基于模拟的岩石类材料在动载作用下的裂缝扩展研究
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摘要
随着高层建筑和地下工程的发展,岩石类材料的动力特性在理论和工程中越来越受到重视。岩石作为一种非均匀性显著的准脆性材料,在动态荷载达到强度极限时,能量的瞬间释放会引发应力的重分布,诱使局部力学性质迅速劣化,引发裂缝高速扩展,并以弯曲和分叉为基本表现形式。因此,研究岩石类材料在动荷载作用下的裂缝扩展,直是研究者关注的重要问题。
本文基于统计分布和损伤力学的RFPA(Realistic Failure Process Analysis)方法,从细观力学角度对岩石类材料的裂缝动态扩展问题展开详细研究,具体研究可以分为以下几个方面：
1.基于Weibull随机分布函数可以描述岩石类材料的细观非均匀性的普遍规律,在考虑细观单元非均匀性的基础上,建立了岩石在动力作用下的弹脆性损伤演化本构模型。通过引入粘弹性边界方法,研究了非均匀无限域的波动问题。
2.基于动接触二步法和细观线性行为可以反映宏观非线性行为的原理,详细研究了非均匀材料的碰撞问题。由于考虑了撞块和被撞击物的相互作用,可以通过接触方法反映因材料损伤引起的加载变化,模型与实际更贴近。通过选取有代表性的三个侧向撞击模型,并与试验现象进行了验证对比,验证了该方法可行性的同时,更系统分析了不同程度的非均匀性对裂缝扩展的影响,丰富和扩展了前人的研究成果。
3.分析了冲击作用下不同均质度的岩石以及砂砾岩的响应规律。结果表明：应力波传播过程中产生的拉应力是裂缝萌生和扩展的关键。与静态岩石破碎过程相比,冲击作用下岩石的应力改变具有时间效应,应力波传播过程中表现出压、拉变化。
4.利用数值模拟方法,从细观力学角度揭示宏观裂缝扩展的非对称性和非连续性的形成机理。数值模拟结果较好的再现了试验现象和规律,说明考虑细观上的非均匀性可以实现宏观破坏过程中的非线性,细观上的简单本构关系可以模拟复杂的宏观破裂现象。
With the development of high-rise buildings and underground projects, more attentions have been paid to the dynamic properties of bedrock structures in both theoretical studies and engineering applications. As a heterogeneous material, when the stress is higher than the strength of rock, instantaneous energy release results in stress redistribution, which triggers dramatic deterioration of rock mechanical properties and rapid propagation of cracks. Under the combined effect of heterogeneity and internal stresses in the rock material, crack propaga-tion is essentially featured by crack curving and branching. Therefore, crack growth in rock-like materials subjected to dynamic loading, especially crack curving and branching, is one of the theoretical and engineering problems attracting attentions of many researchers.
In this study, the dynamic version of RFPA2D(Realistic Failure Process Analysis) pro-gram was employed to simulate crack propagation. The research content was as follows:
1. Since the Weibull distribution of the properties of mesoscopic structures and the linear mesoscopic mechanical behaviors can reflect the macroscopic nonlinear behaviors, a constitutive model for damage evolution was developed to simulate the completely fail-ure process of rock subjected to dynamic stress. By importing the Viscous-spring artifi-cial boundary into the model, the wave propagation in heterogeneous infinite media was investigated.
2. Based on dynamic method and the linear mesoscopic mechanical behaviors can reflect the macroscopic nonlinear behaviors, the collision process between two heterogeneous spe-cimens was researched in details. Because the interaction between the impactor and spe-cimen was considered, the model was closer to the reality. Three typical impact models were investigated in the paper. Comparing with the former experimental results, the availability of the method was verified. Furthermore, the different degree of heterogenity was also discussed in details. The reasearch can enrich and extend the former investiga-tion.
3. Based on damage theory and FEM method, rock fragmentation mechanism induced by a drill bit subjected to dynamic loading was investigated. Compared with rock fragment by static stress, there is a stress transition from compression to tension in the specimens un-der dynamic loading, e.g. the compression stress will be changed to tension during wave propagation. The results show that the process of wave propagation is changed and the emergency of tension is the key of crack initiation and growth.
4. By numerical method, the asymmetric and discontinuous behavior of crack propagation was analyzed at mesoscopic scale based on the damage evolution principle. The results coincide with the experimental laws, so it is certain that the linear mesoscopic mechanical behaviors can reflect the macroscopic nonlinear behaviors, and the complex mechanism of crack propagaion at macroscopic scale can be analyzed by this way.
本文基于统计分布和损伤力学的RFPA(Realistic Failure Process Analysis)方法,从细观力学角度对岩石类材料的裂缝动态扩展问题展开详细研究,具体研究可以分为以下几个方面：
1.基于Weibull随机分布函数可以描述岩石类材料的细观非均匀性的普遍规律,在考虑细观单元非均匀性的基础上,建立了岩石在动力作用下的弹脆性损伤演化本构模型。通过引入粘弹性边界方法,研究了非均匀无限域的波动问题。
2.基于动接触二步法和细观线性行为可以反映宏观非线性行为的原理,详细研究了非均匀材料的碰撞问题。由于考虑了撞块和被撞击物的相互作用,可以通过接触方法反映因材料损伤引起的加载变化,模型与实际更贴近。通过选取有代表性的三个侧向撞击模型,并与试验现象进行了验证对比,验证了该方法可行性的同时,更系统分析了不同程度的非均匀性对裂缝扩展的影响,丰富和扩展了前人的研究成果。
3.分析了冲击作用下不同均质度的岩石以及砂砾岩的响应规律。结果表明：应力波传播过程中产生的拉应力是裂缝萌生和扩展的关键。与静态岩石破碎过程相比,冲击作用下岩石的应力改变具有时间效应,应力波传播过程中表现出压、拉变化。
4.利用数值模拟方法,从细观力学角度揭示宏观裂缝扩展的非对称性和非连续性的形成机理。数值模拟结果较好的再现了试验现象和规律,说明考虑细观上的非均匀性可以实现宏观破坏过程中的非线性,细观上的简单本构关系可以模拟复杂的宏观破裂现象。
With the development of high-rise buildings and underground projects, more attentions have been paid to the dynamic properties of bedrock structures in both theoretical studies and engineering applications. As a heterogeneous material, when the stress is higher than the strength of rock, instantaneous energy release results in stress redistribution, which triggers dramatic deterioration of rock mechanical properties and rapid propagation of cracks. Under the combined effect of heterogeneity and internal stresses in the rock material, crack propaga-tion is essentially featured by crack curving and branching. Therefore, crack growth in rock-like materials subjected to dynamic loading, especially crack curving and branching, is one of the theoretical and engineering problems attracting attentions of many researchers.
In this study, the dynamic version of RFPA2D(Realistic Failure Process Analysis) pro-gram was employed to simulate crack propagation. The research content was as follows:
1. Since the Weibull distribution of the properties of mesoscopic structures and the linear mesoscopic mechanical behaviors can reflect the macroscopic nonlinear behaviors, a constitutive model for damage evolution was developed to simulate the completely fail-ure process of rock subjected to dynamic stress. By importing the Viscous-spring artifi-cial boundary into the model, the wave propagation in heterogeneous infinite media was investigated.
2. Based on dynamic method and the linear mesoscopic mechanical behaviors can reflect the macroscopic nonlinear behaviors, the collision process between two heterogeneous spe-cimens was researched in details. Because the interaction between the impactor and spe-cimen was considered, the model was closer to the reality. Three typical impact models were investigated in the paper. Comparing with the former experimental results, the availability of the method was verified. Furthermore, the different degree of heterogenity was also discussed in details. The reasearch can enrich and extend the former investiga-tion.
3. Based on damage theory and FEM method, rock fragmentation mechanism induced by a drill bit subjected to dynamic loading was investigated. Compared with rock fragment by static stress, there is a stress transition from compression to tension in the specimens un-der dynamic loading, e.g. the compression stress will be changed to tension during wave propagation. The results show that the process of wave propagation is changed and the emergency of tension is the key of crack initiation and growth.
4. By numerical method, the asymmetric and discontinuous behavior of crack propagation was analyzed at mesoscopic scale based on the damage evolution principle. The results coincide with the experimental laws, so it is certain that the linear mesoscopic mechanical behaviors can reflect the macroscopic nonlinear behaviors, and the complex mechanism of crack propagaion at macroscopic scale can be analyzed by this way.
引文
[1]J. D. Campbel,王礼立.塑性动力学的宏观与微观问题[J].力学进展,1980,10(z1)：150-176.
[2]黄理兴.岩石动力学研究现状与展望[J].2009-2010岩石力学与岩石工程学科发展报告2010.
[3]黄理兴.岩石动力学研究成就与趋势[J].岩土力学,201 1,32(10)：2889-2900.
[4]黄理兴,陈奕柏.我国岩石动力学研究状况与发展[J].岩石力学与工程学报,2003,22(11)：1881-1886.
[5]王靖涛.加速发展岩石动力学[J].岩土力学,1989,10(3)：6-12.
[6]王明洋,钱七虎.爆炸应力波通过节理裂隙带的衰减规律[J].岩土工程学报,1995,17(2)：42-46.
[7]李永池,姚磊,沈俊,等.空穴的绕射隔离效应和对后方应力波的削弱作用[J].爆炸与冲击,2005,25(3)：193-199.
[8]李永池,张伟,黄承义,等.损伤材料的热塑性本构关系及对柱壳破裂问题的应用[J].中国科学技术大学学报,1999,29(3)：260-268.
[9]李永池,朱林法,胡秀章,等.粘塑性薄壁管中复合应力波的传播特性研究[J].爆炸与冲击,2003,23(1)：1-5.
[10]宋小林.大理岩动态劈裂拉伸强度和裂纹起裂扩展特性[D].成都：四川大学,2005.
[11]李建春,李海波,Ma G,等.节理岩体的一维动态等效连续介质模型的研究[J].岩石力学与工程学报,2010,29(supp.2)：4063-4067.
[12]王占江,李孝兰,戈琳,等.花岗岩中化爆的自由场应力波传播规律分析[J].岩石力学与工程学报,2003,22(11)：1827-1831.
[13]张继春,肖正学,郑爽英,等.含软弱夹层岩体爆破的夹层土运动特征试验研究[J].岩石力学与工程学报,2009,28(8)：1697-1703.
[14]黄永林,朱升初,张金川.郑庐断裂带鲁苏沂沐段对泣川地震波的隔震效应[J].防灾减灾工程学报,2011,31(6)：666-670.
[15]俞绪,钱七虎,赵晓豹,等.岩体结构面对应力波传播规律影响的研究进展综述[J].河南焦作：第九届全国冲击动力学学术会议论文集,2009.
[16]King M S,Myer L R, Rezowalli J J. EXPERIMENTAL STUDIES OF ELASTIC-WAVE PROPAGATION IN A COLUMNAR-JOINTED ROCK MASS[J]. Geophysical Prospecting,1986,34(8):1185-1199.
[17]Hudson J A. Wave speeds and attenuation of elastic waves in material containing cracks[J]. Geophysical Journal of the Royal Astronomical Society,1981,64(1): 133-150.
[18]Pyrak-Nolte L J,Roy S,Mullenbach B L. Interface waves propagated along a fracture[J]. Journal of Applied Geophysics,1996,35(2-3):79-87.
[19]Roy S, Laura J, Pyrak-Nolte. Observation of a distinct compressional mode interface waVe on a single fracture[J]. Geophysical Research Letters,1997,24(2):173-176.
[20]李永池,王志海,邓世春.爆炸和冲击工程力学近期研究进展[J].中国科学技术大学学报,2007,37(10)：1172-1179.
[21]王礼立,王永刚.应力波在用SHPB研究材料动态本构特性中的重要作用[J].爆炸与冲击,2005,25(1)：17-25.
[22]朱瑞庚.不同加载速率条件下花岗岩的破坏判据[J].爆炸与冲击,1984,4(1)：1-8.
[23]王武林,刘远惠,陆以璐,等.RDT-10000型岩石高压动力三轴仪的研制[J].岩土力学,1989,10(2)：69-82.
[24]王占江,张德志,张向荣,等.蓝田花岗岩冲击压缩特性的实验研究[J].岩石力学与工程学报,2003,22(5)：797-802.
[25]单仁亮,陈石林,李宝强.花岗岩单轴冲击全程本构特性的实验研究[J].爆炸与冲击,2000,20(1)：32-38.
[26]单仁亮,薛友松,张倩.岩石动态破坏的时效损伤本构模型[J].岩石力学与工程学报,2003,22(11)：1171-1776.
[27]钱七虎,戚承志.岩石、岩体的动力强度与动力破坏准则[J].同济大学学报(自然科学版),2008,36(12)：1599-1605.
[28]李海波,赵坚,李俊如,等.花岗岩动态压缩力学特性的实验以及理论研究[J].辽宁工程技术大学学报(自然科学版),2001,20(4)：474-477.
[29]李海波.三轴情况下花岗岩动态力学特性的实验研究[J].爆炸与冲击,2004,24(5)：470-474.
[30]尹土兵,李夕兵,周子龙,等.粉砂岩高温后动态力学特性研究[J].地下空间与工程学报,2007,3(6)：1060-1063.
[31]洪亮,李夕兵,马春德,等.岩石动态强度及其应变率灵敏性的尺寸效应研究[J].岩石力学与工程学报,2008,27(3)：526-533.
[32]Li N, Zhang P, Chen Y S. Dynamic fatigue properties of the cracked sandstone samples under freezing and cyclic loading[J]. Chinese Journal of Geotechnical Engineering,2002,24(5):636-639.
[33]Friedman M, Perkins R D,Green S J. Observation of brittle-deformation features at the maximum stress of westerly granite and solenhofen limestone[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1970, 7(3):297-302.
[34]Janach W. The role of bulking in brittle failure of rocks under rapid compression[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1976,13(6):177-186.
[35]Chong K P, Hoyt P M, Smith J W, et al. Effects of strain rate on oil shale fracturing[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1980,17(1):35-43.
[36]Grady D. Mechanics of fracture under high-rate stress loading[M].1983.
[37]Lankford J. The role of tensile microfracture in the strain rate dependence of compressive strength of fine-grained limestone - analogy with strong ceramics[J]. International Journal of Rock Mechanics and Mining Science,1981, 18(173-175.
[38]Cho S H, Ogata Y, Kaneko K. Strain-rate dependency of the dynamic tensile strength of rock[J], International Journal of Rock Mechanics and Mining Sciences,2003, 40(5):763-777.
[39]Zhu W C. Numerical Modelling of the Effect of Rock Heterogeneity on Dynamic Tensile Strength[J]. Rock Mechanics and Rock Engineering,2008,41(5):771-779.
[40]Brace W F, Martin Iii R J. A test of the law of effective stress for crystalline rocks of low porosity[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1968,5(5):415-426.
[41]Sangha C M, Dhir R K. Strength and deformation of rock subject to multiaxial compressive stresses[J].Int J Rock Mech Min,1975,12(9):277-282.
[42]Bazant Z, Caner F, Carol I, et al. Microplane Model M4 for Concrete. Ⅰ:Formulation with Work-Conjugate Deviatoric Stress[J]. Journal of Engineering Mechanics,2000, 126(9):944-953.
[43]Chen L,Fang Q,Zhang Y, et al. Rate-sensitive numerical analysis of dynamic responses of arched blast doors subjected to blast loading[J]. Transactions of Tianjin University,2008,14(5):348-352.
[44]Izzuddin B A, Fang Q. Rate-sensitive analysis of framed structures Part I:Model formulation and verification [J]. Structure Engineering & mechanics,1997,2 (221-239.
[45]Malvern L E. The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting a strain-rate effect[J]. Journal of Applied Mechanics,1951, 18(203-208.
[46]Wang W M. Stationary and propagative instabilities in metals-a computational point of view [D]. Dissertation:Delft University of Technology,1997.
[47]肖诗云,林皋,王哲Drucker-Prager材料一致率型本构模型[J].工程力学,2003,20(4)：147-151.
[48]冯西桥,徐寿文.准脆性材料细观损伤力学[M].北京：高等教育出版社,2002.
[49]张雪颖,阮怀宁,贾彩虹.岩石损伤力学理论研究进展[J].四川建筑科学研究,2010,36(2)：134-138.
[50]Krajcinovic D,Basista M, Sumarac D. Micromechanically Inspired Phenomenological Damage Model[J]. Journal of Applied Mechanics,1991,58(305-310.
[51]Krajcinovic D,Mastilovic S. Some fundamental issues of damage mechanics[J]. Mechanics of Materials,1995,21(3):217-230.
[52]Marigo J J. Modelling of brittle and fatigue damage for elastic material by growth of microvoids[J]. Engineering Fracture Mechanics,1985,21(4):861-874.
[53]Sidoroff F. Damage mechanics and its application to composite materials[J]. Brussels, Belgium:Proceedings of the 182nd European Mechanics Colloquium,1985.
[54]Kawamoto T, Ichikawa Y, Kyoya T. Deformation and fracturing behaviour of discontinuous rock mass and damage mechanics theory[J]. International Journal For Numerical and Analytical Methods In Geomechanics,1988,12(1):1-30.
[55]Cheng H, Dusseault M B. Deformation and diffusion behaviour in a solid experiencing damage:a continuous damage model and its numerical implementation[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1993,30(7):1323-1331.
[56]朱维申,张强勇,李术才.三维脆弹塑性断裂损伤模型在裂隙岩体工程中的应用[J].固体力学学报,1999,20(2)：164-170.
[57]周维垣,剡公瑞,杨若琼.岩体弹脆性损伤本构模型及工程应用[J].岩石力学与工程学报,1998,20(5)：54-57.
[58]谢和平.岩石混凝土损伤力学[M].徐州：中国矿业大学出版社,1990.
[59]谢和平,彭瑞东,周宏伟,等.基于断裂力学与损伤力学的岩石强度理论研究进展[J].自然科学进展,2004,14(10)：1086-1092.
[60]Sumarac D, Krajcinovic D. A self-consistent model for microcrack-weakened solids [J]. Mechanics of Materials,1987,6(1):39-52.
[61]Lee X, Ju J. Micromechanical Damage Models for Brittle Solids. Part Ⅱ:Compressive Loadings[J]. Journal of Engineering Mechanics,1991,117(7):1515-1536.
[62]Horii H, Nemat-Nasser S. Compression-Induced Microcrack Growth in Brittle Solids: Axial Splitting and Shear Failure [J]. Journal of Geophysical Research,1985,90 (B4): 3105-3125.
[63]Bazant Z P, Jirasek M. Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress[J]. J Eng Mech,2002,128(11):1119-1149.
[64]沈珠江.岩土本构模型研究的进展(1985-1988年)—专题综述报告[J].岩土力学,1989,10(2)：3-13.
[65]唐辉明,孙成伟.岩体损伤力学研究进展[J].地质科技情报,1995,14(4)：85-92.
[66]刘红岩,王根旺,刘国振.以损伤变量为特征的岩石损伤理论研究进展[J].爆破器材,2004,33(6)：25-29.
[67]孙宝玉,庄惠平SHPB试验技术需要注意的几个问题[J].高校实验室工作研究,2009,100(2)：39-42.
[68]Rossmanith H P, Fourney W L. Fracture initiation and stress wave diffraction at cracked interfaces in layered media I. brittle/brittle transition[J]. Rock Mechanics and Rock Engineering,1982,14(4):209-233.
[69]Biegel R L, Bhat H S, Sammis C G, et al. The effect of asymmetric damage on dynamic shear rupture propagation I:No mismatch in bulk elasticity [J]. Tectonophysics,2010, 493(3-4):254-262.
[70]Bhat H S, Biegel R L,Rosakis A J, et al. The effect of asymmetric damage on dynamic shear rupture propagation II:With mismatch in bulk elasticity[J]. Tectonophysics, 2010,493(3-4):263-271.
[71]Mello M, Bhat H S, Rosakis A J, et al. Identifying the unique ground motion signatures of supershear earthquakes:Theory and experiments[J]. Tectonophysics,2010,493(3-4): 297-326.
[72]黄明利,黄凯珠.三维表面裂纹相互作用扩展贯通机制试验研究[J].岩石力学与工程学报,200709)：1794-1799.
[73]Wong R H C, Law C M, Chau K T, et al. Crack propagation from 3-D surface fractures in PMMA and marble specimens under uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences,2004,41, Supplement 1(0):37-42.
[74]Tay T E, Tan V B C, Deng M. Element-failure concepts for dynamic fracture and delamination in low-velocity impact of composites[J]. International Journal of Solids and Structures,2003,40(3):555-571.
[75]RAFIEE S,SEELIG T, GROSS D. Simulation of dynamic crack curving and branching under biaxial loading by a time domain boundary integral equation method [J]. International Journal of Fracture,2003,120(545-561.
[76]Hawong J,Kobayashi A, Dadkhah M, et al. Dynamic crack curving and branching under biaxial loading[J]. Experimental Mechanics,1987,27(2):146-153.
[77]Song J-H, Wang H, Belytschko T. A comparative study on finite element methods for dynamic fracture[J]. Computational Mechanics,2008,42(2):239-250.
[78]李根.基于模拟的水岩耦合变形破坏过程及机理研究[D].大连：大连理工大学,2011.
[79]李根,李连崇,唐春安,等.岩石流固/热固作用下损伤演化并行分析系统及初步应用[J].计算力学学报,2012,29(3)：381-386.
[80]张永彬.岩石破裂过程分析并行计算方法研究[D].沈阳：东北大学,2007.
[81]Yang Y, Tang C, Xia K. Study on crack curving and branching mechanism in quasi-brittle materials under dynamic biaxial loading[J]. International Journal of Fracture,2012, 177(1):53-72.
[82]Armero F, Linder C. Numerical simulation of dynamic fracture using finite elements with embedded discontinuities[J]. International Journal of Fracture,2009,160(2): 119-141.
[83]Rabczuk T,Bordas S,Zi G. On three-dimensional modelling of crack growth using partition of unity methods[J]. Computers & Structures,2010,88(23-24):1391-1411.
[84]Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks [J]. Computer Methods In Applied Mechanics and Engineering, 2007,196(29-30):2777-2799.
[85]雷卫东,Hefny A M,坚赵,等.岩石动力学中离散元程序处理波幅的新方法[J].中国矿业大学学报,2005,34(2)：170-174.
[86]王志亮,郑明新.基于TCK损伤本构的岩石爆破效应数值模拟[J].2008,29(1)：230-234.
[87]高文学,刘运通.岩石动态损伤的数值模拟[J].北京工业大学学报,2000,26(2)：5-10.
[88]夏祥,李海波,李俊如, 等.岩体爆生裂纹的数值模拟[J].岩土力学,2006,27(11)：1987-1991.
[89]Zhu W C, Tang C A. Numerical simulation of Brazilian disk rock failure under static and dynamic loading[J]. International Journal of Rock Mechanics and Mining Sciences, 2006,43(2):236-252.
[90]Zhou F, Molinari J-F,Shioya T. A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials[J]. Engineering Fracture Mechanics, 2005,72(9):1383-1410.
[91]Zhou S J, Lomdahl P S,Thomson R, et al. Dynamic Crack Processes via Molecular Dynamics[J]. Physical Review Letters,1996,76(13):2318.
[92]Ramulu M, Kobayashi A S. Mechanics of crack curving and branching-a dynamic fracture analysis[J]. International Journal of Fracture,1985,27(3):187-201.
[93]Zhang X, Liu Y, Ma S无网格法的理论及应用[J].力学进展,2009,39(1)：1-36.
[94]Schlangen E, Mier J G M V. Experimental and numerical analysis of micromechanisms of fracture of cement-based composites[J]. Cement and Concrete Composites,1992, 14(2):105-118.
[95]陈忠辉,唐春安,傅宇芳.岩石微破裂损伤演化诱致突变的数值模拟研究[J].岩土工程学报,1998,20(6)：9-15.
[96]Tang C A, Liu H, Lee P K K, et al. Numerical studies of the influence of microstructure on rock failure in uniaxial compression -- Part I:effect of heterogeneity [J]. International Journal of Rock Mechanics and Mining Sciences,2000, 37(4):555-569.
[97]Tang C A. Numerical simulation of progressive rock failure and associated seismicity[J]. International Journal of Rock Mechanics and Mining Sciences,1997, 34(2):249-261.
[98]Tang C A, Tham L G, Lee P K K, et al. Numerical studies of the influence of microstructure on rock failure in uniaxial compression -- Part II:constraint, slenderness and size effect[J]. International Journal of Rock Mechanics and Mining Sciences,2000,37(4):571-583.
[99]Vargas-Loli L M, Fenves G L. Effects of concrete cracking on the earthquake response of gravity dams[J]. Earthquake Engineering & Structural Dynamics,1989,18(4): 575-592.
[100]Ghaemian M, Ghobarah A. Nonlinear seismic response of concrete gravity dams with dam-reservoir interaction[J]. Engineering Structures,1999,21(4):306-315.
[101]李俊如,李海波,高建光,等.黄麦岭采场边坡爆破振动响应研究[J].岩石力学与工程学报,2004,23(17)：2954-2958.
[102]卢文波,赖世骧,朱传云,等.三峡工程岩石基础开挖爆破震动控制安全标准[J].爆炸与冲击,2001,21(1)：67-71.
[103]李新平,陈俊桦,李友华,等.溪洛渡电站地下洞室群爆破地震效应的研究[J].岩石力学与工程学报,2010,29(3)：493-501.
[104]蒋金宝,林英松,丁雁生.利用爆炸技术改善低渗透储层的实验研究[J].岩石力学与工程学报,2009,28(Supp.1)：2830-2835.
[105]田和金,李璗,王爱华,等.岩石动力学实验及其在油田开发中的应用[J].岩石力学与工程学报,2000,19(Supp.)：889-894.
[106]李术才,刘斌,李树忱,等.基于激发极化法的隧道含水地质构造超前探测研究[J].岩石力学与工程学报,2011,30(7)：1297-1309.
[107]钱七虎,李树忱.深部岩体工程围岩分区破裂化现象研究综述[J].岩石力学与工程学报,2008,27(6)：1278-1284.
[108]潘一山,李英杰,唐鑫,等.岩石分区碎裂化现象研究[J].岩石力学与工程学报,2007,26(Supp.1)：3335-3341.
[109]黄润秋.汶川8.0级地震触发崩滑灾害机制及其地质力学模式[J].岩石力学与工程学报,2009,28(6)：1239-1249.
[110]黄润秋.岩石高边坡发育的动力过程及其稳定性控制[J].岩石力学与工程学报,2008,27(8)：1525-1544.
[111]赖海辉,朱成忠,李夕兵.机械岩石破碎学[M].长沙：中南大学出版社,1991.
[112]刘柏禄,潘建忠,谢世勇.岩石破碎方法的研究现状及展望[J].中国钨业,2011,26(1)：15-19.
[113]田取珍,刘混举,曹惠斌.冲击式采煤的研究[J].煤炭学报,1998,23(6)：625-629.
[114]谢强,姜崇喜,凌建明.岩石细观力学实验与分析[M].成都：西南交通大学学报,1997.
[115]唐春安.岩石破裂过程中的灾变[M].煤炭工业出版社,1993.
[116]廖振鹏,刘晶波.离散网格中的弹性波动(I)[J].地震工程与工程振动,1986,6(2)：1-16.
[117]刘晶波,廖振鹏.离散网格中的弹性波动(Ⅱ)——几种有限元离散模型的对比分析[J].地震工程与工程振动,1989,9(2)：1-11.
[118]刘晶波,廖振鹏.离散网格中的弹性波动(Ⅲ)——时域离散化对波传播规律的影响[J].地震工程与工程振动,1990,10(2)：1-10.
[119]黄丹,章青,乔丕忠,等.近场动力学方法及其应用[J].力学进展,2010,40(4)：448-459.
[120]Silling S A,Epton M,Weckner O, et al. Peridynamic States and Constitutive Modeling[J]. Journal of Elasticity,2007.
[121]Silling S A. Linearized theory of peridynamic states[R]. Sandia National Laboratories,2009.
[122]朱万成,逢铭璋,黄志平,等.岩石动态剥落破裂的数值模拟[J].东北大学学报,2006,5)：552-555.
[123]Tang C A, Kaiser P K. Numerical Simulation of Cumulative Damage and Seismic Energy Release During Brittle Rock Failure--Part Ⅰ:Fundamentals [J]. International Journal of Rock Mechanics and Mining Sciences,1998,35(2):113-121.
[124]黄明利,唐春安,朱万成.岩石破裂过程的数值模拟研究[J].岩石力学与工程学报,2000,19(4)：468-471.
[125]朱万成,唐春安,杨天鸿,等.岩石破裂过程分析用(RFPA~(2D))系统的细观单元本构关系及验证[J].岩石力学与工程学报,2003,22(1)：24-29.
[126]Weibull W. A statistical distribution function of wide applicability[J]. Journal of Applied Mechanics,1951,18(3):293-297.
[127]Forquin P, Denoual C,Cottenot C E, et al. Experiments and modelling of the compressive behaviour of two SiC ceramics[J]. Mechanics of Materials,2003,35 (10): 987-1002.
[128]Denoual C, Hild F. Dynamic fragmentation of brittle solids:a multi-scale model[J]. European Journal of Mechanics - A/Solids,2002,21(1):105-120.
[129]朱晶晶,李夕兵,宫凤强,等.冲击载荷作用下砂岩的动力学特性及损伤规律[J].中南大学学报(自然科学版),2012,43(7)：2701-2707.
[130]梁正召,唐春安,张永彬,等.准脆性材料的物理力学参数随机概率模型及破坏力学行为特征[J].岩石力学与工程学报,2008,27(4)：718-727.
[131]Grange S,Forquin P,Mencacci S, et al. On the dynamic fragmentation of two limestones using edge-on impact tests[J]. International Journal of Impact Engineering,2008,35(9):977-991.
[132]Rao M P, Sanchez-Herencial A J,Beltz G E, et al. Laminar Ceramics That Exhibit a Threshold Strength[J].Science,1999,286(5437):102-105.
[133]Zhao J,Zhou Y. Advances in Rock Dynamics and Applications[M]. Taylor & Francis, 2011.
[134]Zhao J. Applicability of Mohr-Coulomb and Hoek-Brown strength criteria to the dynamic strength of brittle rock[J]. International Journal of Rock Mechanics and Mining Sciences,2000,37(7):1115-1121.
[135]Zhao J, Li H B. Experimental determination of dynamic tensile properties of a granite[J]. International Journal of Rock Mechanics and Mining Sciences, 2000,37(861-866.
[136]Zhao J, Li H B, Wu M B, et al. Dynamic uniaxial compression tests on a granite[J]. International Journal of Rock Mechanics and Mining Sciences,1999,36(2): 273-277.
[137]戚承志,钱七虎.岩石等脆性材料动力强度依赖应变率的物理机制[J].岩石力学与工程学报,2003,22(2)：177-181.
[138]赵坚,李海波.莫尔-库仑和霍克-布朗强度准则用于评估脆性岩石动态强度的适用性[J].岩石力学与工程学报,2003,22(2)：171-176.
[139]Wang S Y, Sloan S W, Liu H Y, et al. Numerical simulation of the rock fragmentation process induced by two drill bits subjected to static and dynamic (impact) loading[J].Rock Mechanics and Rock Engineering,2011,44(3):317-332.
[140]Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching[J]. International Journal of Fracture,1984,26(2):141-154.
[141]Suzuki S, Sakaue K, Iwanaga K. Measurement of energy release rate and energy flux of rapidly bifurcating crack in Homalite 100 and Araldite B by high-speed holographic microscopy[J]. Journal of The Mechanics and Physics of Solids,2007,55(7):1487-1512.
[142]Fineberg J,Gross S P,Marder M, et al. Instability in the propagation of fast cracks[J]. Physical Review B,1992,45(10):5146.
[143]Sharon E, Fineberg J. Microbranching instability and the dynamic fracture of brittle materials[J]. Physical Review B,1996,54(10):7128-7139.
[144]Sharon E, Fineberg J. Confirming the continuum theory of dynamic brittle fracture for fast cracks[J]. Nature,1999,397(6717):333-335.
[145]Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture: Ⅱ. Microstructural aspects[J].International Journal of Fracture,1984,26(1): 65-80.
[146]唐春安,朱万成.混凝土损伤与断裂-数值试验[M].北京：科学出版社,2003.
[147]王礼立.应力波基础(第二版)[M].北京：国防工业出版社,2010.
[148]Rayleigh. On Waves Propagated along the Plane Surface of an Elastic Solid[J]. Proceedings of The London Mathematical Society,1885.
[149]刘孝敏,胡时胜.大直径SHPB弥散效应的二维数值分析[J].实验力学,2000,15(4)：371-376.
[150]王从约,夏源明.傅立叶弥散分析在冲击拉伸和冲击压缩试验中的应用[J].爆炸与冲击,1998,18(3)：213-219.
[151]王从约,夏源明.圆杆中弹性应力波的傅立叶弥散分析[J].爆炸与冲击,1998,18(1)：1-7.
[152]左宇军,唐春安,朱万成,等.岩石类介质SHPB试验加载波形的数值分析[J].东北大学学报(自然科学版),2007,28(6)：859-862.
[153]李夕兵,古德生,赖海辉.冲击载荷下岩石动态应力-应变全图测试中的合理加载波形[J].爆炸与冲击,1993,13(2)：125-130.
[154]孟益平,胡时胜.混凝土材料冲击压缩试验中的一些问题[J].实验力学,2003,18(1)：108-112.
[155]Wang L L. Influences of Stress Wave Propagation upon Studying Dynamic Response of Materials at High Strain Rates[J]. Journal of BeijingInstituteof Technology,2004,13(3):225-235.
[156]Yang L M, Shim V P W. An analysis of stress uniformity in split Hopkinson bar test specimens[J]. International Journal of Impact Engineering,2005,31 (2):129-150.
[157]张圆.基于Hopkinson束杆技术的混凝土动态实验方法研究[D].宁波：宁波大学,2008.
[158]宁建国,王成,马天宝.爆炸与冲击动力学[M].北京：国防工业大学出版社,2010.
[159]廖振鹏.工程波动导论[M].北京：科学出版社,2002.
[160]廖振鹏,刘晶波.波动的有限元模拟—基本问题和基本研究方法[J].地震工程与工程振动,1989,9(4)：1-14.
[161]廖振鹏,杨光.稳态SH波动的有限元模拟[J].地震学报,1994,16(1)：96-105.
[162]Liu J B, Lv Y D. A direct method for analysis of dynamic soil-structure interaction based on interface idea[J]. Developments in Geotechnical Engineering,1998, Volume 83(261-276.
[163]刘晶波,杜义欣,闫秋实.粘弹性人工边界及地震动输入在通用有限元软件中的实现[J].防灾减灾工程学报,2007,27(Supp.)：37-42.
[164]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9)：1070-1075.
[165]李彬,刘晶波.粘弹性人工边界在Marc中的实现.中国烟台2005.
[166]Lamb H. On the Propagation of Tremors over the Surface of an Elastic Solid[J]. Philosophical Transactions of the Royal Society of London Series A, Containing Papers of a Mathematical or Physical Character,1904,203(359-371):1-42.
[167]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3)：55-64.
[168]陈静曦.应力波对岩石断裂的相关因素分析[J].岩石力学与工程学报,1997,16(2)：148-154.
[169]钱七虎,王明洋.岩土中的冲击爆破效应[M].北京：国防工业出版社,2010.
[170]魏修成,董敏煜,陈运泰.非均匀各向异性介质中弹性波的传播[J].地震学报,1998,20(6)：561-572.
[171]彭朝晖,刘殿魁.竖向非均匀介质中的Love面波[J].地震工程与工程振动,1998,18(2)：1-7.
[172]Tang C A, Tham L G, Wang S H, et al. A numerical study of the influence of heterogeneity on the strength characterization of rock under uniaxial tension[J]. Mechanics of Materials,2007,39(4):326-339.
[173]Emmerich H. PSV-wave propagation in a medium with local heterogeneities:a hybrid formulation and its application[J]. Geophysical Journal International,1992,109(1): 54-64.
[174]Wesolowski Z. Wave reflection on a continuous transition zone between two homogeneous materials[J]. Acta Mechanica,1994,105(1):119-131.
[175]罗松南,周正平.波在非均匀损伤介质中的传播[J].华南理工大学学报(自然科学版),2003,31(supp.)：48-51.
[176]周钟,王肖钧,刘文韬,等.岩石的损伤软化对应力波传播的影响[J].中国科学技术大学学报,2003,33(3)：337-344.
[177]Strassburger E, Senf H,Rothenhausler H. Fracture propagation during impact in three types of ceramics[J]. J Phys IV France,1994,04(C8):C8-653-C8-658.
[178]Strassburger E, Senf H, Denoual C, et al. An Experimental Approach to Validate Damage Evolution Laws for Brittle Materials[J]. J Phys IV France,1997,07(C3): 909-914.
[179]Strassburger E. Visualization of Impact Damage in Ceramics Using the Edge-On Impact Technique[J].International Journal of Applied Ceramic Technology,2004,1(3):235-242.
[180]Grujicic M, Pandurangan B, Coutris N, et al. A simple ballistic material model for soda-lime glass[J]. International Journal of Impact Engineering,2009,36(3): 386-401.
[181]Forquin P, Tran L, Louvigne P-F, et al. Effect of aluminum reinforcement on the dynamic fragmentation of SiC ceramics[J]. International Journal of Impact Engineering,2003,28(10):16.
[182]Erzar B, Forquin P. Experiments and mesoscopic modelling of dynamic testing of concrete[J]. Mechanics of Materials,2011,43(9):505-527.
[183]Hild F, Denoual C, Forquin P, et al. On the probabilistic - deterministic transition involved in a fragmentation process of brittle materials[J].Computers & amp; Structures,2003,81(12):1241-1253.
[184]成名,刘维甫,刘凯欣.高速冲击问题的离散元法数值模拟[J].计算力学学报,2009,26(4)：591-594.
[185]李金柱,黄风雷,张连生.EFP模拟弹丸侵彻陶瓷复合靶的数值模拟研究[J].计算力学学报,2009,26(4)：562-567.
[186]Ohte S. Finite Element Analysis of elastic contact problems[J]. Bulletin of JSME,1973,16(95):797-804.
[187]欧恒安,龚剑霞.三维弹性接触问题有限元改进混合法及数值计算[J].重庆大学学报(自然科学版),1988,1)：52-58.
[188]陈军,潘家铮,段云岭.转换位移自由度法求解滑动接触问题[J].计算力学学报,2006,23(1)：101-106.
[189]温卫东,高德平.接触问题数值分析方法的研究现状与发展[J].南京航空航天大学学报,1994,26(5)：664-675.
[190]刘晶波,王铎.考虑界面摩擦影响的可接触型裂纹动态分析的动接触力模型-弹性动力学最新进展[M].北京：科学出版社,1995.
[191]Riedel W,Hiermaier S, Thoma K. Transient stress and failure analysis of impact experiments with ceramics[J]. Materials Science and Engineering:B,2010,173(1-3): 139-147.
[192]Buehler M J,Abraham F F, Gao H. Hyperelasticity governs dynamic fracture at a critical length scale[J]. Nature,2003,426(6963):141-146.
[193]Buehler M J, Gao H. Dynamical fracture instabilities due to local hyperelasticity at crack tips[J].Nature,2006,439(7074):307-310.
[194]Freund L B. Dynamic Fracture Mechanics. Cambridge University Press; 1990.
[195]Yoffe E. The Moving Griffith Crack[J]. Philosophical Magazine,1951,42(739-750.
[196]James R R, Guo G F. New perspectives on crack and fault dynamics[J]. Advance in mechanics,2001,03):447-460.
[197]Ravi-Chandar K. Dynamic Fracture of Nominally Brittle Materials [J]. International Journal of Fracture,1998,90(1):83-102.
[198]Tay T E,Tan S H N, Tan V B C, et al. Damage progression by the element-failure method (EFM) and strain invariant failure theory (SIFT)[J]. Composites Science and Technology,2005,65(6):935-944.
[199]Pollard D D, Griffith W A. Laboratory Investigation of Damage by Tensile Fracture during Dynamic Shear Rupture Propagation[R]. Stanford:Department of Geological and Environmental Science, Stanford University,2009.
[200]Ha Y D,Bobaru F. Characteristics of dynamic brittle fracture captured with peridynamics[J]. Engineering Fracture Mechanics,2011,78(6):1156-1168.
[201]Budiansky B. Micromechanics[J]. Computer and structures,1982,16(1):3-12.
[202]傅宇方,梁正召,唐春安.岩石介质细观非均匀性对宏观破裂过程的影响[J].岩土工程学报,2000,06)：705-710.
[203]Bowden F P, Brunton J H, Field J E, et al. Controlled Fracture of Brittle Solids and Interruption of Electrical Current[J]. Nature,1967,216(5110):38-42.
[204]Sharon E, Gross S P, Fineberg J. Local Crack Branching as a Mechanism for Instability in Dynamic Fracture[J]. Physical Review Letters,1995,74(25):5096-5100.
[205]Ravi-Chandar K, Yang B. On the role of microcracks in the dynamic fracture of brittle materials[J]. Journal of The Mechanics and Physics of Solids,1997,45(4): 535-563.
[206]Leterrier Y,Pellaton D.Mendels D, et al. Biaxial fragmentation of thin silicon oxide coatings on poly(ethylene terephthalate)[J]. Journal of Materials Science, 2001,36(9):2213-2225.
[207]Andersons J, Leterrier Y, Fescenko I. Analysis of the initial fragmentation stage of oxide coatings on polymer substrates under biaxial tension[J]. Thin Solid Films,2003,434(1-2):203-215.
[208]Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture: Ⅰ. Crack initiation and arrest[J]. International Journal of Fracture,1984, 25(4):247-262.
[209]Krauthammer T, Otani R K. Mesh, gravity and load effects on finite element simulations of blast loaded reinforced concrete structures[J]. Computers & amp; Structures,1997,63(6):1113-1120.
[210]Luccioni B,Ambrosini D,Danesi R. Blast load assessment using hydrocodes[J]. Engineering Structures,2006,28(12):1736-1744.
[211]Chapman T C, Rose T A, Smith P D. Blast wave simulation using AUTODYN2D:A parametric study[J]. International Journal of Impact Engineering,1995,16(5-6):777-787.
[212]Shi Y, Li Z,Hao H. Mesh size effect in numerical simulation of blast wave propagation and interaction with structures [J]. Transactions of Tianjin University, 2008,14(6):396-402.
[213]Kalthoff J. Modes of dynamic shear failure in solids[J]. International Journal of Fracture,2000,101(1):1-31.
[214]Kalthoff J F,Winkler S. Failure Mode Transition at High Rates of Shear Loading [J]. International Conference on Impact Loading and Dynamic Behavior of Materials, 1988.
[215]Mason J J, Rosakis A J,Ravichandran G. Full field measurements of the dynamic deformation field around a growing adiabatic shear band at the tip of a dynamically loaded crack or notch[J]. Journal of The Mechanics and Physics of Solids,1994,42(11):1679-1697.
[216]Zhou M, Rosakis A J, Ravichandran G. Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed[J].Journal of The Mechanics and Physics of Solids,1996,44(6):981-1006.
[217]Remmers J J C, de Borst R, Needleman A. The simulation of dynamic crack propagation using the cohesive segments method[J]. Journal of The Mechanics and Physics of Sol ids,2008,56(1):70-92.
[218]Kalthoff J F. Failure methodology of mode-Ⅱ loaded cracks [J]. Strength, Fracture and Complexity,2003,1(3):121-138.
[219]Dolinski M, Rittel D, Dorogoy A. Modeling adiabatic shear failure from energy considerations[J]. Journal of The Mechanics and Physics of Solids,2010,58(11):1759-1775.
[220]Zhou M, Rosakis A J, Ravichandran G. On the growth of shear bands and failure-mode transition in prenotched plates:A comparison of singly and doubly notched specimens[J]. International Journal of Plasticity,1998,14(4-5):435-451.
[221]Zhou M, Ravichandran G, Rosakis A J. Dynamically propagating shear bands in impact-loaded prenotched plates—Ⅱ. Numerical simulations[J]. Journal of The Mechanics and Physics of Solids,1996,44(6):1007-1032.
[222]Zlotnikov M,Glushikhin F. Equivalent material based on epoxy resin for making models of rock masses[J]. Journal of Mining Science,1979,15(1):73-76.
[223]任松,郭松涛,姜德义,等.盐岩蠕变相似模型及相似材料研究[J].岩土力学,2011,32(Supp.1)：106-110.
[224]张宁,李术才,李明田,等.新型岩石相似材料的研制[J].山东大学学报,2009,39(4)：149-154.
[225]李晓红,卢义正,康勇,等.岩石力学实验模拟技术[M].北京：科学出版社,2007.
[226]Bertram A, Kalthoff J F. Crack propagation toughness of rock for the range from low to very high crack speeds[J]. Key Engineering Materials,2003,251-252(423-430.
[227]Ngo D, Huang Y, Huang Y, et al. Off-fault tensile cracks:A link between geological fault observations, lab experiments and dynamic rupture models[J]. GSA Denver Annual Meeting,2010.
[228]Murphy N, Ali M, Ivankovic A. Dynamic crack bifurcation in PMMA[J]. Engineering Fracture Mechanics,2006,73(16):2569-2587.
[229]Bertram A. Bruchenergie laufender Risse in Gestein [D]. Bochum:Ruhr-University, 2008.
[230]梁正召.三维条件下的岩石破裂过程分析及其数值试验方法研究[D]：东北大学,2005.
[231]Healy D,Jones R R, Holdsworth R E. Three-dimensional brittle shear fracturing by tensile crack interaction[J]. Nature,2006,439(7072):64-67.
[232]梁正召,杨天鸿,唐春安,等.非均匀性岩石破坏过程的三维损伤软化模型与数值模拟[J].岩土工程学报,2005,12)：1447-1452.
[233]唐春安.岩石声发射规律数值模拟初探[J].岩石力学与工程学报,1997,16(4)：368-377.
[234]唐春安,朱万成,李连崇,等.材料破坏过程中应力分布的数值光弹图[J].力学与实践,200205)：47-50.
[235]谭成文,王富耻,李树奎；.绝热剪切变形局部化研究进展及发展趋势[J].兵器材料科学与工程,2003,26(5)：62-67.
[236]徐永波,白以龙.动态载荷下剪切变形局部化、微结构演化与剪切断裂研究进展[J].力学进展,2007,37(4)：496-516.
[237]寇绍全.绝热剪切—一个值得重视的材料破坏问题[J].力学进展,1979,(3)：52-59.
[238]Winter R E. Adiabatic shear of titanium and polymethylmethacrylate[J]. Philosophical Magazine,1975,31(4):765-773.
[239]Johnson W, Sengupta A K, Ghosh S K. High velocity oblique impact and ricochet mainly of long rod projectiles:An overview[J]. International Journal of Mechanical Sciences,1982,24(7):425-436.
[240]Zerilli F J, Armstrong R W. Dislocation-mechanics-based constitutive relations for material dynamics calculations[J]. Journal of Applied Physics,1987,61 (5): 1816-1825.
[241]Nemat-Nasser S,Guo W-G, Nesterenko V F, et al. Dynamic response of conventional and hot isostatically pressed Ti-6A1-4V alloys:experiments and modeling[J]. Mechanics of Materials,2001,33(8):425-439.
[242]Wright T W.Walter J W. On stress collapse in adiabatic shear bands[J]. Journal of The Mechanics and Physics of Solids,1987,35 (6):701-720.
[243]Wright T W,Ockendon H. A model for fully formed shear bands[J]. Journal of The Mechanics and Physics of Solids,1992,40(6):1217-1226.
[244]Love B M,Batra R C. Effect of particulate/matrix debonding on the formation of adiabatic shear bands[J]. International Journal of Mechanical Sciences,2010, 52(2):386-397.
[245]Ruan H H,Zhang L C, Lu J. A new constitutive model for shear banding instability in metallic glass[J]. International Journal of Solids and Structures,2011,48 (21): 3112-3127.
[246]Li S, Liu W-K, Qian D, et al. Dynamic shear band propagation and micro-structure of adiabatic shear band[J]. Computer Methods In Applied Mechanics and Engineering, 2001,191(1-2):73-92.
[247]肖大武,李英雷,蔡灵仓.绝热剪切研究进展[J].实验力学,2010,25(4)：463-475.
[248]Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture: IV. On the interaction of stress waves with propagating cracks[J]. International Journal of Fracture,1984,26(3):189-200.
[249]Liu H, Kou S Q, Lindqvist P A. Numerical Studies on bit-rock fragmentation mechanisms[J]. International Journal of Geomechanics,2008,8(1):45-67.
[250]万圣.液压凿岩机冲头新型换向系统的研究开发[D].兰州：兰州理工大学,2011.
[251]赵伏军.动静载荷耦合作用下岩石破碎理论及试验研究[D].长沙：中南大学,2004.
[252]Denoual C,Cottenot C, Hild F. On the identification of damage during impact of a ceramic by a hard steel projectile[J]. San Francisco. CA:Proc 16th Int Symp on Ballistics,1996.
[253]李宇彤,焦明若.宏观非均匀性对岩石微震序列类型和破裂方式影响的数值试验研究[J].地震,2005,25(4)：98-104.
[254]Kumano A, Goldsmith W. An analytical and experimental investigation of the effect of impact on coarse granular rocks[J]. Rock Mechanics and Rock Engineering, 1982,15(2):67-97.
[255]Bernardino C. Fracture mechanisms induced in a brittle material by a hard cutting indenter[J]. International Journal of Solids and Structures,2001,38(44-45): 7747-7768.
[256]Itasca Consulting Group Inc. PFC2D/3D(Particle Flow Code in 2/3 Dimensions), Vesion 2.0[M]. Minneapolis:MN:ICG,1999.
[257]尤明庆.岩石的力学性质[M].北京：地质大学出版社,2008.
[258]Zhu W C, Tang C A. Numerical simulation on shear fracture process of concrete using mesoscopic mechanical model[J]. Construction and Building Materials,2002,16(8): 453-463.
[259]许金余,范建设,吕晓聪.围压条件下岩石的动态力学特性[M].西安：西北工业大学出版社,2012.
[260]张阿漫,戴绍仕.流固耦合动力学[M].北京：国防工业出版社,2011.
[2]黄理兴.岩石动力学研究现状与展望[J].2009-2010岩石力学与岩石工程学科发展报告2010.
[3]黄理兴.岩石动力学研究成就与趋势[J].岩土力学,201 1,32(10)：2889-2900.
[4]黄理兴,陈奕柏.我国岩石动力学研究状况与发展[J].岩石力学与工程学报,2003,22(11)：1881-1886.
[5]王靖涛.加速发展岩石动力学[J].岩土力学,1989,10(3)：6-12.
[6]王明洋,钱七虎.爆炸应力波通过节理裂隙带的衰减规律[J].岩土工程学报,1995,17(2)：42-46.
[7]李永池,姚磊,沈俊,等.空穴的绕射隔离效应和对后方应力波的削弱作用[J].爆炸与冲击,2005,25(3)：193-199.
[8]李永池,张伟,黄承义,等.损伤材料的热塑性本构关系及对柱壳破裂问题的应用[J].中国科学技术大学学报,1999,29(3)：260-268.
[9]李永池,朱林法,胡秀章,等.粘塑性薄壁管中复合应力波的传播特性研究[J].爆炸与冲击,2003,23(1)：1-5.
[10]宋小林.大理岩动态劈裂拉伸强度和裂纹起裂扩展特性[D].成都：四川大学,2005.
[11]李建春,李海波,Ma G,等.节理岩体的一维动态等效连续介质模型的研究[J].岩石力学与工程学报,2010,29(supp.2)：4063-4067.
[12]王占江,李孝兰,戈琳,等.花岗岩中化爆的自由场应力波传播规律分析[J].岩石力学与工程学报,2003,22(11)：1827-1831.
[13]张继春,肖正学,郑爽英,等.含软弱夹层岩体爆破的夹层土运动特征试验研究[J].岩石力学与工程学报,2009,28(8)：1697-1703.
[14]黄永林,朱升初,张金川.郑庐断裂带鲁苏沂沐段对泣川地震波的隔震效应[J].防灾减灾工程学报,2011,31(6)：666-670.
[15]俞绪,钱七虎,赵晓豹,等.岩体结构面对应力波传播规律影响的研究进展综述[J].河南焦作：第九届全国冲击动力学学术会议论文集,2009.
[16]King M S,Myer L R, Rezowalli J J. EXPERIMENTAL STUDIES OF ELASTIC-WAVE PROPAGATION IN A COLUMNAR-JOINTED ROCK MASS[J]. Geophysical Prospecting,1986,34(8):1185-1199.
[17]Hudson J A. Wave speeds and attenuation of elastic waves in material containing cracks[J]. Geophysical Journal of the Royal Astronomical Society,1981,64(1): 133-150.
[18]Pyrak-Nolte L J,Roy S,Mullenbach B L. Interface waves propagated along a fracture[J]. Journal of Applied Geophysics,1996,35(2-3):79-87.
[19]Roy S, Laura J, Pyrak-Nolte. Observation of a distinct compressional mode interface waVe on a single fracture[J]. Geophysical Research Letters,1997,24(2):173-176.
[20]李永池,王志海,邓世春.爆炸和冲击工程力学近期研究进展[J].中国科学技术大学学报,2007,37(10)：1172-1179.
[21]王礼立,王永刚.应力波在用SHPB研究材料动态本构特性中的重要作用[J].爆炸与冲击,2005,25(1)：17-25.
[22]朱瑞庚.不同加载速率条件下花岗岩的破坏判据[J].爆炸与冲击,1984,4(1)：1-8.
[23]王武林,刘远惠,陆以璐,等.RDT-10000型岩石高压动力三轴仪的研制[J].岩土力学,1989,10(2)：69-82.
[24]王占江,张德志,张向荣,等.蓝田花岗岩冲击压缩特性的实验研究[J].岩石力学与工程学报,2003,22(5)：797-802.
[25]单仁亮,陈石林,李宝强.花岗岩单轴冲击全程本构特性的实验研究[J].爆炸与冲击,2000,20(1)：32-38.
[26]单仁亮,薛友松,张倩.岩石动态破坏的时效损伤本构模型[J].岩石力学与工程学报,2003,22(11)：1171-1776.
[27]钱七虎,戚承志.岩石、岩体的动力强度与动力破坏准则[J].同济大学学报(自然科学版),2008,36(12)：1599-1605.
[28]李海波,赵坚,李俊如,等.花岗岩动态压缩力学特性的实验以及理论研究[J].辽宁工程技术大学学报(自然科学版),2001,20(4)：474-477.
[29]李海波.三轴情况下花岗岩动态力学特性的实验研究[J].爆炸与冲击,2004,24(5)：470-474.
[30]尹土兵,李夕兵,周子龙,等.粉砂岩高温后动态力学特性研究[J].地下空间与工程学报,2007,3(6)：1060-1063.
[31]洪亮,李夕兵,马春德,等.岩石动态强度及其应变率灵敏性的尺寸效应研究[J].岩石力学与工程学报,2008,27(3)：526-533.
[32]Li N, Zhang P, Chen Y S. Dynamic fatigue properties of the cracked sandstone samples under freezing and cyclic loading[J]. Chinese Journal of Geotechnical Engineering,2002,24(5):636-639.
[33]Friedman M, Perkins R D,Green S J. Observation of brittle-deformation features at the maximum stress of westerly granite and solenhofen limestone[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1970, 7(3):297-302.
[34]Janach W. The role of bulking in brittle failure of rocks under rapid compression[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1976,13(6):177-186.
[35]Chong K P, Hoyt P M, Smith J W, et al. Effects of strain rate on oil shale fracturing[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1980,17(1):35-43.
[36]Grady D. Mechanics of fracture under high-rate stress loading[M].1983.
[37]Lankford J. The role of tensile microfracture in the strain rate dependence of compressive strength of fine-grained limestone - analogy with strong ceramics[J]. International Journal of Rock Mechanics and Mining Science,1981, 18(173-175.
[38]Cho S H, Ogata Y, Kaneko K. Strain-rate dependency of the dynamic tensile strength of rock[J], International Journal of Rock Mechanics and Mining Sciences,2003, 40(5):763-777.
[39]Zhu W C. Numerical Modelling of the Effect of Rock Heterogeneity on Dynamic Tensile Strength[J]. Rock Mechanics and Rock Engineering,2008,41(5):771-779.
[40]Brace W F, Martin Iii R J. A test of the law of effective stress for crystalline rocks of low porosity[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1968,5(5):415-426.
[41]Sangha C M, Dhir R K. Strength and deformation of rock subject to multiaxial compressive stresses[J].Int J Rock Mech Min,1975,12(9):277-282.
[42]Bazant Z, Caner F, Carol I, et al. Microplane Model M4 for Concrete. Ⅰ:Formulation with Work-Conjugate Deviatoric Stress[J]. Journal of Engineering Mechanics,2000, 126(9):944-953.
[43]Chen L,Fang Q,Zhang Y, et al. Rate-sensitive numerical analysis of dynamic responses of arched blast doors subjected to blast loading[J]. Transactions of Tianjin University,2008,14(5):348-352.
[44]Izzuddin B A, Fang Q. Rate-sensitive analysis of framed structures Part I:Model formulation and verification [J]. Structure Engineering & mechanics,1997,2 (221-239.
[45]Malvern L E. The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting a strain-rate effect[J]. Journal of Applied Mechanics,1951, 18(203-208.
[46]Wang W M. Stationary and propagative instabilities in metals-a computational point of view [D]. Dissertation:Delft University of Technology,1997.
[47]肖诗云,林皋,王哲Drucker-Prager材料一致率型本构模型[J].工程力学,2003,20(4)：147-151.
[48]冯西桥,徐寿文.准脆性材料细观损伤力学[M].北京：高等教育出版社,2002.
[49]张雪颖,阮怀宁,贾彩虹.岩石损伤力学理论研究进展[J].四川建筑科学研究,2010,36(2)：134-138.
[50]Krajcinovic D,Basista M, Sumarac D. Micromechanically Inspired Phenomenological Damage Model[J]. Journal of Applied Mechanics,1991,58(305-310.
[51]Krajcinovic D,Mastilovic S. Some fundamental issues of damage mechanics[J]. Mechanics of Materials,1995,21(3):217-230.
[52]Marigo J J. Modelling of brittle and fatigue damage for elastic material by growth of microvoids[J]. Engineering Fracture Mechanics,1985,21(4):861-874.
[53]Sidoroff F. Damage mechanics and its application to composite materials[J]. Brussels, Belgium:Proceedings of the 182nd European Mechanics Colloquium,1985.
[54]Kawamoto T, Ichikawa Y, Kyoya T. Deformation and fracturing behaviour of discontinuous rock mass and damage mechanics theory[J]. International Journal For Numerical and Analytical Methods In Geomechanics,1988,12(1):1-30.
[55]Cheng H, Dusseault M B. Deformation and diffusion behaviour in a solid experiencing damage:a continuous damage model and its numerical implementation[J]. International Journal of Rock Mechanics and Mining Sciences & amp; Geomechanics Abstracts,1993,30(7):1323-1331.
[56]朱维申,张强勇,李术才.三维脆弹塑性断裂损伤模型在裂隙岩体工程中的应用[J].固体力学学报,1999,20(2)：164-170.
[57]周维垣,剡公瑞,杨若琼.岩体弹脆性损伤本构模型及工程应用[J].岩石力学与工程学报,1998,20(5)：54-57.
[58]谢和平.岩石混凝土损伤力学[M].徐州：中国矿业大学出版社,1990.
[59]谢和平,彭瑞东,周宏伟,等.基于断裂力学与损伤力学的岩石强度理论研究进展[J].自然科学进展,2004,14(10)：1086-1092.
[60]Sumarac D, Krajcinovic D. A self-consistent model for microcrack-weakened solids [J]. Mechanics of Materials,1987,6(1):39-52.
[61]Lee X, Ju J. Micromechanical Damage Models for Brittle Solids. Part Ⅱ:Compressive Loadings[J]. Journal of Engineering Mechanics,1991,117(7):1515-1536.
[62]Horii H, Nemat-Nasser S. Compression-Induced Microcrack Growth in Brittle Solids: Axial Splitting and Shear Failure [J]. Journal of Geophysical Research,1985,90 (B4): 3105-3125.
[63]Bazant Z P, Jirasek M. Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress[J]. J Eng Mech,2002,128(11):1119-1149.
[64]沈珠江.岩土本构模型研究的进展(1985-1988年)—专题综述报告[J].岩土力学,1989,10(2)：3-13.
[65]唐辉明,孙成伟.岩体损伤力学研究进展[J].地质科技情报,1995,14(4)：85-92.
[66]刘红岩,王根旺,刘国振.以损伤变量为特征的岩石损伤理论研究进展[J].爆破器材,2004,33(6)：25-29.
[67]孙宝玉,庄惠平SHPB试验技术需要注意的几个问题[J].高校实验室工作研究,2009,100(2)：39-42.
[68]Rossmanith H P, Fourney W L. Fracture initiation and stress wave diffraction at cracked interfaces in layered media I. brittle/brittle transition[J]. Rock Mechanics and Rock Engineering,1982,14(4):209-233.
[69]Biegel R L, Bhat H S, Sammis C G, et al. The effect of asymmetric damage on dynamic shear rupture propagation I:No mismatch in bulk elasticity [J]. Tectonophysics,2010, 493(3-4):254-262.
[70]Bhat H S, Biegel R L,Rosakis A J, et al. The effect of asymmetric damage on dynamic shear rupture propagation II:With mismatch in bulk elasticity[J]. Tectonophysics, 2010,493(3-4):263-271.
[71]Mello M, Bhat H S, Rosakis A J, et al. Identifying the unique ground motion signatures of supershear earthquakes:Theory and experiments[J]. Tectonophysics,2010,493(3-4): 297-326.
[72]黄明利,黄凯珠.三维表面裂纹相互作用扩展贯通机制试验研究[J].岩石力学与工程学报,200709)：1794-1799.
[73]Wong R H C, Law C M, Chau K T, et al. Crack propagation from 3-D surface fractures in PMMA and marble specimens under uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences,2004,41, Supplement 1(0):37-42.
[74]Tay T E, Tan V B C, Deng M. Element-failure concepts for dynamic fracture and delamination in low-velocity impact of composites[J]. International Journal of Solids and Structures,2003,40(3):555-571.
[75]RAFIEE S,SEELIG T, GROSS D. Simulation of dynamic crack curving and branching under biaxial loading by a time domain boundary integral equation method [J]. International Journal of Fracture,2003,120(545-561.
[76]Hawong J,Kobayashi A, Dadkhah M, et al. Dynamic crack curving and branching under biaxial loading[J]. Experimental Mechanics,1987,27(2):146-153.
[77]Song J-H, Wang H, Belytschko T. A comparative study on finite element methods for dynamic fracture[J]. Computational Mechanics,2008,42(2):239-250.
[78]李根.基于模拟的水岩耦合变形破坏过程及机理研究[D].大连：大连理工大学,2011.
[79]李根,李连崇,唐春安,等.岩石流固/热固作用下损伤演化并行分析系统及初步应用[J].计算力学学报,2012,29(3)：381-386.
[80]张永彬.岩石破裂过程分析并行计算方法研究[D].沈阳：东北大学,2007.
[81]Yang Y, Tang C, Xia K. Study on crack curving and branching mechanism in quasi-brittle materials under dynamic biaxial loading[J]. International Journal of Fracture,2012, 177(1):53-72.
[82]Armero F, Linder C. Numerical simulation of dynamic fracture using finite elements with embedded discontinuities[J]. International Journal of Fracture,2009,160(2): 119-141.
[83]Rabczuk T,Bordas S,Zi G. On three-dimensional modelling of crack growth using partition of unity methods[J]. Computers & Structures,2010,88(23-24):1391-1411.
[84]Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks [J]. Computer Methods In Applied Mechanics and Engineering, 2007,196(29-30):2777-2799.
[85]雷卫东,Hefny A M,坚赵,等.岩石动力学中离散元程序处理波幅的新方法[J].中国矿业大学学报,2005,34(2)：170-174.
[86]王志亮,郑明新.基于TCK损伤本构的岩石爆破效应数值模拟[J].2008,29(1)：230-234.
[87]高文学,刘运通.岩石动态损伤的数值模拟[J].北京工业大学学报,2000,26(2)：5-10.
[88]夏祥,李海波,李俊如, 等.岩体爆生裂纹的数值模拟[J].岩土力学,2006,27(11)：1987-1991.
[89]Zhu W C, Tang C A. Numerical simulation of Brazilian disk rock failure under static and dynamic loading[J]. International Journal of Rock Mechanics and Mining Sciences, 2006,43(2):236-252.
[90]Zhou F, Molinari J-F,Shioya T. A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials[J]. Engineering Fracture Mechanics, 2005,72(9):1383-1410.
[91]Zhou S J, Lomdahl P S,Thomson R, et al. Dynamic Crack Processes via Molecular Dynamics[J]. Physical Review Letters,1996,76(13):2318.
[92]Ramulu M, Kobayashi A S. Mechanics of crack curving and branching-a dynamic fracture analysis[J]. International Journal of Fracture,1985,27(3):187-201.
[93]Zhang X, Liu Y, Ma S无网格法的理论及应用[J].力学进展,2009,39(1)：1-36.
[94]Schlangen E, Mier J G M V. Experimental and numerical analysis of micromechanisms of fracture of cement-based composites[J]. Cement and Concrete Composites,1992, 14(2):105-118.
[95]陈忠辉,唐春安,傅宇芳.岩石微破裂损伤演化诱致突变的数值模拟研究[J].岩土工程学报,1998,20(6)：9-15.
[96]Tang C A, Liu H, Lee P K K, et al. Numerical studies of the influence of microstructure on rock failure in uniaxial compression -- Part I:effect of heterogeneity [J]. International Journal of Rock Mechanics and Mining Sciences,2000, 37(4):555-569.
[97]Tang C A. Numerical simulation of progressive rock failure and associated seismicity[J]. International Journal of Rock Mechanics and Mining Sciences,1997, 34(2):249-261.
[98]Tang C A, Tham L G, Lee P K K, et al. Numerical studies of the influence of microstructure on rock failure in uniaxial compression -- Part II:constraint, slenderness and size effect[J]. International Journal of Rock Mechanics and Mining Sciences,2000,37(4):571-583.
[99]Vargas-Loli L M, Fenves G L. Effects of concrete cracking on the earthquake response of gravity dams[J]. Earthquake Engineering & Structural Dynamics,1989,18(4): 575-592.
[100]Ghaemian M, Ghobarah A. Nonlinear seismic response of concrete gravity dams with dam-reservoir interaction[J]. Engineering Structures,1999,21(4):306-315.
[101]李俊如,李海波,高建光,等.黄麦岭采场边坡爆破振动响应研究[J].岩石力学与工程学报,2004,23(17)：2954-2958.
[102]卢文波,赖世骧,朱传云,等.三峡工程岩石基础开挖爆破震动控制安全标准[J].爆炸与冲击,2001,21(1)：67-71.
[103]李新平,陈俊桦,李友华,等.溪洛渡电站地下洞室群爆破地震效应的研究[J].岩石力学与工程学报,2010,29(3)：493-501.
[104]蒋金宝,林英松,丁雁生.利用爆炸技术改善低渗透储层的实验研究[J].岩石力学与工程学报,2009,28(Supp.1)：2830-2835.
[105]田和金,李璗,王爱华,等.岩石动力学实验及其在油田开发中的应用[J].岩石力学与工程学报,2000,19(Supp.)：889-894.
[106]李术才,刘斌,李树忱,等.基于激发极化法的隧道含水地质构造超前探测研究[J].岩石力学与工程学报,2011,30(7)：1297-1309.
[107]钱七虎,李树忱.深部岩体工程围岩分区破裂化现象研究综述[J].岩石力学与工程学报,2008,27(6)：1278-1284.
[108]潘一山,李英杰,唐鑫,等.岩石分区碎裂化现象研究[J].岩石力学与工程学报,2007,26(Supp.1)：3335-3341.
[109]黄润秋.汶川8.0级地震触发崩滑灾害机制及其地质力学模式[J].岩石力学与工程学报,2009,28(6)：1239-1249.
[110]黄润秋.岩石高边坡发育的动力过程及其稳定性控制[J].岩石力学与工程学报,2008,27(8)：1525-1544.
[111]赖海辉,朱成忠,李夕兵.机械岩石破碎学[M].长沙：中南大学出版社,1991.
[112]刘柏禄,潘建忠,谢世勇.岩石破碎方法的研究现状及展望[J].中国钨业,2011,26(1)：15-19.
[113]田取珍,刘混举,曹惠斌.冲击式采煤的研究[J].煤炭学报,1998,23(6)：625-629.
[114]谢强,姜崇喜,凌建明.岩石细观力学实验与分析[M].成都：西南交通大学学报,1997.
[115]唐春安.岩石破裂过程中的灾变[M].煤炭工业出版社,1993.
[116]廖振鹏,刘晶波.离散网格中的弹性波动(I)[J].地震工程与工程振动,1986,6(2)：1-16.
[117]刘晶波,廖振鹏.离散网格中的弹性波动(Ⅱ)——几种有限元离散模型的对比分析[J].地震工程与工程振动,1989,9(2)：1-11.
[118]刘晶波,廖振鹏.离散网格中的弹性波动(Ⅲ)——时域离散化对波传播规律的影响[J].地震工程与工程振动,1990,10(2)：1-10.
[119]黄丹,章青,乔丕忠,等.近场动力学方法及其应用[J].力学进展,2010,40(4)：448-459.
[120]Silling S A,Epton M,Weckner O, et al. Peridynamic States and Constitutive Modeling[J]. Journal of Elasticity,2007.
[121]Silling S A. Linearized theory of peridynamic states[R]. Sandia National Laboratories,2009.
[122]朱万成,逢铭璋,黄志平,等.岩石动态剥落破裂的数值模拟[J].东北大学学报,2006,5)：552-555.
[123]Tang C A, Kaiser P K. Numerical Simulation of Cumulative Damage and Seismic Energy Release During Brittle Rock Failure--Part Ⅰ:Fundamentals [J]. International Journal of Rock Mechanics and Mining Sciences,1998,35(2):113-121.
[124]黄明利,唐春安,朱万成.岩石破裂过程的数值模拟研究[J].岩石力学与工程学报,2000,19(4)：468-471.
[125]朱万成,唐春安,杨天鸿,等.岩石破裂过程分析用(RFPA~(2D))系统的细观单元本构关系及验证[J].岩石力学与工程学报,2003,22(1)：24-29.
[126]Weibull W. A statistical distribution function of wide applicability[J]. Journal of Applied Mechanics,1951,18(3):293-297.
[127]Forquin P, Denoual C,Cottenot C E, et al. Experiments and modelling of the compressive behaviour of two SiC ceramics[J]. Mechanics of Materials,2003,35 (10): 987-1002.
[128]Denoual C, Hild F. Dynamic fragmentation of brittle solids:a multi-scale model[J]. European Journal of Mechanics - A/Solids,2002,21(1):105-120.
[129]朱晶晶,李夕兵,宫凤强,等.冲击载荷作用下砂岩的动力学特性及损伤规律[J].中南大学学报(自然科学版),2012,43(7)：2701-2707.
[130]梁正召,唐春安,张永彬,等.准脆性材料的物理力学参数随机概率模型及破坏力学行为特征[J].岩石力学与工程学报,2008,27(4)：718-727.
[131]Grange S,Forquin P,Mencacci S, et al. On the dynamic fragmentation of two limestones using edge-on impact tests[J]. International Journal of Impact Engineering,2008,35(9):977-991.
[132]Rao M P, Sanchez-Herencial A J,Beltz G E, et al. Laminar Ceramics That Exhibit a Threshold Strength[J].Science,1999,286(5437):102-105.
[133]Zhao J,Zhou Y. Advances in Rock Dynamics and Applications[M]. Taylor & Francis, 2011.
[134]Zhao J. Applicability of Mohr-Coulomb and Hoek-Brown strength criteria to the dynamic strength of brittle rock[J]. International Journal of Rock Mechanics and Mining Sciences,2000,37(7):1115-1121.
[135]Zhao J, Li H B. Experimental determination of dynamic tensile properties of a granite[J]. International Journal of Rock Mechanics and Mining Sciences, 2000,37(861-866.
[136]Zhao J, Li H B, Wu M B, et al. Dynamic uniaxial compression tests on a granite[J]. International Journal of Rock Mechanics and Mining Sciences,1999,36(2): 273-277.
[137]戚承志,钱七虎.岩石等脆性材料动力强度依赖应变率的物理机制[J].岩石力学与工程学报,2003,22(2)：177-181.
[138]赵坚,李海波.莫尔-库仑和霍克-布朗强度准则用于评估脆性岩石动态强度的适用性[J].岩石力学与工程学报,2003,22(2)：171-176.
[139]Wang S Y, Sloan S W, Liu H Y, et al. Numerical simulation of the rock fragmentation process induced by two drill bits subjected to static and dynamic (impact) loading[J].Rock Mechanics and Rock Engineering,2011,44(3):317-332.
[140]Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching[J]. International Journal of Fracture,1984,26(2):141-154.
[141]Suzuki S, Sakaue K, Iwanaga K. Measurement of energy release rate and energy flux of rapidly bifurcating crack in Homalite 100 and Araldite B by high-speed holographic microscopy[J]. Journal of The Mechanics and Physics of Solids,2007,55(7):1487-1512.
[142]Fineberg J,Gross S P,Marder M, et al. Instability in the propagation of fast cracks[J]. Physical Review B,1992,45(10):5146.
[143]Sharon E, Fineberg J. Microbranching instability and the dynamic fracture of brittle materials[J]. Physical Review B,1996,54(10):7128-7139.
[144]Sharon E, Fineberg J. Confirming the continuum theory of dynamic brittle fracture for fast cracks[J]. Nature,1999,397(6717):333-335.
[145]Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture: Ⅱ. Microstructural aspects[J].International Journal of Fracture,1984,26(1): 65-80.
[146]唐春安,朱万成.混凝土损伤与断裂-数值试验[M].北京：科学出版社,2003.
[147]王礼立.应力波基础(第二版)[M].北京：国防工业出版社,2010.
[148]Rayleigh. On Waves Propagated along the Plane Surface of an Elastic Solid[J]. Proceedings of The London Mathematical Society,1885.
[149]刘孝敏,胡时胜.大直径SHPB弥散效应的二维数值分析[J].实验力学,2000,15(4)：371-376.
[150]王从约,夏源明.傅立叶弥散分析在冲击拉伸和冲击压缩试验中的应用[J].爆炸与冲击,1998,18(3)：213-219.
[151]王从约,夏源明.圆杆中弹性应力波的傅立叶弥散分析[J].爆炸与冲击,1998,18(1)：1-7.
[152]左宇军,唐春安,朱万成,等.岩石类介质SHPB试验加载波形的数值分析[J].东北大学学报(自然科学版),2007,28(6)：859-862.
[153]李夕兵,古德生,赖海辉.冲击载荷下岩石动态应力-应变全图测试中的合理加载波形[J].爆炸与冲击,1993,13(2)：125-130.
[154]孟益平,胡时胜.混凝土材料冲击压缩试验中的一些问题[J].实验力学,2003,18(1)：108-112.
[155]Wang L L. Influences of Stress Wave Propagation upon Studying Dynamic Response of Materials at High Strain Rates[J]. Journal of BeijingInstituteof Technology,2004,13(3):225-235.
[156]Yang L M, Shim V P W. An analysis of stress uniformity in split Hopkinson bar test specimens[J]. International Journal of Impact Engineering,2005,31 (2):129-150.
[157]张圆.基于Hopkinson束杆技术的混凝土动态实验方法研究[D].宁波：宁波大学,2008.
[158]宁建国,王成,马天宝.爆炸与冲击动力学[M].北京：国防工业大学出版社,2010.
[159]廖振鹏.工程波动导论[M].北京：科学出版社,2002.
[160]廖振鹏,刘晶波.波动的有限元模拟—基本问题和基本研究方法[J].地震工程与工程振动,1989,9(4)：1-14.
[161]廖振鹏,杨光.稳态SH波动的有限元模拟[J].地震学报,1994,16(1)：96-105.
[162]Liu J B, Lv Y D. A direct method for analysis of dynamic soil-structure interaction based on interface idea[J]. Developments in Geotechnical Engineering,1998, Volume 83(261-276.
[163]刘晶波,杜义欣,闫秋实.粘弹性人工边界及地震动输入在通用有限元软件中的实现[J].防灾减灾工程学报,2007,27(Supp.)：37-42.
[164]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9)：1070-1075.
[165]李彬,刘晶波.粘弹性人工边界在Marc中的实现.中国烟台2005.
[166]Lamb H. On the Propagation of Tremors over the Surface of an Elastic Solid[J]. Philosophical Transactions of the Royal Society of London Series A, Containing Papers of a Mathematical or Physical Character,1904,203(359-371):1-42.
[167]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3)：55-64.
[168]陈静曦.应力波对岩石断裂的相关因素分析[J].岩石力学与工程学报,1997,16(2)：148-154.
[169]钱七虎,王明洋.岩土中的冲击爆破效应[M].北京：国防工业出版社,2010.
[170]魏修成,董敏煜,陈运泰.非均匀各向异性介质中弹性波的传播[J].地震学报,1998,20(6)：561-572.
[171]彭朝晖,刘殿魁.竖向非均匀介质中的Love面波[J].地震工程与工程振动,1998,18(2)：1-7.
[172]Tang C A, Tham L G, Wang S H, et al. A numerical study of the influence of heterogeneity on the strength characterization of rock under uniaxial tension[J]. Mechanics of Materials,2007,39(4):326-339.
[173]Emmerich H. PSV-wave propagation in a medium with local heterogeneities:a hybrid formulation and its application[J]. Geophysical Journal International,1992,109(1): 54-64.
[174]Wesolowski Z. Wave reflection on a continuous transition zone between two homogeneous materials[J]. Acta Mechanica,1994,105(1):119-131.
[175]罗松南,周正平.波在非均匀损伤介质中的传播[J].华南理工大学学报(自然科学版),2003,31(supp.)：48-51.
[176]周钟,王肖钧,刘文韬,等.岩石的损伤软化对应力波传播的影响[J].中国科学技术大学学报,2003,33(3)：337-344.
[177]Strassburger E, Senf H,Rothenhausler H. Fracture propagation during impact in three types of ceramics[J]. J Phys IV France,1994,04(C8):C8-653-C8-658.
[178]Strassburger E, Senf H, Denoual C, et al. An Experimental Approach to Validate Damage Evolution Laws for Brittle Materials[J]. J Phys IV France,1997,07(C3): 909-914.
[179]Strassburger E. Visualization of Impact Damage in Ceramics Using the Edge-On Impact Technique[J].International Journal of Applied Ceramic Technology,2004,1(3):235-242.
[180]Grujicic M, Pandurangan B, Coutris N, et al. A simple ballistic material model for soda-lime glass[J]. International Journal of Impact Engineering,2009,36(3): 386-401.
[181]Forquin P, Tran L, Louvigne P-F, et al. Effect of aluminum reinforcement on the dynamic fragmentation of SiC ceramics[J]. International Journal of Impact Engineering,2003,28(10):16.
[182]Erzar B, Forquin P. Experiments and mesoscopic modelling of dynamic testing of concrete[J]. Mechanics of Materials,2011,43(9):505-527.
[183]Hild F, Denoual C, Forquin P, et al. On the probabilistic - deterministic transition involved in a fragmentation process of brittle materials[J].Computers & amp; Structures,2003,81(12):1241-1253.
[184]成名,刘维甫,刘凯欣.高速冲击问题的离散元法数值模拟[J].计算力学学报,2009,26(4)：591-594.
[185]李金柱,黄风雷,张连生.EFP模拟弹丸侵彻陶瓷复合靶的数值模拟研究[J].计算力学学报,2009,26(4)：562-567.
[186]Ohte S. Finite Element Analysis of elastic contact problems[J]. Bulletin of JSME,1973,16(95):797-804.
[187]欧恒安,龚剑霞.三维弹性接触问题有限元改进混合法及数值计算[J].重庆大学学报(自然科学版),1988,1)：52-58.
[188]陈军,潘家铮,段云岭.转换位移自由度法求解滑动接触问题[J].计算力学学报,2006,23(1)：101-106.
[189]温卫东,高德平.接触问题数值分析方法的研究现状与发展[J].南京航空航天大学学报,1994,26(5)：664-675.
[190]刘晶波,王铎.考虑界面摩擦影响的可接触型裂纹动态分析的动接触力模型-弹性动力学最新进展[M].北京：科学出版社,1995.
[191]Riedel W,Hiermaier S, Thoma K. Transient stress and failure analysis of impact experiments with ceramics[J]. Materials Science and Engineering:B,2010,173(1-3): 139-147.
[192]Buehler M J,Abraham F F, Gao H. Hyperelasticity governs dynamic fracture at a critical length scale[J]. Nature,2003,426(6963):141-146.
[193]Buehler M J, Gao H. Dynamical fracture instabilities due to local hyperelasticity at crack tips[J].Nature,2006,439(7074):307-310.
[194]Freund L B. Dynamic Fracture Mechanics. Cambridge University Press; 1990.
[195]Yoffe E. The Moving Griffith Crack[J]. Philosophical Magazine,1951,42(739-750.
[196]James R R, Guo G F. New perspectives on crack and fault dynamics[J]. Advance in mechanics,2001,03):447-460.
[197]Ravi-Chandar K. Dynamic Fracture of Nominally Brittle Materials [J]. International Journal of Fracture,1998,90(1):83-102.
[198]Tay T E,Tan S H N, Tan V B C, et al. Damage progression by the element-failure method (EFM) and strain invariant failure theory (SIFT)[J]. Composites Science and Technology,2005,65(6):935-944.
[199]Pollard D D, Griffith W A. Laboratory Investigation of Damage by Tensile Fracture during Dynamic Shear Rupture Propagation[R]. Stanford:Department of Geological and Environmental Science, Stanford University,2009.
[200]Ha Y D,Bobaru F. Characteristics of dynamic brittle fracture captured with peridynamics[J]. Engineering Fracture Mechanics,2011,78(6):1156-1168.
[201]Budiansky B. Micromechanics[J]. Computer and structures,1982,16(1):3-12.
[202]傅宇方,梁正召,唐春安.岩石介质细观非均匀性对宏观破裂过程的影响[J].岩土工程学报,2000,06)：705-710.
[203]Bowden F P, Brunton J H, Field J E, et al. Controlled Fracture of Brittle Solids and Interruption of Electrical Current[J]. Nature,1967,216(5110):38-42.
[204]Sharon E, Gross S P, Fineberg J. Local Crack Branching as a Mechanism for Instability in Dynamic Fracture[J]. Physical Review Letters,1995,74(25):5096-5100.
[205]Ravi-Chandar K, Yang B. On the role of microcracks in the dynamic fracture of brittle materials[J]. Journal of The Mechanics and Physics of Solids,1997,45(4): 535-563.
[206]Leterrier Y,Pellaton D.Mendels D, et al. Biaxial fragmentation of thin silicon oxide coatings on poly(ethylene terephthalate)[J]. Journal of Materials Science, 2001,36(9):2213-2225.
[207]Andersons J, Leterrier Y, Fescenko I. Analysis of the initial fragmentation stage of oxide coatings on polymer substrates under biaxial tension[J]. Thin Solid Films,2003,434(1-2):203-215.
[208]Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture: Ⅰ. Crack initiation and arrest[J]. International Journal of Fracture,1984, 25(4):247-262.
[209]Krauthammer T, Otani R K. Mesh, gravity and load effects on finite element simulations of blast loaded reinforced concrete structures[J]. Computers & amp; Structures,1997,63(6):1113-1120.
[210]Luccioni B,Ambrosini D,Danesi R. Blast load assessment using hydrocodes[J]. Engineering Structures,2006,28(12):1736-1744.
[211]Chapman T C, Rose T A, Smith P D. Blast wave simulation using AUTODYN2D:A parametric study[J]. International Journal of Impact Engineering,1995,16(5-6):777-787.
[212]Shi Y, Li Z,Hao H. Mesh size effect in numerical simulation of blast wave propagation and interaction with structures [J]. Transactions of Tianjin University, 2008,14(6):396-402.
[213]Kalthoff J. Modes of dynamic shear failure in solids[J]. International Journal of Fracture,2000,101(1):1-31.
[214]Kalthoff J F,Winkler S. Failure Mode Transition at High Rates of Shear Loading [J]. International Conference on Impact Loading and Dynamic Behavior of Materials, 1988.
[215]Mason J J, Rosakis A J,Ravichandran G. Full field measurements of the dynamic deformation field around a growing adiabatic shear band at the tip of a dynamically loaded crack or notch[J]. Journal of The Mechanics and Physics of Solids,1994,42(11):1679-1697.
[216]Zhou M, Rosakis A J, Ravichandran G. Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed[J].Journal of The Mechanics and Physics of Solids,1996,44(6):981-1006.
[217]Remmers J J C, de Borst R, Needleman A. The simulation of dynamic crack propagation using the cohesive segments method[J]. Journal of The Mechanics and Physics of Sol ids,2008,56(1):70-92.
[218]Kalthoff J F. Failure methodology of mode-Ⅱ loaded cracks [J]. Strength, Fracture and Complexity,2003,1(3):121-138.
[219]Dolinski M, Rittel D, Dorogoy A. Modeling adiabatic shear failure from energy considerations[J]. Journal of The Mechanics and Physics of Solids,2010,58(11):1759-1775.
[220]Zhou M, Rosakis A J, Ravichandran G. On the growth of shear bands and failure-mode transition in prenotched plates:A comparison of singly and doubly notched specimens[J]. International Journal of Plasticity,1998,14(4-5):435-451.
[221]Zhou M, Ravichandran G, Rosakis A J. Dynamically propagating shear bands in impact-loaded prenotched plates—Ⅱ. Numerical simulations[J]. Journal of The Mechanics and Physics of Solids,1996,44(6):1007-1032.
[222]Zlotnikov M,Glushikhin F. Equivalent material based on epoxy resin for making models of rock masses[J]. Journal of Mining Science,1979,15(1):73-76.
[223]任松,郭松涛,姜德义,等.盐岩蠕变相似模型及相似材料研究[J].岩土力学,2011,32(Supp.1)：106-110.
[224]张宁,李术才,李明田,等.新型岩石相似材料的研制[J].山东大学学报,2009,39(4)：149-154.
[225]李晓红,卢义正,康勇,等.岩石力学实验模拟技术[M].北京：科学出版社,2007.
[226]Bertram A, Kalthoff J F. Crack propagation toughness of rock for the range from low to very high crack speeds[J]. Key Engineering Materials,2003,251-252(423-430.
[227]Ngo D, Huang Y, Huang Y, et al. Off-fault tensile cracks:A link between geological fault observations, lab experiments and dynamic rupture models[J]. GSA Denver Annual Meeting,2010.
[228]Murphy N, Ali M, Ivankovic A. Dynamic crack bifurcation in PMMA[J]. Engineering Fracture Mechanics,2006,73(16):2569-2587.
[229]Bertram A. Bruchenergie laufender Risse in Gestein [D]. Bochum:Ruhr-University, 2008.
[230]梁正召.三维条件下的岩石破裂过程分析及其数值试验方法研究[D]：东北大学,2005.
[231]Healy D,Jones R R, Holdsworth R E. Three-dimensional brittle shear fracturing by tensile crack interaction[J]. Nature,2006,439(7072):64-67.
[232]梁正召,杨天鸿,唐春安,等.非均匀性岩石破坏过程的三维损伤软化模型与数值模拟[J].岩土工程学报,2005,12)：1447-1452.
[233]唐春安.岩石声发射规律数值模拟初探[J].岩石力学与工程学报,1997,16(4)：368-377.
[234]唐春安,朱万成,李连崇,等.材料破坏过程中应力分布的数值光弹图[J].力学与实践,200205)：47-50.
[235]谭成文,王富耻,李树奎；.绝热剪切变形局部化研究进展及发展趋势[J].兵器材料科学与工程,2003,26(5)：62-67.
[236]徐永波,白以龙.动态载荷下剪切变形局部化、微结构演化与剪切断裂研究进展[J].力学进展,2007,37(4)：496-516.
[237]寇绍全.绝热剪切—一个值得重视的材料破坏问题[J].力学进展,1979,(3)：52-59.
[238]Winter R E. Adiabatic shear of titanium and polymethylmethacrylate[J]. Philosophical Magazine,1975,31(4):765-773.
[239]Johnson W, Sengupta A K, Ghosh S K. High velocity oblique impact and ricochet mainly of long rod projectiles:An overview[J]. International Journal of Mechanical Sciences,1982,24(7):425-436.
[240]Zerilli F J, Armstrong R W. Dislocation-mechanics-based constitutive relations for material dynamics calculations[J]. Journal of Applied Physics,1987,61 (5): 1816-1825.
[241]Nemat-Nasser S,Guo W-G, Nesterenko V F, et al. Dynamic response of conventional and hot isostatically pressed Ti-6A1-4V alloys:experiments and modeling[J]. Mechanics of Materials,2001,33(8):425-439.
[242]Wright T W.Walter J W. On stress collapse in adiabatic shear bands[J]. Journal of The Mechanics and Physics of Solids,1987,35 (6):701-720.
[243]Wright T W,Ockendon H. A model for fully formed shear bands[J]. Journal of The Mechanics and Physics of Solids,1992,40(6):1217-1226.
[244]Love B M,Batra R C. Effect of particulate/matrix debonding on the formation of adiabatic shear bands[J]. International Journal of Mechanical Sciences,2010, 52(2):386-397.
[245]Ruan H H,Zhang L C, Lu J. A new constitutive model for shear banding instability in metallic glass[J]. International Journal of Solids and Structures,2011,48 (21): 3112-3127.
[246]Li S, Liu W-K, Qian D, et al. Dynamic shear band propagation and micro-structure of adiabatic shear band[J]. Computer Methods In Applied Mechanics and Engineering, 2001,191(1-2):73-92.
[247]肖大武,李英雷,蔡灵仓.绝热剪切研究进展[J].实验力学,2010,25(4)：463-475.
[248]Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture: IV. On the interaction of stress waves with propagating cracks[J]. International Journal of Fracture,1984,26(3):189-200.
[249]Liu H, Kou S Q, Lindqvist P A. Numerical Studies on bit-rock fragmentation mechanisms[J]. International Journal of Geomechanics,2008,8(1):45-67.
[250]万圣.液压凿岩机冲头新型换向系统的研究开发[D].兰州：兰州理工大学,2011.
[251]赵伏军.动静载荷耦合作用下岩石破碎理论及试验研究[D].长沙：中南大学,2004.
[252]Denoual C,Cottenot C, Hild F. On the identification of damage during impact of a ceramic by a hard steel projectile[J]. San Francisco. CA:Proc 16th Int Symp on Ballistics,1996.
[253]李宇彤,焦明若.宏观非均匀性对岩石微震序列类型和破裂方式影响的数值试验研究[J].地震,2005,25(4)：98-104.
[254]Kumano A, Goldsmith W. An analytical and experimental investigation of the effect of impact on coarse granular rocks[J]. Rock Mechanics and Rock Engineering, 1982,15(2):67-97.
[255]Bernardino C. Fracture mechanisms induced in a brittle material by a hard cutting indenter[J]. International Journal of Solids and Structures,2001,38(44-45): 7747-7768.
[256]Itasca Consulting Group Inc. PFC2D/3D(Particle Flow Code in 2/3 Dimensions), Vesion 2.0[M]. Minneapolis:MN:ICG,1999.
[257]尤明庆.岩石的力学性质[M].北京：地质大学出版社,2008.
[258]Zhu W C, Tang C A. Numerical simulation on shear fracture process of concrete using mesoscopic mechanical model[J]. Construction and Building Materials,2002,16(8): 453-463.
[259]许金余,范建设,吕晓聪.围压条件下岩石的动态力学特性[M].西安：西北工业大学出版社,2012.
[260]张阿漫,戴绍仕.流固耦合动力学[M].北京：国防工业出版社,2011.