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岩土材料变形局部化问题理论及数值分析研究
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摘要
变形局部化作为岩土材料在荷载作用下常见的一种变形模式,是材料失稳及破坏的起因和前兆。而变形局部化理论将材料的失稳和破坏归因于材料在变形过程中某个局部区域的变形模式发生了分叉,即其应力应变关系发生了分叉。对岩土材料而言,无论是几何非线性或材料非线性问题都可能存在分叉现象,该现象早已为实验室实验所观察并加以研究。
     不同应力路径下岩土材料的变形局部化分析一直是岩土力学界研究的重点。然而,目前较多的研究集中于对平面应变状态下岩土材料变形局部化分析,而对真三维应力状态下变形局部化问题研究较少。更重要的是岩土材料的力学性质强烈依赖于应力状态、加载路径等条件,导致平面应变条件下的变形局部化分析并不能真正反映三维应力状态下的变形局部化特性。因此,建立真三维应力状态下的变形局部化分析,用分叉理论来分析和解决材料变形局部化问题仍是当前国内外学者研究的热点。
     超固结黏土和密砂是两种常见的岩土工程材料,在剪切试验过程中伴随有剪胀及软化现象的发生。而有限元软件自带的本构模型大多不能很好的反映上述变形特性。因此,为了实现上述两类岩土材料本构模型(姚仰平等提出的超固结黏土及砂的临界状态本构模型)在变形局部化数值模拟中的应用。首先,本文基于回映应力更新算法,推导了两类本构模型的应力更新算法表达式,编写了用户材料子程序。通过单元测试,验证了子程序的正确性及合理性,成功实现了两类本构模型在ABAQUS有限元软件中的应用。
     其次,探讨了两类材料本构模型变形局部化分叉特性,推导了真三维应力状态下分叉条件的判别式。给出了两类本构模型在不同应力路径下分叉理论解,并通过数值模拟的方法捕捉到了分叉点的应力状态,使理论解与数值模拟结果得到了相互验证。除此之外,还针对两类本构模型,讨论了超固结比(超固结黏土本构模型)、初始孔隙比和围压(砂的临界状态本构模型)、土水耦合、流动法则及软化等对变形局部化分叉的影响。
     再次,作为弹塑性本构模型在剪切带数值分析中应用的实例,本文利用有限元软件ABAQUS,采用超固结黏土本构模型材料子程序,对单相介质和两相介质(饱和土)立方体试样,在三轴压缩、三轴伸长及平面应变应力路径下剪切带问题进行了三维数值模拟。讨论了不同应力路径下剪胀性、剪切速率以及孔压对剪切带形成的影响。
     最后,针对经典连续体计算模型在引入应变软化本构行为时,在某些应力路径下本构模型出现分叉,导致模型的初边值问题在数学上成为不适定,并导致有限元网格病态的依赖解。为正确地模拟由应变软化引起的变形局部化问题,须在经典连续体中引入某种类型的正则化机制以保持变形局部化问题的正定性。本文采用非局部理论,对影响软化特性的塑性乘子采用过非局部变量,并通过构造权函数的方法,将过非局部变量的积分形式退化为一个二阶梯度项。从而使数值计算上得以简化,并且也保证了正则化的有效性。通过引入非局部变量,将两类岩土材料本构模型扩展为非局部弹塑性本构模型,并给出了非局部本构模型的一致算法模量表达式。
Deformation localization is a commonly phenomenon in the failures of geomaterials under different loading conditions and it is also the precursor of catastrophic material failure. Accoding to the theory of deformation localization, stability of geomaterials attributes to occurrence of the localization. That is bifurcation occourence in characteristics of stress-strain relationship. As far as geomaterials is concerned, no mater what geometric nonlinearity or material nonlinearity is, bifurcation probably exists and this phenomenon have been already discovered and studied in laboratory.
     Bifurcation of geomaterials along different stress paths are always importants concerns in soil mechanics and engineering. Many analytical works have been conducted to understand the bifurcation of geomaterials under plane strain condition while very limited bifurcation results in true triaxial stress condition are available at present. Because the mechanical behaviour of geomaterials much depending on stress state and stress paths, bifurcation theory under plane strain condition cannot express accurately predictions of bifurcation points under true triaxial condition. So extending bifurcation theory to three dimensional stress conditions and applying it to deformation localization analysis are still a research hotspot.
     Overconsolidated clay and dense sand are two kinds of typical soil materials in geotechnical enineering, which display the hardening-softening and shear dilatancy features during shearing. But the constitutive models implemented in most of the commom finite element software cannot describe the above defotmation characteristics. In order to apply two elastoplastic constitutive models proposed by Yao et al. (2004, 2009) for overconsolidated clays and sands to numerical analysis of deformation localization, the subroutines are developed for the implementation of the models into a nonlinear finite element software ABAQUS by using the return mapping algorithm. Numerical simulations of triaxial compression, triaxial extension and plane strain tests are performed. The algorithm is verified by simulating the mechanical behaviour of overconsolidated clays and sands.
     Secondly, bifurcation features for the two constitutive models are probed. Analytical solutions to three-dimensional bifurcation are deduced. And the solution of the model along different stress paths under constant mean effective stress is resolved. Furthermore, numerical simulations for isotropically homogenous cubic true triaxial specimens along different stress paths under constant mean effective stress are carried out. The comparisons between the numerical results and theoretical solutions show that the numerical results agree with the theoretical solutions. Effects of overconsolidation ratio, initial void ratio, confining pressure, coupling of soil and water, flow rule and softening on bifurcation for geomaterial are discussed.
     Thirdly, because of limited analytical works for the shear bands of overconsolidated clay, numerical simulations have been conducted for an example of application. By using the implemented program, three-dimensional finite element analysis of shear band is carried out under triaxial compression, triaxial extension and plane strain stress paths by appling a nonlinear finite element software ABAQUS. Effects of shear dilatancy, shear rate and pore pressure on shear bands are discussed.
     Finally, the bifurcation exists in the constitutive models with description of softening developed within the framework of conventional continuum theory along some stress paths. As a result, the corresponding boundary value problem becomes no definite type and numerical modeling of bifurcation behaviour suffers from severe mesh-dependence. In order to avoid this problem, one available approach is to consider some regularization techniques. According to non-local theory, gradient term can be got by a Taylor series expansion through construction a weight function, which can keep the regularization techniques effective. So two extended non-local elastoplastic constitutive models are abtained by introducting the second order gradient term and consistent approach modulus is deduced.
引文
【1】.李国琛,耶那.塑性大应变微结构力学[M].北京:科学出版社, 1993.
    【2】.李国琛.剪切带状分叉的力学条件[J].力学学报, 1988, (4): 20-24.
    【3】.李国琛.韧性材料的剪切带状分叉[J].力学学报, 1987, (1): 19-23.
    【4】. Terzaghi K. Stability of slopes of natural clay [C]. In: Proceeding 1st International .Conferrnce. Soil Mechanics & Fundation. Engineering, Harvard, 1936, 1: 161-165.
    【5】.赵冰,李宁,盛国刚.软化岩土介质的应变局部化研究进展[J].岩土力学, 2005, 26(3): 494-499.
    【6】.李宁,张鹏.岩质边坡稳定分析与设计的几个基本问题[A].中国岩石力学与工程学会第七次学术大会论文集[C].北京:中国科学技术出版社, 2002, 395-398.
    【7】.谢和平,刘夕才,王金安.关于21世纪岩石力学发展战略的思考[J].岩土工程学报, 1996,18(4): 98-102.
    【8】.沈珠江.土体结构性的数学模型-21世纪土力学的核心问题[J].岩土工程学报, 1996, 18(1):95-97.
    【9】.沈珠江.现代土力学的基本问题[J].力学与实践, 1998, 20 (6): 1-6.
    【10】.沈珠江.理论土力学[M].北京:水利水电出版社, 2000.
    【11】. Rudnicki J. W, Rice J. R. Conditions for the localization of deformation in pressure-sensitive dilatant materials [J]. Journal of Mechanics and Physics of Solids, 1975, 23: 371-394.
    【12】. Li X. K., Zhang J. B., Zhang H. W. Instability of wave progagation in saturated poroelastoplastic media [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2002, 26: 563-578.
    【13】. Borst R. Bifurcations in finite element models with a non associated flow law [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12: 99-116.
    【14】. Desai C. S., Somasundaram S., Frantziskonis G. A hierarchical approach for constitutive modelling of geologic materials[J]. I International Journal for Numericaland Analytical Methods in Geomechanics, 1986, 10: 225-257.
    【15】. Cividini A., Gioda G. Finite element analysis of direct shear tests of stiff clays [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1992, 16: 869-886.
    【16】. Sterpi D. An analysis of geotechnical problems involving strain softening effects [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1999, 23: 1427-1454.
    【17】. Finno R. J., Rhee Y. Consolidation, pre-and post peak shearing responses from internally instrumented biaxial compression apparatus [J]. Geotechnical Testing Journal, ASTM, 1993, 16: 496-509.
    【18】. Han C., Vardoulakis I. Plane strain compression experiments on watersaturated fine-grained sand [J]. Geotechnique, 1991, 41: 49-78.
    【19】. Sabatini P., J, Finno R. J. Effect of consolidation on strain localization of soft clays [J]. Computers and Geotechnics, 1996, 18(4): 311-339.
    【20】. Khalid A. A., Stein S. Shear band formation in plane strain experiments of sand [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(6): 495-503.
    【21】.陈波.上海软土的力学特性及弹塑性模拟[M].上海大学硕士论文, 2009.
    【22】. Yao Y. P., Sun D. A., Luo T. A critical state model for sands dependent on stress and density [J]. International Journal for Numerical and Analytical methods in Geomechanics, 2004, 28(4): 323-337.
    【23】.黄克智,黄永刚.固体本构关系[M].北京:清华大学出版社, 1999, 65-69.
    【24】. Hill R. A. General theory of uniqueness and stability in elastic-plastic solids [J]. Journal of Mechanics and Physics of Solids, 1958, 5: 236-249.
    【25】. Hill R. A. Acceleration waves in solids [J]. Journal of Mechanics and Physics of Solids, 1962, 10: 12-16.
    【26】. Bishop J. F. W., Hill R. A. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses [J]. Philosophical Magazine Letters, 1951, 42: 414-427.
    【27】. Mandel J. Condition de stabilitéet postulate de Drucker [C]. In IUTAM Symposium on Rheology and Applied Mechanics, 1964. Gernoble.
    【28】. Mroz Z. Non-associatied flow laws in plasticity [J]. Journal de mecaniqus, 1963, 2: 21-42.
    【29】. Naghdi P. M., Trapp J. A. The significance of formulating plasticity theory with reference to loading surfaces in strain space [J]. International Journal of Engineering Science, 1975, 13: 785-797.
    【30】. Prevost J. H., Hoeg H. Soil mechanics and plasticity analysis of strain softening [J]. Geotechnique, 1975, 25(2): 279-297.
    【31】.陆启韶.分岔与奇异性[M].上海科技教育出版社,上海, 1997.
    【32】. Hill R. A., Hutchinson J. W. Bifurcation phenomena in the plane tension test [J]. Journal of the Mechanics and Physics of Solids, 1975, 23: 239-264.
    【33】. Rice J. R. The localization of plastic deformation [C], Proc 14th International Conference on Theoretical and Applied Mechanics, 1976, 207-220.
    【34】. Morgenstern N. R., Tchalenko J. S. Microscopic strictures in kaolin subjected to direct shear [J]. Géotechnique, 1967, 17(1): 309-328.
    【35】. Scarpelli G., Wood D. M. Experimental observation of shear band pattern in direct shear tests [C]. In IUTAM Conference on Deformation and Failure of Granular Materials. 1982. Delft, Holland.
    【36】. Roscoe K. H. The influence of strains in soil mechanics [J]. Géotechnique, 1970, 20(2): 129-70.
    【37】. Han C. H., Vardoulakis I. Plane strain compression experiment on water-saturated fine-grained sand [J]. Géotechnique, 1991, 41(1): 49-78.
    【38】. Alshibli K. A., Sture L. S. Shear band formation in plane strain experiments of sand [J]. Journal Geotechnical and Geoenvironmental Engineering, ASCE, 2000, 126(6): 495-503.
    【39】. Perice D., Runesson K., Store S. Evaluation of plastic bifurcation for plane strain versus axisymmetry [J]. Journal of Engineering Mechanics, 1992, 118(3): 512-524.
    【40】. Vardoulakis I. Shear band inclination and shear modulus of sand in biaxial tests [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1980, 4: 103-119.
    【41】. Ord A., Vardoulakis I., Kajewski R. Shear band formation in Gosford sandstone [J]. International Journal of Rock Mechanics Mining Science & Geomechanics Abstract, 1990, 23(5): 397-409.
    【42】. Vardoulakis I., Graf B. Shear band formation in fine-grained sand [A]. Proceeding. Fifth International Conference Numerical Methods in Geomechanics, Nagoya, Rotterdam: Balkema.1985, 517-521.
    【43】. Yoshida T., Tatsuoka F. Deformation property of shear band subjected to plane strain compression and its relation to particle characteristics [A]. Proceeding of 14th conference on Soil Mechanics and Foundations Engineering, 1997, 1(1): 237-240.
    【44】. Finno R. J., Larton A. A., Mooney M. A., Viggiani. Shear bands in plane strain active tests of moist tamped and pluviated sands [A]. Proceeding of the Mechanics and Foundations Engineering, 1997, 1:295-298.
    【45】. Drescher A., Lannier J., Struts P. Localization of the deformation in test on sand sample [J]. Engineering Fracture Mechanics, 1985, 21(4): 909-911.
    【46】. Finno R. J., Harris W. W., Mooney M. A., Viggiani G. Shear bands in plain strain compression of loose sand [J]. Geotechnique, 1997, 47(1): 149-165.
    【47】. Oda M., Kazama H. Microstructure of shear bands and its relation to the mechanism of dilatancy and failure of dense granular soils [J]. Geotechnique, 1998, 48(4): 465-481.
    【48】.李蓓,赵锡宏,策建国.上海粘性土剪切带倾角的实验研究[J].岩土力学, 2002, 23(4): 423-427.
    【49】. Labuz J. F., Dai S. T., Papamichos E. Plane strain compression of rock-like materials [J]. International Journal of Rock Mechanics Mining Science & Geomechanics Abstract, 1996, 33(4): 573-584.
    【50】. Wang Q., Lade P. V. Shear banding in true triaxial tests and its effect on failure in sand [J]. Journal of Engineering Mechanics, 2001, 127(8): 754-761.
    【51】. Lade P. V., Wang Q. Analysis of shear banding in true triaxial test on sand [J]. Journal of Engineering Mechanics, 2001, 127(8): 762-766.
    【52】. Chu J., Lo S.C.R., Lee I.K. Strain softening and shear band formation of sand in multi-axial test [J]. Geotechnique, 1996, 46(1): 63-82.
    【53】. Yamamuro J. A., Shapiro S. Failure and shear band in three dimensional experiments on loose sands [C]. 15th ASCE Engineering Mechanics Conference, New York, 2002.
    【54】. Sun D. A., Huang W. X., Yao Y. P. An experimental study of failure and softening in sand under three-dimensional stress condition [J]. Granular Matter, 2008, 10(3): 187-195.
    【55】. Saada A. S., Liang L., Figueroa J. L., Cope C. T. Bifurcation and shear band propagation in sands [J]. Géotechnique, 1999, 49(3): 367-385.
    【56】.郑捷,姚孝新,陈融.岩石变形局部化的实验研究[J].地球物理学报, 1982, 26 (6): 554-562.
    【57】. Berthaud Y., Torrenti J. M, Fond C. Analysis of localization in brittle materials through optical techniques [J]. Experimental Mechanics, 1997, 37(2): 216-220.
    【58】.潘一山,杨小彬.白光数字散斑相关方法研究岩石变形局部化[J].岩土工程学报, 2002, 24(1): 97-100.
    【59】.王春华,康小敏,张平.煤岩截割的变形局部化实验研究[J].煤矿开采, 2002, 49: 6-8.
    【60】.蒋明镜,沈珠江.结构性黏土剪切带的微观分析[J].岩土工程学报. 1998, 20(2): 102-108.
    【61】. Howell D., Behringer R. P., Veje C. Stress fluctuations in a 2D granular coquette experiment: a continuous transition [J]. Physical Review Letters, 1999, 82(26): 5241-5244.
    【62】. Mueth D. M., Debregeas G. F., Karczmar G. S., Eng P. J., Nagle S .R., Jaeger H. M. Signatures of granular microstructure in dense shear flows [J]. Nature, 2000, 406(27):385-389.
    【63】. Bardet J. P. A comprehensive review of strain localization in elastoplastic soils [J].Computers and Geotechnics, 1990, 10:163-188.
    【64】. Bardet J. P. Orientation of shear bands in frictional soils [J]. Journal of Engineering Mechanics, ASCE, 1991, 117(7): 1466-1484.
    【65】. Ruina A. L. Constitutive relations for frictional slip [J]. Mechanics of Geomaterials Rocks, Concretes, Soils, Singapore: John Wiley and Sons, Eds. Bazant Z. P., 1985.
    【66】. Thomas T. Y. Plastic flow and fracture in solids [M]. 1961, New York: Academic Press.
    【67】. Needleman A. Non-normality and bifurcation in plane strain tension and compression [J]. Journal of the Mechanics and Physics of Solids, 1979, 27: 231-254.
    【68】. Vardoulakis I., Goldscheider M., Gudehus G. Formation of shear bands in sand bodies as a bifurcation problem [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1978, 2(2): 99-128.
    【69】. Ottosen N. S., Runesson K. Properties of discontinuous bifurcation solutions in elasto-plasticity [J]. International Journal of Soilds and Structures, 1991, 27: 231-254.
    【70】. Molenkamp F. Comparison of friction materical models with respect to shear band initiation [J]. Geotechnique, 1985, 35(2):127-143.
    【71】. Kolymbas D., Rombach G. Shear band formation in generalized hypoelasticity [J]. Archive of Applied Mechanics, 1989, 59:177-186.
    【72】. Wu W., Sikora Z. Localized bifurcation in hypoelasticity [J]. International Journal of Engneering Science, 1991, 29(2):195-201.
    【73】. Huang W. X., Bauer E., Sloan S. W. Behaviour of interfacial layer along granular soil-structure interfaces [J]. Structureal Engineering and Mechanics, 2003, 15(3):315-329.
    【74】.张永强,俞茂宏.弹塑性材料的平面应力非连续分岔[J].力学学报, 2001, 33(5): 706-713.
    【75】.黄茂松,钱建固.平面应变条件下饱和土体分叉后的力学性状[J].工程力学, 2005, 22(1): 48-53.
    【76】.杨强,陈新,周维坦.岩土材料弹塑性损伤模型及变形局部化分析[J].岩石力学与工程学报, 2004, 23(21): 3577-3583.
    【77】.徐松林,吴文.岩土材料局部化变形分岔分析[J].岩石力学与工程学报, 2004, 23 (20): 3430-3438.
    【78】.徐松林,吴文,李廷等.三轴压缩大理岩局部化变形的实验研究及其分岔行为[J].岩土工程学报, 2001, 23(3): 296-301.
    【79】.钱建固,黄茂松.土体变形分叉的非共轴理论[J].岩土工程学报, 2004, 26(6):7 77-781.
    【80】. Huang M. S, Lu X. L, Qian J. G. Non-coaxial elasto-plasticity model and bifurcation prediction of shear banding in sands [J]. International Journal for Numerical and Analytical Methods in Geomechanica, 2009. (In press). DOI:10.1002/nag.838.
    【81】.吕玺琳,黄茂松,钱建固.基于非共轴本构模型的砂土真三轴试验分叉分析[J]. 岩土工程学报, 2008, 30(5): 646-651.
    【82】. Yu H. S., Yuan X. On a class of non-coaxial plasticity model for granular assemblies [J]. Proceedings of the Royal Society, 2006, 462:725-748.
    【83】. Spencer A. J. M. A theory of the kinematics of ideal soils under plane strain conditions [J]. Journal of Mechanics and Physics of Solids, 1964, 12:337-351.
    【84】. Darve F. An incrementally nonlinear constitutive law of second order and its application to localization [J]. In Mechanics of Engineering Materials, 1984, John Wiley and Sons.
    【85】. Chambon R., Desrues J. Quelques remarques sur le probleme de la localization en bande de cisaillement [J]. Mechanics Research Communications, 1984, 11(2):145-153.
    【86】. Desrues J., Chambon R. Shear band analysis for granular materials: The question of incremental non-linearity [J]. Archive of Applied Mechanics, 1989, 59(3):187-196.
    【87】. De Borst R. Bifurcation in finite element models with a non-associated flow law [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12: 99-166.
    【88】. Pvovest J. H., Hughes T. J. R. Finite element solution of elastic plastic boundary value problems [J]. Journal of Applied Mechanics, 1984, 48: 69-74.
    【89】.许泽善,张志超,吴子修.不排水条件下完全饱和土剪切带之形成的模拟分析[J].中国土木水利工程学刊(中国台湾), 1994, 6(1): 21-28.
    【90】.王学滨,潘一山,丁秀丽.孔隙流体对岩体变形局部化的影响及数值模拟研究[J].地质力学学报, 2001, 7(2): 139-143.
    【91】.王学滨,潘一山,盛谦.平面应变岩样局部化变形场数值模拟研究[J].岩石力学与工程学报, 2003, 22(4): 521-524.
    【92】.俆连民,王兴然.用有限变形理论研究黏性土试样中变形的局部化问题[J].岩土工程学报, 2004, 26(2): 225-228.
    【93】.徐连民,朱合华,中井照夫,西村智.超固结黏土的剪切带数值模拟[J].岩土力学, 2006, 27(1):61-66.
    【94】. Bazant Z. P., Belytschko T., Chang T. P. Continuum theory for strain softening [J]. J. of Engng. Mech., ASCE, 1984, 110: 1666-1962.
    【95】. Kolymbas D. Bifurcation analysis for sand samples with non-linear constitutive equation [J]. Ingenieur-Archive, 1981, 50: 131-140.
    【96】. Wu W., Sikora Z. Localized bifurcation in hypoplasticity [J]. International Journal of Engineering Science, 1991, 29: 195-201.
    【97】. Bauer E. Analysis of shear band bifurcation with a hypoplastic model for a pressure and density sensitive granular material [J]. Mechanics of Materials, 1999, 31:597-609.
    【98】. Valanis K. C, Peters J. F. Ill-posedness of the initial and boundary value problems in non-associative plasticity [J]. Acta Mechanica, 1996, 114: 1-25.
    【99】. Manzari M. T. Application of micropolar plasticity to post failure analysis in geomechanics [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2004, 28: 1011-1032.
    【100】. Zienkiewicz O. C., Huang G. C. A noto on localization phenomena and adaptive finite element analysis in forming processes [J]. Communications in Applied Numerical Methods, 1990, 6: 71-76.
    【101】. Zienkiewicz O. C., Huang M. S. Localization problems in plasticity using finite elements with adaptive remeshing [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1995, 19: 127-148.
    【102】.黄茂松,钱建固,吴世明.土坝动应力应变局部化与渐进破坏的自适应有限元分析[J].岩土工程学报, 2001, 23(3): 306-310.
    【103】. Belytschko T., Tabbara M. H-adaptive finite element methods for dynamic problems with emphasis on localization [J]. International Journal for Numerical Methods in Engineering, 1993, 36: 4245-4265.
    【104】. Pastor M., Peraire J., Zienkiewicz O. C. Adaptive remeshing for shear band localization problems [J]. Archive of Applied Mechanics, 1991, 61: 30-39.
    【105】. Deb A. D., Prevost J. H., Loret B. Adaptive meshing for dynamic strain localization [J]. Computer Method in Applied Mechanics and Engineering, 1996, 137:285-306.
    【106】. Pastor M., Rubio C., Mira P., Peraire J., Vilotte J. P., Zienkiewicz O. C. Numerical analysis of localization [P]. In Numerical Methods in Geomechanics, 1992.
    【107】. Belyyschko T., Fish J., Engelmann B. E. A finite element with embedded localization zones [J]. Computer Method in Applied Mechanics and Engineering, 1988, 70: 59-89.
    【108】. Simo J. C., Oliver J., Armero F. An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids [J]. Computational Mechanics, 1993, 12: 277-296.
    【109】. Simo J. C., Oliver J. A new approach to analysis and simulation of strain softening in solids [M]. In Fracture and Damage in Quasi-brittle Structures-Experiment, Modelling and Computer Analysis, Editors: Bazant Z. P., London, 1994, p: 25-39
    【110】. Oliver J. Modelling strong discontinuities in soild mechanics via strain softening constitutive equations. Part 1: Fundamentals [J]. International Journal for Numerical Methods in Engineering, 1996, 39(21): 3575-3600.
    【111】. Larrson R., Runesson K. Element-embedded localization band based on regularized displacement discontinuity [J]. Journal of Engineering Mechanics, ASCE, 1996, 122: 422-411.
    【112】. Borja R. I. A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation [J]. Computer Method in Applied Mechanics and Engineering, 2000, 190: 1529-1549.
    【113】. Mosler J. A novel algorithmic framework for the numerical implementation of locally embedded strong discontinuities [J]. Computer Method in Applied Mechanics and Engineering, 2005, 194: 4731-4757.
    【114】. Wang X. R., Chan D., Morgenstern N. Kinematic modeling of shear band localization using discrete finite elements [J]. International Journal for Numerical and Analytical Method in Geomechanics, 2003, 27(4):289-324.
    【115】. Pietruszczak S., Mroz Z. Finite element analysis of deformation of strain softening materials [J]. International Journal for Numerical Methods in Engineering, 1981, 17: 327-334.
    【116】. Pietruszczak S., Niu X. On the description of localized deformation [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1993, 17: 791-805.
    【117】.黄茂松,钱建固,吴世明.饱和土体应变局部化的复合体理论[J].岩土工程学报, 2002, 24(1): 21-25.
    【118】. Needleman A. Material rate dependence and mesh sensitivity on localization problems [J]. Computer Methods of Applied Mechanical and Engineering, 1988, 67(1): 69-86.
    【119】. Higo Y. Instability and strain localization analysis of water-saturated clay by elasto-viscoplastic constitutive models [D]. Japan: Graduate School of Engineering, Kyoto University, 2003.
    【120】. Oka F., Higo Y., Kimoto S. Effect of dilatancy on the strain localization of water-saturated elasto-viscoplastic soil [J]. International Journal of Solids and Structures, 2002, 39: 3625-3647.
    【121】. Loret B., Prevost J. H. Dynamic strain localization in elasto-visco-plastic solids, part 1: general formulation and one-dimensional examples [J]. Computer Methods of Applied Mechanical and Engineering, 1990, 83(1): 247-273.
    【122】. Loret B., Prevost J. H. Dynamic strain localization in fluid-saturated porous media [J]. Journal of Engineering Mechanics, ASCE, 1991, 11: 177-190.
    【123】. Oka F., Adachi T., Yashima A. Instability of an elasto-viscoplastic constitutive model for clay and strain localization [J]. Mechanics of Materials, 1994, 18: 119-129.
    【124】. Oka F., Adachi T., Yahima A. A strain localization analysis using a viscoplastic softening model for clay [J]. International Journal of Plasticity, 1995, 11(5): 523-545.
    【125】. Sluys L. J. Wave propagation. Localization and dispersionin softening solids [D]. Netherlands: Civil Engineering Department of Delft University of Technology, 1992.
    【126】. Glema A., Lodygowski T., Perzyna P. Interaction of deformation waves and localization phenomena in inelastic solids [J]. Computer Methods of Applied Mechanical and Engineering, 2000, 183: 123-140.
    【127】. Wang W. M., Sluys L. J., Borst R. Interaction between material length scale and imperfection size for localization phenomena in visco-plastic media [J]. European Journal of Mechanics A: Solids, 1996, 15(3): 447-464.
    【128】. Wang W. M., Askes H., Sluys L. J. Gradient viscoplastic modeling of material instabilities in metals [J]. Metals and Materials-Korea, 1998, 4(3): 537-542.
    【129】. Muhlhaus H. B., Vardoulakis I. The thickness of shear band in granular materials [J]. Geotechnique, 1987, 37(3): 271-283.
    【130】.李锡夔,唐洪祥.压力相关弹塑性Cosserat连续体模型与应变局部化有限元模拟[J].岩石力学与工程学报, 2005, 24(9): 1497-1505.
    【131】. Bardet J. P., Proubet J. A numerical investigation of the structure of persistent shear bands in granular media [J]. Geotechnique, 1991, 41(4): 559-613.
    【132】. Oda M., Iwashita I., Kazama H. Micro-structure mechanism of dilatancy and failure [P]. In IUTAM Symposium on Mechanics of Granular and Porous Materials, 1997: Kluwer Academic Publishers: Dordrecht.
    【133】. De Borst R., Sluys L. J. Localization in a Cosserat continuum under static and dynamic loading conditions [J]. Computer Methods in Applied Mechanics and Engineering, 1991, 90(1-3): 805-827.
    【134】. Ristinmaa M., Vecchi M. Use of couple-stress theory in elasto-plasticity [J]. Computer Methods in Applied Mechanics and Engineering, 1996, 136: 205-224.
    【135】. Willam K., Dietsche A., Iordache M. M., Steinmann P. Localization on mocropolar continua [P]. In Continuum Methods for Materials with Microstructure, 1995, Willy:New York.
    【136】. Huang F. Y., Liang K. Z. Boundary element method for micropolar thermoelasticity [J]. Engineering Analysis with Boundary Elements, 1995, 17:19-26.
    【137】. Tejchman J., Bauer E. Numerical simulation of shear band formation with a polar hypoplastic constitutive models [J]. Computers and Geotechnics, 1996, 19(3): 221-224.
    【138】. Tejchman J., Gorski J. Computations of size effects in granular bodies within micro-polar hypoplasticity during plane strain compression [J]. International Journal of Solids and Structures, 2008, 45(6): 1546-1569.
    【139】. Huang W. X., Sun D. A., Sloan S. W. Analysis of the failure mode and softening behaviour of sands in true triaxial tests [J]. International Journal of Solids and Structures, 2007, 44:1423-1437.
    【140】. Li X. K., Tang H. X. A consistent return mapping algorithm for pressure-dependent elastoplastic Cosserat continua and modeling of strain localization [J]. Computer and Structure, 2005, 83:1-10.
    【141】. Eringen A. C., Edelen D. G. On nonlocal elasticity [J]. International Journal of Engineering Science, 1972, 10: 233-248.
    【142】. Eeingen A. C., Kim B. S. Stress concentration at the tip of a crack [J]. Mechanics Research Communications, 1974, 1: 233-237.
    【143】. Eeingen A. C. On nonlocal plasticity [J]. International Journal of Engineering Science, 1981, 19: 1461-1474.
    【144】. Eeingen A. C. Theories of nonlocal plasticity [J]. International Journal of Engineering Science, 1983, 21:741-751.
    【145】. Bazant Z. P., Lin F. B. Nonlocal yield limit degradation [J]. International Journal for Numerical Methods in Engineering, 1988, 26: 1805-1823.
    【146】. Bazant Z. P., Pijaudier C. G. Nonlocal continuum damage, localization instability and convergence [J]. Journal of Applied Mechanics, Transactions of ASME, 1988, 55(2): 287-293.
    【147】. Bazant Z. P., Pijaudier C. G. Nonlocal continuum damage, localization instability and convergence [J]. Journal of Applied Mechanics, 1988, 55: 287-293.
    【148】. Bazant Z. P. Nonlocal damage theory based on micromechanics of crack interactions [J]. Journal of Engineering Mechanics, 1994, 120(3): 593-617.
    【149】. Ozbolt J., Bazant Z. P. Numerical smeared fracture analysis: nonlocal microcrack interaction approach [J]. International Journal for Numerical Methods in Engineering, 1996, 36: 635-66.
    【150】. Bazant Z. P. Reminiscences on four decades of struggle and progress in softening damage and size effect [J]. Concrete Journal, 2002, 40: 16-28.
    【151】. Zhou W. Y., Zhao J. D., Liu Y. G., Yang Q. Simulation of localization failure with strain-gradient–enhanced damage mechanics [J]. International Journal for Numerical and Analytical Method in Geomechanics, 2002, 26: 793-813.
    【152】. De Borst R., Muhlhaus H. B. Gradient-dependent plasticity: formulation and algorithmic aspects [J]. International Journal for Numerical Methods in Engineering, 1992, 35: 521-539.
    【153】. Sluys L. J, de Borst R, Muhlhaus H. B. Wave propagation, localization and dispersion in a gradientdependent medium [J]. International Journal of Solids and Structures, 1993, 30(6): 1153-1171.
    【154】.佘成学,熊文林,陈胜宏.层状岩体弹黏塑性Cosserat介质理论及工程应用[J].水利学报,1996, (4):10-17.
    【155】. De Borst R., Wang W. M., Geers M. G. D. Material instabilities and internal length scales [C]. Proceedings of the Fifth International Conference on Computational Plasticity CIMNE. Barcelona Spain: Pineridge Press, 1997: 56-71.
    【156】.庄茁.连续体和结构的有限元分析[M].北京:清华大学出版社, 2002.
    【157】. Zhang Z. L. Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models [J]. Computer Methods in Applied Mechanics and Engineering, 1995, 121: 29-44.
    【158】. Hashash Y. M. A., Whittle A. J. Integration of the modified Cam-clay model innon-linear finite element analysis [J]. Computers and Geotechnics, 1992, 14(2): 59-83.
    【159】. Kumar P., Nukala V. V. A return mapping algorithm for cyclic viscoplastic constitutive models [J]. Computer Mathods in Applied Mechanics and Engineering, 2006, 195: 148-178.
    【160】. Li X. K., Tang H. X. A consistent return mapping algorithm for pressure-dependent elastoplastic Cosserat continua and modeling of strain localisation [J]. Computers and Structures, 2005, 83: 1-10.
    【161】. Gadala M. S., Wang J. Computational implementation of stress integration in FEM analysis of elasto-plastic large deformation problems [J]. Finite Elements in Analysis and Design, 2000, 35: 379-396.
    【162】. Liu Y., Glaucio H. P., Liang L. H. Elasto-viscoplastic consistent tangent operator concept-based implicit boundary element methods [J]. Science in China, 2000, 43 (2): 154-164.
    【163】. Clausen J., Damkilde L., Andersen L. An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space [J]. Computers & Structures, 2007, 85(23): 1795-1807.
    【164】. Borja R. I., Lee S. R. Cam-clay plasticity, Part 1: Implicit integration of elasto-plastic constitutive relations [J]. Computer Methods in Applied Mechanics and Engineering, 1990, 78(1): 49-72.
    【165】. Borja R. I., Sama K. M., Sanz P. F. On the numerical integration of three-invariant elastoplastic constitutive models [J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(9): 1227-1258.
    【166】. Wei L., Abu-Farsakh M. Y., Tumay M. T. Finite-element analysis of inclined piezocone penetration test in clays [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2005, 5(3): 167-178.
    【167】. Simo J. C., Hughes T. J. R. On the varitational foundations of assumed strain methods [J]. Journal of Applied Mechanics, 1986, 53(1): 51-55.
    【168】. Hughes T. J. R., Liu W. K. Implicit-explicit finite elements in transient analysis:stability theory [J]. Journal of Applied Mechanics, 1978, 45(2): 371-375.
    【169】. Moran B., Ortiz M., Shih C.F. Formulation of implicit finite-element methods for multiplicative finite deformation plasticity [J]. International Journal for Numerical Methods in Engineering, 1990, 29(3): 483-514.
    【170】.姚仰平,侯伟,周安楠.基于Hvorslev面的超固结黏土本构模型[J].中国科学E辑:技术科学, 2007, 37(11): 1417-1429.
    【171】. Yao Y. P., Hou W., Zhou A. N. UH model: three-dimensional unified hardening model for overconsolidated clays [J]. Geotechnique, 2009, 59(5): 451-469.
    【172】. Matsuoka H., Nakai T. Stress-deformation and strength characteristics of soil under three different principal stresses [J]. Proceeding of JSCE, 1974, 232: 59-74.
    【173】. Matsuoka H., Yao Y.P., Sun D. A. The Cam-clay model revised by the SMP criterion, Soils and Foundations, 1999, 39(1): 81-95.
    【174】.孙德安,甄文战,黄文雄.三维弹塑性模型在路堤软基固结分析中应用[J].岩土力学, 2009, 30(3): 669-674.
    【175】. Matsuoka H., Sun D. A. The SMP concept-based 3D constitutive models for geomaterials [M]. Taylor & Francis, 2006. London, UK.
    【176】.松冈元,中井照夫. Closure to discussion on“Stress-deformation and strength characteristics of soil under three-different principal stress (published in 1974, No.232)”, (日本)土木学会論文集, 1976, No.246, 139-140.
    【177】. Zhang H W., Schrefer B. A. Uniqueness and localization analysis of elastic-plastic saturated porous media [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25(1): 29-48

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