[1] Labuz J F, Zang A.Mohr-Coulomb failure criterion[J].Rock Mechanics and Rock Engineering, 2012, 45(6):975-979.
[2] Drucker D C, Prager W.Soil mechanics and plastic analysis or limit design[J].Quarterly of Applied Mathematics, 1952, 10(2):157-165.
[3] Hoek E, Brown E T.Practical estimates of rock mass strength[J].International Journal of Rock Mechanics and Mining Sciences, 1997, 34(8):1165-1186.
[4] Bui H D, Ehrlacher A.Propagation of damage in elastic and plastic solids[C]//Proceedings of the 5th International Conference of Fracture, Cannes:Pergamon Press, 1981:533-551.
[5] 朱万成,唐春安,左宇军.深部岩体动态损伤与破裂过程[M].北京:科学出版社, 2014.
[6] Brooks J J, Samaraie N H.Influence of rate of stressing on tensile stress-strain behavior of concrete[C]//Fracture of Concrete and Rock:Recent Developments.London:Elsevier, 1989:397-408.
[7] 卢文波,杨建华,严鹏.深部岩体开挖瞬态卸荷机制与效应[M].北京:科学出版社, 2018.
[8] 陶俊林,李奎.水泥砂浆的一个热粘弹性率型损伤本构模型[J].爆炸与冲击, 2011, 31(3):268-273.
[9] Dubé J F, Pijaudier C G, Christian L B.Rate dependent damage model for concrete in dynamics[J].Journal of Engineering Mechanics, 1996, 122:939-947.
[10] Deng J, Gu D S.On a statistical damage constitutive model for rock materials[J].Computers and Geosciences, 2011, 37(2):122-128.
[11] Eibl J, Schmidt H B.Strain-rate-sensitive constitutive law for concrete[J].Journal of Engineering Mechanics, 1999, 125(12):1411-1420.
[12] Forquin P, Erzar B.Dynamic fragmentation process in concrete under impact and spalling tests[J].International Journal of Fracture, 2010, 163(1/2):193-215.
[13] Addessio F L, Johnson J N.A constitutive model for the dynamic response of brittle materials[J].Journal of Applied Physics, 1990, 67(7):3275-3286.
[14] 李庆斌,张楚汉,王光纶.单压状态下混凝土的动力损伤本构模型[J].水利学报, 1994(3):85-89.
[15] 李庆斌,邓宗才,张立翔.考虑初始弹模变化的混凝土动力损伤本构模型[J].清华大学学报(自然科学版), 2003, 43(8):1088-1091.
[16] Liu H Y, Lü S R, Zhang L M, et al.A dynamic damage constitutive model for a rock mass with persistent joints[J].International Journal of Rock Mechanics & Mining Sciences, 2015, 75:132-139.
[17] Zhu Z W, Cao C X, Fu T T.SHPB test analysis and a constitutive model for frozen soil under multiaxial loading[J].International Journal of Damage Mechanics, 2019(4):626-645.
[18] Zhang F L, Zhu Z W, Fu T T, et al.Damage mechanism and dynamic constitutive model of frozen soil under uniaxial impact loading[J].Mechanics of Materials, 2019, 140:103217.
[19] 谢理想,赵光明,孟祥瑞.软岩及混凝土材料损伤型黏弹性动态本构模型研究[J].岩石力学与工程学报, 2013, 32(4):857-864.
[20] 朱兆祥,徐大本,王礼立.环氧树脂在高应变率下的热粘弹性本构方程和时温等效性[J].宁波大学学报(理工版), 1988(1):58-68.
[21] 陈江瑛,王礼立.水泥砂浆的率型本构方程[J].宁波大学学报(理工版), 2000(2):1-5.
[22] 胡时胜,王道荣.冲击载荷下混凝土材料的动态本构关系[J].爆炸与冲击, 2002(3):242-246.
[23] Zhou F H, Wang L L, Hu S S.A damage-modified nonlinear visco-elastic constitutive relation and failure criterion of PMMA at high strain-rates[J].Explosion and Shock waves, 1992, 12(4):333-342.
[24] 唐志平.高应变率下环氧树脂的力学性能研究[D].合肥:中国科技大学, 1981
[25] Wang L L, Zhou F H, Sun Z J, et al.Studies on rate-dependent macro-damage evolution of materials at high strain rates[J].International Journal of Damage Mechanics, 2010, 19(7):805-820.
[26] 单仁亮,程瑞强,高文蛟.云驾岭煤矿无烟煤的动态本构模型研究[J].岩石力学与工程学报, 2006(11):2258-2263.
[27] Tao J L, Li K.A thermo-viscoelastic rate-dependent constitutive equation for cement mortar with damage[J].Explosion and Shock Waves, 2011, 31(3):268-273.
[28] Zhao G M, Xie L X, Meng X R.Aconstitutive model for soft rock under impact load[J].Explosion and Shock Waves, 2013, 33(2):126-132.
[29] 梁书锋.恒应变率冲击作用下花岗岩的损伤演化与本构模型研究[D].北京:中国矿业大学(北京)岩土工程系, 2016.
[30] Zhang H, Wang B, Xie A, et al.Experimental study on dynamic mechanical properties and constitutive model of basalt fiber reinforced concrete[J].Construction and Building Materials, 2017, 152(2017):154-167.
[31] 马冬冬.动静组合加载下人工冻土动态力学特性及本构模型研究[D].淮南:安徽理工大学, 2018.
[32] Yang J M, Zhang Y H, Li Q W, et al.Dynamic constitutive model of penetrating jointed rock mass based on ZTW model[C]//IOP Conference Series:Earth and Environmental Science.Bristol:IOP Publishing, 2019, 237(3):032110.
[33] 郑永来,夏颂佑.岩石黏弹性连续损伤本构模型[J].岩石力学与工程学报, 1996, 15(增刊1):428-432.
[34] 尚仁杰.混凝土动态本构行为研究[D].大连:大连理工大学, 1994.
[35] Izzuddin B A, Fang Q.Rate-sensitive analysis of framed structures part I:Model formulation and verification[J].Structural Engineering and Mechanics, 1997, 5(3):221-237.
[36] 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(11):1771-1776.
[37] Chong K P, Boresi A P.Strain rate dependent mechanical properties of new albany reference shale[J].International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1990, 27(3):199-205.
[38] 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.
[39] Perzyna P.Fundamental problems in viscoplasticity[J].Advances in Applied Mechanics, 1966, 9:243-377.
[40] Lindholm U S, Yeakley L M, Nagy A.The dynamic strength and fracture properties of dresser basalt[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1974, 11(2):181-191.
[41] 孙建运,李国强.动力荷载作用下固体材料本构模型研究的进展[J].四川建筑科学研究, 2006(5):144-149.
[42] Fang X Y, Xu J Y.A modified overstress model to simulate dynamic split tensile tests and its experimental validation[J].Rock Mechanics & Rock Engineering, 2016, 49(9):3823-3828.
[43] 赵光明,谢理想,孟祥瑞.软岩的动态力学本构模型[J].爆炸与冲击, 2013, 33(2):126-132.
[44] 于亚伦.用三轴SHPB装置研究岩石的动载特性[J].岩土工程学报, 1992, 14(3):76-79.
[45] Tashman L, Masad E, Little D, et al.A microstructurebased viscoplastic model for asphalt concrete[J].International Journal of Plasticity, 2005, 21(9):1659-1685.
[46] Winnicki A, Pearce C J, Biani N.Viscoplastic Hoffman consistency model for concrete[J].Computers & Structures, 2001, 79(1):7-19,
[47] 王哲,林皋,逯静洲.混凝土的单轴率型本构模型[J].大连理工大学学报, 2000(5):597-601.
[48] Bianić N, Zienkiewicz O C.Constitutive model for concrete under dynamic loading[J].Earthquake Engineering & Structural Dynamics, 1983, 11(5):689-710.
[49] 夏才初,闫子舰,王晓东,等.大理岩卸荷条件下弹黏塑性本构关系研究[J].岩石力学与工程学报, 2009, 28(3):459-466.
[50] Cristescu N D.A general constitutive equation for transient and stationary creep of rock salt[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1993, 30(2):125-140.
[51] 翟越.岩石类材料的动态性能研究[D].西安:长安大学结构工程系, 2008.
[52] 翟越,赵均海,李寻昌,等.岩石类材料损伤黏弹塑性动态本构模型研究[J].岩石力学与工程学报, 2011(Suppl 2):3820-3824.
[53] Huang S, Zhang C, Ding X, et al.Viscoelastic-plastic constitutive model with non-constant parameters for brittle rock under high stress conditions[J].European Journal of Environmental and Civil Engineering, 2020(3):1-19.
[54] Pu S Y, Zhu Z D, Song L, et al.Fractional-order viscoelastoplastic constitutive model for rock under cyclic loading[J].Arabian Journal of Geosciences, 2020, 13(9):326-337.
[55] 张俊,李志伟.循环荷载作用下沥青混合料的黏弹塑性损伤本构模型[J].东北大学学报(自然科学版), 2019, 40(10):1496-1503.
[56] Zhang J, Wang Y D, Su Y.Fatigue damage evolution model of asphalt mixture considering influence of loading frequency[J].Construction and Building Materials, 2019, 218:712-720.
[57] Johnson G R, Cook W H.Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures[J].Engineering Fracture Mechanics, 1985, 21(1):31-48.
[58] Johnson H G R.A computational constitutive model for glass subjected to large strains, high strain rates and high pressures[J].Journal of Applied Mechanics, 2011, 78(5):051003.
[59] Holmquist T J, Johnson G R, Gerlach C A.An improved computational constitutive model for glass[J].Philosophical Transactions, 2017, 375(2085):20160182.
[60] 杨震琦,庞宝君,王立闻,等.JH-2模型及其在Al2O3陶瓷低速撞击数值模拟中的应用[J].爆炸与冲击, 2010, 30(5):463-471.
[61] Holmquist T J, Johnson G R, Grady D E, et al.High strain rate properties and constitutive modeling of glass[C]//Proceedings of 15th International Symposium on Ballistics.Jerusalem:Sandia National Labs, 1995:234-244.
[62] 李世民,李晓军.几种常用混凝土动态损伤本构模型评述[J].混凝土, 2011(6):19-22.
[63] Polanco-Loria M, Hopperstad O S, Børvik T, et al.Numerical predictions of ballistic limits for concrete slabs using a modified version of the HJC concrete model[J].International Journal of Impact Engineering, 2008, 35(5):290-303.
[64] Xie L X, Lu W B, Zhang Q B, et al.Analysis of damage mechanisms and optimization of cut basting design under high in-situ stresses[J].Tunnelling & Underground Space Technology, 2017, 66:19-33.
[65] Liu K, Wu C Q, Li X B, et al.A modified HJC model for improved dynamic response of brittle materials under blasting loads[J].Computers and Geotechnics, 2020, 123:103584.
[66] Kong X Z, Fang Q, Wu H, et al.Numerical predictions of cratering and scabbing in concrete slabs subjected to projectile impact using a modified version of HJC material model[J].International Journal of Impact Engineering, 2016, 95:61-71.
[67] Riedel W.Beton unter dynamischen lasten meso-und makromechanische modelle und ihre parameter[D].Freiburg:Institut für Kurzzeitdynamik, Ernst-Mach-Institut, 2000:210.
[68] Tu Z, Lu Y.Modifications of RHT material model for improved numerical simulation of dynamic response of concrete[J].International Journal of Impact Engineering, 2010, 37(10):1072-1082.
[69] Abdel-Kader M.Modified settings of concrete parameters in RHT model for predicting the response of concrete panels to impact[J].International Journal of Impact Engineering, 2019, 132:103312.
[70] LS-DYNA keyword manual version 971[R].Livermore:Livermore Software Technology Corporation, 2007.
[71] Malvar L J, Crawford J E, Wesevich J W, et al.A plasticity concrete material model for DYNA3D[J].International Journal of Impact Engineering, 1997, 19(9/10):847-873.
[72] Taylor L M, Chen E P, Kuszmaul J S.Microcrack-induced damage accumulation in brittle rock under dynamic loading[J].Computer Methods in Applied Mechanics & Engineering, 1986, 55(3):301-320.
[73] BudianskyB, O' Connell R J.Elasticmoduli of a cracked solid[J].International Journal of Solids Structures, 1976, 12(2):81-97.
[74] Grady D E, Kipp M E.Continuum modelling of explosive fracture in oil shale[J].International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts, 1980, 17(3):147-157.
[75] Kuszmaul J S.A new constitutive model for fragmentation of rock under dynamic loading[C]//Proceedings of the 2nd International Symposium on Rock Fragmentation by Blasting.Columbia, USA:Colorado Keystone, 1987:412-423.
[76] Throne B J, Hommert P J, Brown B.Experimental and computational investigation of the fundamental mechanisms of cratering[C]//International Symposium on Rock Fragmentation by Blasting, Brisbane, 26-31 Aug, 1990.
[77] Yang R, Brwden W F, Katsabanis P D.A new constitutive model for blast damage[J].International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1996, 33(3):245-254.
[78] Yang L, Wang G S, Zhao G F, et al.A rate-and pressure-dependent damage-plasticity constitutive model for rock[J].International Journal of Rock Mechanics and Mining Sciences, 2020, 133:104394.
[79] Xie L X, Yang S Q, Gu J C, et al.JHR constitutive model for rock under dynamic loads[J].Computers and Geotechnics, 2019, 108:161-172.
[80] Milasinovic D D, Landovic A.Rheological-dynamical analogy for analysis of vibrations and low cycle fatigue in internally damped inelastic frame structures[J].Computers & Structures, 2018, 196:76-93.
[81] Liu L Q, Katsabanis P D.Development of a continuum damage model for blasting analysis[J].International Journal of Rock Mechanics and Mining Sciences, 1997, 34(2):217-231.
[82] Yang L, Lin X, Li H Y, et al.A new constitutive model for steel fibre reinforced concrete subjected to dynamic loads[J].Composite Structures, 2019, 221:110849.
[83] Valanis K C.A theory of viscoplasticity without a yield surface.Part 1.General Theory[R].Iowa:University of Iowa, 1970.
[84] 胡亚元.论塑性因子与塑性时间的一般关系[J].岩石力学与工程学报, 2008(Suppl 2):3490-3497.
[85] Bazant Z P, Ching-Long S.Endochronic model for nonlinear triaxial behavior of concrete[J].Nuclear Engineering and Design, 1978, 47(2):305-315.
[86] Bazant Z P, Oh B H.Strain rate effect in rapid triaxial loading of concrete[J].Journal of the Engineering Mechanics Division-ASCE, 1982, 108(5):764-782.
[87] 宋玉普,刘浩.混凝土率型内时损伤本构模型[J].计算力学学报, 2012, 29(4):589-593,
[88] 刘运思,王世鸣,郭志广,等.横观各向同性岩体内时损伤本构模型研究[J].铁道科学与工程学报, 2017, 14(7):1407-1414.
[89] Jeremiah M S, John F P, Youssef H, et al.A kinematic hardening model based on endochronic theory for complex stress histories[J].Computers and Geotechnics, 2019, 114(10):103117.
[90] Bazant Z P, Xiang Y, Adley M, et al.Microplane model for concrete.Ⅱ:Data delocalization and verification[J].Journal of Engineering Mechanics, 1996, 122(3):255-262.
[91] Taylor G I.Plastic strain in metals[J].Journal of the Institute of Metals, 1938, 62(1938):307-324.
[92] Batdorf S B, Budiansky B.A mathematical theory of plasticity based on the concept of slip[R].Washington DC:National Advisory Committee for Aeronautics, 1949.
[93] Bazant Z P, Caner F C, Adley M D, et al.Fracturing rate effect and creep in microplane model for dynamics[J].Journal of Engineering Mechanics, 2000, 126(9):962-970.
[94] Li J B, Tue N V, Caner F C.Microplane constitutive model M4L for concrete.II:Calibration and validation[J].Computers & Structures, 2013, 128:146-159.
[95] Bažant Z P, Caner F C.Microplane model M5 with kinematic and static constraints for concrete fracture and anelasticity.I:Theory[J].Journal of Engineering Mmechanics, 2005, 131(1):31-40.
[96] Bažant Z P, Caner F C.Microplane model M5 with kinematic and static constraints for concrete fracture and anelasticity.II:Computation[J].Journal of Engineering mechanics, 2005, 131(1):41-47.
[97] Caner F C, Bažant Z P.Microplane model M7 for plain concrete.I:Formulation[J].Journal of Engineering Mechanics, 2012, 139(12):1714-1723.
[98] Caner F C, Bažant Z P.Microplane model M7 for plain concrete.II:Calibration and verification[J].Journal of Engineering Mechanics, 2012, 139(12):1724-1735.
[99] Zhai Y, Zhao R F, Li Y B, et al.Stochastic inversion method for dynamic constitutive model of rock materials based on improved DREAM[J].International Journal of Impact Engineering, 2021, 147:103739.
[100] Li X Z, Qi C Z.A micro-macro dynamic compressiveshear fracture model under static confining pressure in brittle rocks[J].International Journal of Impact Engineering, 2018, 122:109-118.
[101] Wu B B, Yao W, Xia K W.Theoretical modeling of the dynamic tensile response of Laurentian granite using the dominant crack algorithm[J].International Journal of Rock Mechanics and Mining Siences, 2019, 123:104077.
[102] Yang L, Wang G S, Zhao G F, et al.A rate-and pressure-dependent damage-plasticity constitutive model for rock[J].International Journal of Rock Mechanics and Mining Sciences, 2020, 133:104394.