类岩石材料动态本构模型研究进展

doi:10.3981/j.issn.1000-7857.2022.08.011

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摘要类岩石材料的动态本构关系是研究冲击地压和岩爆等地质灾害现象、评估围岩或工程材料抗冲击破坏能力的重要手段，特别是高应变率下的类岩石材料动态本构关系对解决工程问题和设计施工方案具有重要参考意义。总结了类岩石材料动态本构方程的研究方法，阐述了损伤模型、动态黏弹性模型、动态黏塑性模型、动态黏弹塑性模型、经验模型等动态本构关系的优点和局限性；归纳了不同理论模型和经验模型的最新进展，并对动态本构关系的未来发展趋势进行了展望，提出使类岩石材料在动静组合加载下的理论计算值与试验数据较好地吻合是未来的一个发展趋势。

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	陈思羽
	王青成
	杨立云

关键词 ：类岩石材料, 动态本构关系, 高应变率

Abstract：The dynamic constitutive relationship of the rock-like materials is important in the study of the failure threshold of the rock structures and the impact resistance of the structures surrounding the rock and the engineering materials. Especially, the dynamic constitutive relation of the rock-like materials under high strain rate is important for solving engineering problems and designing construction schemes. This paper reviews the dynamic constitutive models of the rock-like materials, focusing on the advantages and the limitations of various dynamic constitutive models, such as the damage model, the dynamic viscoelastic model, the dynamic viscoplastic model, the dynamic viscoelastic plastic model and the empirical model, as well as the latest developments of different theoretical and empirical models, and the future development trend of the dynamic constitutive models. It is pointed out that as a development feature, the theoretical calculation values of the rock-like materials under combined dynamic and static loading are in good agreement with the experimental data.

Key words： rock-like material dynamic constitutive relation high strain rate

收稿日期: 2020-11-12

基金资助:国家自然科学基金项目（51974316，51934001）；国家重点研发计划项目（2016YFC0600903）；中国矿业大学（北京）越崎学者专项资金项目（800015Z1125）

通讯作者: 杨立云(通信作者),教授,研究方向为工程爆破与岩石破碎,电子信箱:yangly@cumtb.edu.cn E-mail: yangly@cumtb.edu.cn

作者简介: 陈思羽,博士研究生,研究方向为工程爆破,电子信箱:bqt_siyuchen@163.com

引用本文:

陈思羽, 王青成, 杨立云. 类岩石材料动态本构模型研究进展[J]. 科技导报, 2022, 40(8): 115-126.
CHEN Siyu, WANG Qingcheng, YANG Liyun. Review of dynamic constitutive models of rock-like materials. Science & Technology Review, 2022, 40(8): 115-126.

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http://www.kjdb.org/CN/10.3981/j.issn.1000-7857.2022.08.011 或 http://www.kjdb.org/CN/Y2022/V40/I8/115

[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.