准脆性材料损伤斑图生长的数值模拟
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摘要
准脆性材料损伤斑图的生长过程研究,对于认识重大工程动力学灾变孕育、发生的机制具有特别重要的基础性意义。尤其是岩石类动力学灾害如地震、岩爆、煤矿开采中的三突,其形成机制都可归结为岩石损伤演化诱致结构灾变的模式。损伤斑图的生长过程可以再现灾变的孕育、发生过程,具有非常深刻的物理力学背景。该文根据微损伤不可逆演化原理,利用格形有限元模型,模拟二维平板在自适应位移加载条件下,从点状微损伤斑图到宏观贯通断裂的不可逆的分形生长过程。其中的微损伤机制全部采用拉应变准则,数值程序是在ANSYS平台上开发。结论表明,形态复杂的斑图可由细观单元简单的动力学规则和单元间的相互耦合演绎形成,斑图边界呈分形向外移动。最后,对斑图生长过程对工程灾变预测的启示作了初步讨论。
The study of damage pattern growth in brittle materials is of fundamental importance for understanding the gestation mechanism and the occurrence conditions of catastrophe in some key project constructions.It is especially important in understanding the dynamic catastrophe in rock,such as seismic,rock burst,and the three kinds of outburst which are the outburst of water,gas and coal in coal underground mining.A great many studies showed that the mechanism of formation of the dynamics catastrophe in rock can be explained in the same mode that irreversible evolution of damage in material induces catastrophe in structure.So the study of the growth of damage pattern is a great important method to understand the course of gestation and occurrence of the catastrophe,and the simulation of growth of damage pattern is a good way to demonstrate the course of gestation and occurrence of the catastrophe.In the paper,damage pattern growth in a 2-D sample of quasi-brittle material is simulated,which is based on the principle that the damage evolution is irreversible,and the lattice finite element is used for the numeric model.The simulation displayed that the damage pattern in the 2-D sample grows in a way of irreversible expandedness from a point to large scale cracks,which are fractals formed of lines and planes.The damage mechanism is based on the strength theory of tension strain for brittle materials,and the computer program is developed on the platform of ANSYS.The conclusion showed that the complex shape of a damage pattern can be deduced from the simple dynamic rule of the meso-element and the interaction between the meso-elements,and the boundary of the pattern moves forth in fractal shape.In the end of the paper,some inspirations for catastrophe prediction are discussed.
The study of damage pattern growth in brittle materials is of fundamental importance for understanding the gestation mechanism and the occurrence conditions of catastrophe in some key project constructions.It is especially important in understanding the dynamic catastrophe in rock,such as seismic,rock burst,and the three kinds of outburst which are the outburst of water,gas and coal in coal underground mining.A great many studies showed that the mechanism of formation of the dynamics catastrophe in rock can be explained in the same mode that irreversible evolution of damage in material induces catastrophe in structure.So the study of the growth of damage pattern is a great important method to understand the course of gestation and occurrence of the catastrophe,and the simulation of growth of damage pattern is a good way to demonstrate the course of gestation and occurrence of the catastrophe.In the paper,damage pattern growth in a 2-D sample of quasi-brittle material is simulated,which is based on the principle that the damage evolution is irreversible,and the lattice finite element is used for the numeric model.The simulation displayed that the damage pattern in the 2-D sample grows in a way of irreversible expandedness from a point to large scale cracks,which are fractals formed of lines and planes.The damage mechanism is based on the strength theory of tension strain for brittle materials,and the computer program is developed on the platform of ANSYS.The conclusion showed that the complex shape of a damage pattern can be deduced from the simple dynamic rule of the meso-element and the interaction between the meso-elements,and the boundary of the pattern moves forth in fractal shape.In the end of the paper,some inspirations for catastrophe prediction are discussed.
引文
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[11]Tang C A,Kaiser P K.Numerical simulation ofcumulative damage and seismic energy release duringbrittle rock failure-Part I:Fundamentals[J].Int J RockMech Min Sci,35(2):113―121.
[12]陈永强,郑小平,姚振汉.三维非均匀脆性材料破坏过程的数值模拟[J].力学学报,2002,34(3):351―361.Chen Yongqiang,Zheng Xiaoping,Yao Zhenhan.Numerical simulation of fracture procresses in 3-Dheterogeneous brittle material[J].Acta Mechanica Sinica,2002,34(3):351―361.(in Chinese)
[13]於崇文.地质系统的复杂性(上册)[M].北京:地质出版社,2003.Yu Chongwen.Complexity of the geologic system(I)[M].Beijing:Geological Publishing House,2003.(inChinese)
[14]Shen B,King A,Guo H.Displacement,stress andseismicity in roadway roofs during mining-inducedfailure[J].International Journal of Rock Mechanics andMining Sciences,2008,45(5):672―688.
[15]Scholz C H.Experimental study of fracturing process inbrittle rock[J].J.Geophys.Res,1968,73:1447―1486.
[16]Brady B T,Rowell Glen A.Laboratory investigation ofthe electro-dynamics of rock fracture[J].Nature,1986,332:522―525.
[17]陈顒,姚孝新,谢鸿森.辉长岩的破裂研究[J].地震学报,1981,3(3):321―327.Chen Yu,Yao Xiaoxin,Xie Hongsen.Studies on fractureof gabbro[J].Acta Seismologica Sinica,1981,3(3):321―327.(in Chinese)
[18]陆菜平,窦林名,曹安业.深部高应力集中区域矿震活动规律研究[J].岩石力学与工程学报,2008,27(11):2302―2308.Lu Caiping,Dou Linming,Cao Anye.Research onmicroseismic activity rules in deep high-stressconcentration district[J].Chinese Journal of RockMechanics and Engineering,2008,27(11):2302―2308.(in Chinese)
[2]夏蒙棼,韩闻生,柯浮久.统计细观损伤力学和损伤演化诱致突变(I)[J].力学进展,1995,25(1):1―24.Xia Mengfen,Han Wensheng,Ke Fujiu.Statisticalmesoscopic damage mechanics and damage evolutioninduced catastrophe(II)[J].Advances in Mechanics,1995,25(1):1―24.(in Chinese)
[3]夏蒙棼,韩闻生,柯浮久.统计细观损伤力学和损伤演化诱致突变(II)[J].力学进展,1995,25(2):145―159.Xia Mengfen,Han Wensheng,Ke Fujiu.Statisticalmesoscopic damage mechanics and damage evolutioninduced catastrophe(II)[J].Advances in Mechanics,1995,25(2):145―159.(in Chinese)
[4]夏梦棼.斑图动力学——非线性科学专题之九[J].物理通报,1999(4):3―6.Xia Mengfen.Pattern dynamics——The special report(9)of nonlinear science[J].Physics Report,1999(4):3―6.(in Chinese)
[5]Aidun J B,Lo D C S,Trucano T G,Fye R M.Representative volume size:A comparison of statisticalcontinuum mechanics and statistical physics[R].SAND99-1176,1999.
[6]Xia M F,Song Z Q,Xu J B,Zhao K H.Sample-specificbehavior in failure models of disordered media[J].Commun Theor Phys,1996,25(1):49―54.
[7]白以龙,汪海英,夏梦棼.固体的统计细观力学——连接多个耦合的时空尺度[J].力学进展,2006,36(2):286―305.Bai Yilong,Wang Haiying,Xia Mengfen.Statisticalmesomechanics of solid,linking coupled multiple spaceand time scales[J].Advances in Mechanics,2006,36(2):286―305.(in Chinese)
[8]夏梦棼,柯浮久,白洁.破坏现象耦合斑图演化诱致灾变的系综统计[J].科学通报,1999,44(6):562―572.Xia Mengfen,Ke Fujiu,Bai Jie.Ensemble statistic offracture pattern growth induced catastrophe[J].ChineseScience Bulletin,1999,44(6):562―572.(in Chinese)
[9]俞茂宏,Yoshimine M,强洪夫.强度理论的发展和展望[J].工程力学,2004,21(6):1―20.Yu Maohong,Yoshimine M,Qiang Hongfu.Advancesand prospects for strength theory[J].EngineeringMechanics,2004,21(6):1―20.(in Chinese)
[10]Bazant Z P,Chen E P.Scaling of structural failure[J].Appl Mech Rev,1997,50(10):593―627.
[11]Tang C A,Kaiser P K.Numerical simulation ofcumulative damage and seismic energy release duringbrittle rock failure-Part I:Fundamentals[J].Int J RockMech Min Sci,35(2):113―121.
[12]陈永强,郑小平,姚振汉.三维非均匀脆性材料破坏过程的数值模拟[J].力学学报,2002,34(3):351―361.Chen Yongqiang,Zheng Xiaoping,Yao Zhenhan.Numerical simulation of fracture procresses in 3-Dheterogeneous brittle material[J].Acta Mechanica Sinica,2002,34(3):351―361.(in Chinese)
[13]於崇文.地质系统的复杂性(上册)[M].北京:地质出版社,2003.Yu Chongwen.Complexity of the geologic system(I)[M].Beijing:Geological Publishing House,2003.(inChinese)
[14]Shen B,King A,Guo H.Displacement,stress andseismicity in roadway roofs during mining-inducedfailure[J].International Journal of Rock Mechanics andMining Sciences,2008,45(5):672―688.
[15]Scholz C H.Experimental study of fracturing process inbrittle rock[J].J.Geophys.Res,1968,73:1447―1486.
[16]Brady B T,Rowell Glen A.Laboratory investigation ofthe electro-dynamics of rock fracture[J].Nature,1986,332:522―525.
[17]陈顒,姚孝新,谢鸿森.辉长岩的破裂研究[J].地震学报,1981,3(3):321―327.Chen Yu,Yao Xiaoxin,Xie Hongsen.Studies on fractureof gabbro[J].Acta Seismologica Sinica,1981,3(3):321―327.(in Chinese)
[18]陆菜平,窦林名,曹安业.深部高应力集中区域矿震活动规律研究[J].岩石力学与工程学报,2008,27(11):2302―2308.Lu Caiping,Dou Linming,Cao Anye.Research onmicroseismic activity rules in deep high-stressconcentration district[J].Chinese Journal of RockMechanics and Engineering,2008,27(11):2302―2308.(in Chinese)
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