量试验研究[J].火炸药学报,1999,(2)：5-7.
[47]R. Caracciolo,M. Giovagnoni.Frequency dependence of Poisson's ratio using the method of reduced variables[J].Mechanics of Materials,1996,24(1):75-85.
[48]HARRY H. HILTON.Implications and Constraints of Time-Independent Poisson Ratios in Linear Isotropic and Anisotropic Viscoelasticity[J]. Journal of Elasticity, 2001,63(3):221-251.
[49]P. H. Mott,J. R. Dorgan,C. M. Roland.The bulk modulus and Poisson's ratio of "incompressible" materials. Journal of Sound and Vibration,2008,312(4-5):572-575.
[50]Taniguchi Yusuke,Ando Kosei.Time dependence of Poisson's effect in wood I:the lateral strain behavior. Journal of Wood Science,2009,56(2):100-106.
[51]何铁山,张劲民.环境压强对固体推进剂力学行为的影响[J].推进技术,2005,26(4)：367-370.
[52]郭翔,张小平,张炜.拉伸速率对NEPE推进剂力学性能的影响[J].固体火箭技术,2007,30(4)：321-323,327.
[53]王玉峰,李高春,刘著卿等.应变率和加载方式对HTPB推进剂力学性能及耗散特性的影响[J].含能材料,2010,18(4)：377-382.
[54]罗天元,黄文明,王艳艳等.湿度对HTPB复合推进剂力学性能的影响[J].火炸药学报,2009,32(6)：84-86.
[55]刘著卿,李高春,王玉峰等.应变加载历史对推进剂力学性能的影响[J].火炸药学报,2010,33(4)：5-9.
[56]王瑛,张晓宏,陈雪莉等.改性双基推进剂组合装药界面力学性能[J].含能材料,2011,19(3)：287-290.
[57]杨凤林,庞爱民,张小平.复合固体推进剂单向拉伸曲线分析[J].固体火箭技术,2001,24(3)：1-4.
[58]宋丹平,翟鹏程,郑剑等.一种固体推进剂本构关系的研究[J].固体力学学报,2008,29(S1)：6-8.
[59]M. S. Matecic,M. S. Suceska.Artificial ageing of double base rocket propellant[J]. Journal of Thermal Analysis and Calorimetry,2009,96(2):523-529.
[60]S. M.Walley,C. R.Siviour,D. R. Drodge.et al.High-rate mechanical properties of energetic materials[J].JOM Journal of the Minerals, Metals and Materials,2010, 62(1):31-34.
[61]Wang Ling,Song Yuming,Gyanda Reena.et al.Preparation and mechanical properties of crosslinked 1,2,3-triazole-polymers as potential propellant binders[J] Journal of Applied Polymer Science,2010,117(5):2612-2621.
[62]Sui Xin,Wang Ningfei,Wan Qian.et al.Effects of Relaxed Modulus on the Structure Integrity of NEPE Propellant Grains during High Temperature Aging[J].Propellants, Explosives, Pyrotechnics,2010,35(6):535-539.
[63]Deng Kai,Yang Jianhong,Huang Weiwei.et al.A new method to obtain shear modulus of solid propellant[J].Acta Astronautica,2011,69(7-8):440-444.
[64]C. A. Coulomb.English translation:Note on an application of the rules of maximum and minimum to some statical problems,relevant to architecture, Heyman J.,1997,41-74.
[65]Hu L. W. An experimental study of the fracture of metals under hydrostatic pressure[J]. J. Mech. Phys. Solids,1956,4(2):96-103.
[66]W. Prager.Strain hardening under combined stress[J].J. Appl.Phys.,1945,16:837-840.
[67]W. Whitney,R. D. Andres.The behaviour of polystyrene,polymrthl, methacrylate, polycarbonate,and polyvinyl formale under conplex stress state[J].J. Polym. Sci., 1967,16,2961.
[68]P. B. Bowder,J. A. Jukes.Plastic flow of polymers[J].J. Mater.Sci.,1972,7:52-63.
[69]R. Raghava,R. M. Caddell,S. Y.Yeh Gregory.The macroscopic yield behaviour of Polymers[J] Journal of Materials Science,1973,8(2):225-232.
[70]R. H. Sigley,A. S. Wronski,T. V. Parry.Three-parameter yield criterion for a brittle polyester resin[J]. Journal of Materials Science,1991,26(15):3985-3990.
[71]R. Quinson,J. Perez,M.Rink.et al.Yield criteria for amorphous glassy polymers[J]. Journal of Materials Science,1997,32(5):1371-1379.
[72]R. D. Sudduth.Development of a Simplified Relationship Between Uniaxial Creep,Stress Relaxation,and Constant Strain-Rate Results for Viscoelastic Polymeric Materials[J].Journal of Applied Polymer Science,2001,82(3):527-540.
[73]R. D. Sudduth.Indications that the yield point at constant strain rate and the inception of tertiary creep are manifestations of the same failure criterion using the universal viscoelastic model[J]. Journal of Materials Science,2003,6 (38):1123-1134.
[74]R. M. Christensen.A Comprehensive Theory of Yielding and Failure for Isotropic Materials[J] Journal of Engineering Materials and Technology,2007,129(2):173-181.
[75]沈怀荣.温度相依固体推进剂的蠕变损伤模型[J].固体推进技术,1992,11(4)：39-43.
[76]R. M.Muthiah,V. N. Krishnamurthy,B. R. Gupta.Rheology of HTPB propellant.I. Effect of solid loading, oxidizer particle size, and aluminum content[J]. Journal of Applied Polymer Science,1992,44(11):2043-2052.
[77]Yu Mao-hong.Advances in strength theories for materials under complex stress state in the 20th Century[J]. Appl Mech Rev,2002,55(3):169-218.
[78]Li Dong-wei,Fan Ju-hong,Wang Ren-he.Research on visco-elastic-plastic creep model of artificially frozen soil under high confining pressures[J].Cold Regions Science and Technology,2011,65(2):219-225.
[79]Sung Shinjang,Liu Li-wei,Hong Hongki. et al.Evolution of yield surface in the 2D and 3D stress spaces[J].International Journal of Solids and Structures,2011,48(6):1054-1069.
[80]贾乃文.粘塑性力学及工程应用[M].北京：地震出版社,2000.
[81]A. C. Lund,C. A. Schuh.The Mohr-Coulomb criterion from unit shear processes in metallic glass[J].Intermetallics,2004,12(10-11):1159-1165.
[82]杨璐,沈新普.基于Coulomb准则的混凝土塑性损伤本构模型及其数值验证[J].岩土力学,2008,29(12)：3318-3322.
[83]Zhang Lian-yang,Cao Ping,Radha K C.Evaluation of rock strength criteria for wellbore stability analysis[J].International Journal of Rock Mechanics and Mining Sciences,2010,47(8):1304-1316.
[84]常晓林,马刚,刘杏红.基于复合屈服准则的混凝土塑性损伤模型[J].四川大学学报,2011,43(1)：1-7.
[85]D. Debasis,C. D. Kamal.Modelling of fully grouted rock bolt based on enriched finite element method[J].International Journal of Rock Mechanics and Mining Sciences,2011,48(2):283-293.
[86]Rocio Seltzer,Adrian P. Cisilino,Patricia M.Frontini.et al.Determination of the Drucker-Prager parameters of polymers exhibiting pressure-sensitive plastic behaviour by depth-sensing indentation[J].International Journal of Mechanical Sciences,2011,53 (6):471-478.
[87]Rezaiee-Pajand Mohammad, Sharifian Mehrzad,Sharifian Mehrda.Accurate and approximate integrations of Drucker-Prager plasticity with linear isotropic and kinematic hardening[J].European Journal of Mechanics A:Solids,2011,30(3):345-361.
[88]Khan Akhtar,Zhang Hao-yue.Finite deformation of a polymer:Experiments and modeling[J].International Journal of Plasticity,2001,17(9):1167-1188.
[89]A. Sides,J. Uzan,Perl M.A comprehensive viscoelasto-plastic characterization of sand-asphalt compressive and tensile cyclic loading[J].Test Evaluat,1985,13(1):49-59.
[90]Y. Lu,P. J. Wright.Numerical approach of visco-elastoplastic analysis for asphalt mixtures[J]. Computers and Structures,1998,69(2):139-147.
[91]J. M. Gonzalez,C. J. Miquel,S. Oller, et al. A viscoplastic constitutive model with strain rate variables for asphalt mixtures'numerical simulation [J]. Computational Materials Science 2007,38(4):543-560.
[92]Wang Zhong-jin,Liu Jian-guang.Sectional finite element analysis of coupled deformation between elastoplastic sheet metal and visco-elastoplastic body[J]. Acta Mechanica Solida Sinica,2011,24(2):153-165.
[93]刘建光,王忠金,刘岩.VPF用粘性介质粘弹塑性本构模型及参数确定[J].材料科学与工艺,2010,18(6)：843-846.
[94]曹树刚,鲜学福.煤岩的广义弹粘塑性模型分析[J].煤炭学报,2001,26(4)：364-369.
[95]邹友平,郭军杰,邹友峰.煤岩的改进广义弹粘塑性模型分析[J].矿业研究与开 发,2004,24(6)：30-31,78.
[96]邓荣贵,周德培,张倬元等.一种新的岩石流变模型[J].岩石力学与工程学报,2001,20(6)：780-784.
[97]韦立德,徐卫亚,朱珍德等.岩石粘弹塑性模型的研究[J].岩土力学,2002,23(5)：583-586.
[98]Yoon Wonseo,Huang Xin-yu.A nonlinear viscoelastic-viscoplastic constitutive model for ionomer membranes in polymer electrolyte membrane fuel cells. Journal of Power Sources,2011,196(8):3933-3941.
[99]A. F. Epee,F. Lauro,B. Bennani.et al.Constitutive model for a semi-crystalline polymer under dynamic loading[J].International Journal of Solids and Structures,2011,48(10): 1590-1599.
[100]曹树刚,边金,李鹏.岩石蠕变本构关系及改进的西原正夫模型[J].岩石力学与工程学报,2002,21(5)：632-634.
[101]M. C. Weng,L. S. Tsai,C. Y. Liao. et al.Numerical modeling of tunnel excavation in weak sandstone using a time-dependent anisotropic degradation model [J].Tunnelling and Underground Space Technology,2010,25(4):397-406.
[102]Ye Yong,Yang Xin-hua,Chen Chuan-yao.Experimental researches on visco-elastoplastic constitutive model of asphalt mastic[J].Construction and Building Materials,2009,23(10):3161-3165.
[103]Y. C. Lou.Viscoelastic Characterization of a Nonlinear Fiber-Reinforced Plastic Journal of Composite Materials,1971,5(2):208-234.
[104]J. Lai,A. Bakker.3-D schapery representation for non-linear viscoelasticity and finite element implementation[J].Computational Mechanics,1996,18(3):182-191.
[105]G. R. Chehab.Characterization of asphalt concrete in tension using a viscoelasto-plastic model.Ph.D. dissertation, Dept.of Civil Engineering,North Carolina State Univ.,Raleigh, N.C.,2002
[106]Y. Q. Zhao.Permanent deformation characterization of asphalt concrete using a viscoelastoplastic model.Ph.D. dissertation,Dept.of Civil Engineering,North Carolina State Univ., Raleigh, N.C.,2002
[107]Abdel-Rahman Saadeh Shadi.Characterization of asphalt concrete using anisot-ropic damage iscoelastic-viscoplastic model.Ph.D. Civil Engineering. Texas A&M University,2006
[108]Ye Yong,Yang Xin-hua,Chen Chuanyao.Modified Schapery's Model for Asphalt Sand[J]. Journal of Engineering Mechanics,2010,136(4):448-454.
[109]Ye Yong,Yang Xin-hua,Chen Chuan-yao.Viscoplastic behaviour of asphalt mixture in compression[J].Materials Research Innovations,2011,15(1):s45-s48.
[110]E. Chailleux,P. Davies.Modelling the Non-Linear Viscoelastic and Viscoplastic Behaviour of Aramid Fibre Yarns[J].Mechanics of time-dependent materials, 2003,7(3):291-303.
[111]邓凯,阳建红,陈飞等HTPB复合固体推进剂本构方程[J].宇航学报,2010,31(7)：1815-1818.
[112]O. C. Zienkiewicz,M. Wattson.Some Creep Effects Stress Analysis with Particular Reference to Concrete Pressure Vessel[J].Nuclear Engineering and Design,1966,4: 406-412.
[113]O. C. Zienkiewicz,M. WattsonJ. P. King.A Numerical Method of Viscoelastic Sress Analysis[J].Int.J.Mech.Sci,1968,10:807-827.
[114]D. Touati,G. Cederbaum.On the prediction of stress relaxation from known creep of nonlinear materials [J] Journal of Engineering Materials and Technology, 1997,119(2):121-124.
[115]D. Touati,G. Cederbaum.Post buckling of non-linear viscoelastic imperfect laminated plates Part I:Material considerations[J].Composite Structures,1998,42(1):33-41.
[116]Huang Chien-Wei,Masad Eyad,Muliana Anastasia.et al.Nonlinearly viscoelastic analysis of asphalt mixes subjected to shear loading[J].Mechanics of time-dependent materials,2007,11(2):91-110.
[117]Masad Eyad,Huang Chien-Wei,Airey Gordon.et al.Nonlinear viscoelastic analysis of unaged and aged asphalt binders[J].Construction and Building Materials,2008,22(11):2170-2179.
[118]Rami. M. Haj-Ali,Aanstasia. H. Muliana.Numerical finite element formulation of the Schapery non-linear viscoelastic material model [J]. International Journal for Numerical Methods in Engineering,2004,59(1):25-45.
[119]Jung Gyoo-Dong,Youn Sung-Kie,Kim Bong-Kyu.A three-dimensional nonlinear viscoelastic constitutive model of solid propellant[J].International Journal of Solids and Structures,2000,37(34):4715-4732.
[120]潘晓明,杨钊,雷春娟等.广义西原粘弹塑流变模型在ABAQUS中开发与应用[J].建筑结构学报,2010(S2)：324-329.
[121]潘晓明,杨钊,许建聪.非定常西原黏弹塑性流变模型的应用研究[J].岩石力学与工程学报,2011,30(S1)：2640-2646.
[122]J. S. Kim,A. H. Muliana.A combined viscoelastic-viscoplastic behavior of particle reinforced composites[J].International Journal of Solids and Structures,2010,47(5):580-594.
[123]M. K. Darabi,R. K. Abu Al-Rub,E.A. Masad.et al.A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials[J].International Journal of Solids and Structures,2011,48(1):191-207.
[124]S. H. Dessouky.Multiscale approach for modeling hot mix asphalt[D].Ph.D. Texas A&M University,2005.
[125]Huang Chien-Wei,Abu Al-Rub Rashid K.,Masad Eyad A.et al.Three-Dimensional Simulations of Asphalt Pavement Permanent Deformation Using a Nonlinear Viscoelastic and Viscoplastic Model [J] Journal of Materials in Civil Engineering,2011,23(1):56-68.
[126]Huang Chien-Wei,Abu Al-Rub Rashid K.,Masad Eyad A.et al.Numerical implementation and validation of a nonlinear viscoelastic and viscoplastic model for asphalt concrete mixes[J].International Journal of Pavement Engineering,2011,12(4): 433-447.
[127]P. Tandaiya,U. Ramamurty,R. Narasimhan.On numerical implementation of an isotropic elastic-viscoplastic constitutive model for bulk metallic glasses[J]. Modelling & Simulation in Materials Science & Engineering,2011,19(1):015002-015002.
[128]钟涛.大长径比固体火箭发动机点火瞬态过程研究[D].国防科学技术大学博士论文,2005.
[129]刘中兵,利凤祥,李越森等.高过载条件下固体推进剂药柱结构完整性分析计算[J].固体火箭技术,2003,6(2)：12-16.
[130]刘中兵,利凤祥,李越森等.轴向过载下固体推进剂药柱变形研究[J].推进技术,2004,25(2)：162-164.
[131]郑颖建.高过载下固体火箭发动机药柱结构的完整性分析[D]哈尔滨工程大学,2005.
[132]利凤祥,刘中兵,李越森等.药柱结构对其抗轴向过载能力的影响[J].推进技术,2004,25(2)：165-169.
[133]田四朋.固体火箭发动机药柱三维粘弹性响应面随机有限元分析[J].固体火箭技术,2010,33(1)：17-20.
[134]Kalaycioglu Baris,Dirikolu M. Husnu,Celik Veli.An elasto-viscoplastic analysis of direct extrusion of a double base solid propellant[J].Advances in Engineering Software,2010,41(9):1110-1114.
[135]职世君,孙冰,张建伟.固体推进剂复合型裂纹扩展数值计算[J].固体火箭技术,2011, 34(1)：28-31,47.
[136]Chyuan Shiang-Woei.Dynamic analysis of solid propellant grains subjected to ignition pressurization loading[J] Journal of Sound and Vibration,2003,268(3):465-483.
[137]孟红磊,周长省,鞠玉涛等.非均布瞬态内压作用下星孔药柱应力分析[J].固体火箭技术,2010,33(3)：289-293.
[138]R. M. Hinterhoelzl,R. A. Schapery.FEM implementation of a three-demensional viscoelastic constitutive model for particulate composites with damage growth[J]. Mechanics of time-dependent materials,2004,8:65-94.
[139]Gutierrez-Lemini,Danton.Single-Specimen Technique to Establish the J-Resistance of Linear Viscoelastic Solids with Constant Poisson's Ratio [R]. Alabama:Marshall Space Flight Center,2001
[140]R. M. Pidaparti,A. Vogt.Experimental investigation of Poisson's ratio as a damage parameter for bone fatigue. Journal of Biomedical Materials Research,2002,59(2):282-287.
[141]沈庭芳,高鸣,赵伯华.固体火箭药柱泊松比的表征与诊断[J].宇航学报,1996,17(4)：86-90.
[142]郝松林.粘弹性泊松比的各种表述方法[J].国防科技大学学报,1992,14(4)：7-12.
[143]郝晓剑,靳鸿.动态测试技术及应用[M].北京：电子工业出版社,2008.
[144]尹福炎.箔式应变片结构模型与有限元分析[J].衡器,2009,38(6)：49-52.
[145]HARRY H. HILTON, SUNG YI.The significance of (an) isotropic viscoelastic Poisson ratio stressand time dependencies[J]. International Journal of Solids and Structures, 1998,35(23):3081-3095.
[146]李东,周长省,鞠玉涛等.双基固体推进剂药柱本构关系的实验研究[J].弹道学报,2009,21(2)：6-9.
[147]Jia Zhanning.The glass transition temprature measurement of nitrocellulose by torsional braid analysis[J].Propellants, Explosives, Pyrotechnics,1992,17(1):34-37.
[148]R. C. Warren.Transition and relaxation in plasticized nitrocellulose[J].Polymer,1988,29: 919-923.
[149]D. J. Townend,R. C. Warren.Relaxation in double base propellants[J].Polymer,1985, 1(26):79-83.
[150]赵伯华,辛振河.双钴-1推进剂粘弹力学性能的实验研究[J].推进技术,1989,(1)：43-46.
[151]贾展宁,周起槐.硝化纤维素、双基粘合剂和改性双基推进剂动态粘弹性分析[J].北京工业学院报,1984,(3)：72-80.
[152]周舟,贾展宁,周起槐.改性双基(CMDB)推进剂动态力学性能的研究[J].兵工学报,1985,(2)：49-58.
[153]刘子如,张腊莹,衡淑云等.双基推进剂的玻璃化温度[J].火炸药学报,2009,32(2)：56-59.
[154]赵伯华,沈庭芳,沈月萍.动态力学实验诊断应力松弛模量的研究[J].北京理工大学,1995,15(3)：339-343.
[155]Y. Traissac,J. Ninous,R. Neviere.et al.Mechanical behavior of a solid composite propellant during motor ignition[J].Rubber Chemistry and Technology,1994,68:146-157.
[156]I. Sridhar,N. A. Fleck.The multiaxial yield behaviour of an aluminium alloy foam[J]. Journal of Materials Science,2005,40(15):4005-4008.
[157]Lorenzo Peroni,Massimiliano Avalle,Marco Peroni.The mechanical behaviour of aluminium foam structures in different loading conditions[J].International Journal of Impact Engineering,2008,35(7):644-658.
[158]Voyiadjis George Z,Shojaei Amir,Li Guoqiang.A generalized coupled viscoplastic-viscodamage-viscohealing theory for glassy polymers [J].International Journal of Plasticity,2012,28(1):21-45.
[159]O. C.Zienkiewicz, R. L.Taylor.The finit element method for solid and structural mechanics[M].Elsevier (Singapore) Pte Ltd,2009.
[160]H. Poon,M. F. Ahmad.A finite element constitutive update scheme for anisotropic, viscoelastic solids exhibiting non-linearity of the Schapery type[J].International Journal for Numerical Methods in Engineering,1999,46(12):2027-2041.
[161]R. L.Taylor, K. S.Pister, G L.Goudreau.Thermomechanical Analysis of Viscoelastic Solids[J].International Journal for Numerical Methods in Engineering,1970,2(1):45-59.
[162]D.R.J. OWEN,E. HINTON.Finite elements in plasticity—theory and practice[M]. Swansea:Pineridge Press,1980.
[163]J. Varna,L. Rozite,R.Joffe. et al.Non-linear behaviour of PLA based flax composites [J]. Plastics, Rubber and Composites,2012,41(2):49-60.