物理细胞自动机与岩石弹-脆-塑性性质的细观机制研究
摘要
基于能量守恒定律和岩石的基本力学性质,进一步发展了由作者提出的一种用于模拟岩石非线性破坏演化的新方法—物理细胞自动机(PCA)模型。该模型通过岩石内部(或细观)基元(或细胞)间简单的随机相互作用的综合结果来反映岩石系统整体的稳定宏观力学现象。利用PCA模型,研究了形成不同岩石本构关系的本质影响因素,揭示了岩石弹-脆-塑性性质的细观机制,为进一步认知岩石等非均质材料的力学性质提供了一种新的理论方法。同时,其研究思路和结论也可为微观和细观力学的数值模拟方法及新型复合材料的设计提供重要的借鉴。
Based on the energy conservation law and mechanical properties of rock, the physical cellular automat (PCA), a new model set up by authors to simulate the nonlinear evolution of rock failure, is developed; and the PCA model can be used to simulate the macroscopic mechanical behaviors of rock system caused by the compositive results of the simple reciprocity among the partial cells in the rock. Entitative influence on the constitutive relation of rock is studied by way of PCA; and micro-mechanism of elasticity, brittleness and plasticity of rock is profoundly revealed. The ideas and conclusions of the paper can be used as an important reference to numerical simulation of meso-mechanics and design of new composite materials.
Based on the energy conservation law and mechanical properties of rock, the physical cellular automat (PCA), a new model set up by authors to simulate the nonlinear evolution of rock failure, is developed; and the PCA model can be used to simulate the macroscopic mechanical behaviors of rock system caused by the compositive results of the simple reciprocity among the partial cells in the rock. Entitative influence on the constitutive relation of rock is studied by way of PCA; and micro-mechanism of elasticity, brittleness and plasticity of rock is profoundly revealed. The ideas and conclusions of the paper can be used as an important reference to numerical simulation of meso-mechanics and design of new composite materials.
引文
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[2]李宗全,陈湘明.材料结构与性能[M].杭州:浙江大学出版社.2001.159-160.
[3]VonNeumannJ.Theory of self-reproducing automata[M].University ofIllinoisPress.1996.
[4]StephenWolfram.Statistical mechanics of cellular automata[J].Reviews of modern physics,1983,55(3):601-643.
[5]PeterGrassberger.Long-range effects in an elementary cellular automata[J].Journal ofStatisticalPhysics,1986,45(172):27-39.
[6]HardyJ,PomeauY, dePazzisO.Time evolution of a two-dimensional model system[J].J.Math.Phys,1973,14:1746-1759.
[7]HasslacherB.Discrete fluids[J].LsAlamosScienceSpecialIssue,1987,175-217.
[8] d扝umièresD,LallemandP,FrischU.Lattice gas methods for3D hydrodynamics[J].Europhys.Lett.,1986,2:291-297.
[9]HiizuNakanishi.Cellular-automata of earthquakes with deterministic dynamics[J].PhysicalReview(A),1990,41(12):7086-7089.
[10]BakP,ChaoT.Earthquakes as a self-organized critical phenomenon[J].J.Geophysical.Research,1989,94(1311):15635-15637.
[11]ChenK,BakP.Self-organized criticality in a crack-propagation model of earthquakes[J].PhysicalReviews.(A),1991,43(2):625-630.
[12]ItoK,MatsuzakiM.Earthquakes as self-organized critical phenomenon[J].J.Geophys.Res,1990,95(135):6853-6860.
[13]SornetteA,SornetteD.Self-organized criticality and earthquakes[J].Europhys.Lett,1989,9(3):197-202.
[14]郑捷.研究地震和岩石破裂现象的非线性科学方法[A].非线性科学在地震中的应用[M].北京:地震出版社,1992.45-538.
[15]陆远忠,吕悦军.带断层的细胞自动机及其算法复杂性[J].地震学报,1994,16(2):183-189.
[16]刘长海,陈军,凌学书.三维大型CA的“地震”能量—频度、时空分布[J].地震学报,1997,19(3):299-302
[17]刘杰,刘桂萍,李丽等.基于大陆地震活动特点建立的简化动力学模型—细胞自动机模型[J].地震,1999,19(3):230-238.
[18]周辉.矿震孕育过程的混沌性及非线性预测理论研究[博士论文D].沈阳:东北大学,2000.723.
[19]周辉,王泳嘉,谭云亮等.岩石破坏过程的物理细胞自动机模型(I)—基本模型[J].岩石力学与工程学报,2002,21(4):475-478
[20]周辉,谭云亮,冯夏庭等.岩石破坏过程的物理细胞自动机模型(Ⅱ)—模拟例证[J].岩石力学与工程学报,2002,21(4):782-786.
[21]谭云亮,周辉,王泳嘉等.模拟细观非均质材料破坏演化的物理元胞自动机PCA理论[J].物理学报,2001,(4):704-709.
[22]谭云亮,周辉.模拟岩体破坏演化的新途径—物理细胞自动机理论[J].岩石力学与工程学报,2000(增刊):371-373.
[23]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):368-374.
[24]唐春安.岩石破裂过程中的灾变[M].北京:煤炭工业出版社,1993.26-27.
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