无厚度三节点节理单元在裂纹扩展模拟中的应用
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摘要
节理厚度在实际工程中很难用常量描述,为便于描述节理的力学行为,在原三节点节理单元的基础上构造无厚度三节点节理单元,并推导出相应的刚度矩阵。由于三节点节理单元与原三角形单元共享节点,因而它在模拟裂纹扩展过程中无需对网格进行重新划分;另外,在网格剖分时,也无需考虑裂纹体的几何完整性,可直接对结构进行三角网格剖分。因此,该方法可为裂纹的模拟提供极大的便利,并显著提高计算效率。相应的大理石模拟试验表明,该方法在岩石裂纹扩展的模拟中是有效可行的。
It is difficult to describe the thickness of joint with a constant in practical engineering.In order to model the mechanical behaviors of joints conveniently,a non-thickness three-node joint element is proposed on the basis of the existed three-node joint element;and the stiffness matrix of non-thickness three-node element is deduced.For it shares the same nodes with original three-node triangle element,the non-thickness three-node joint element is adopted to model crack propagation without remeshing or adjustment of the original mesh.Another advantage is that the cracked body is meshed without considering its geometry integrity and the existence of joints or pre-existed crack in the procedure of mesh generation;and then the triangular element intersected by crack or joint is automatically transformed into the three-node joint element to represent pre-existed cracks.These make the numerical simulation of crack propagation highly convenient and efficient.After the maximum strain failure criterion is chosen to determine whether the element is intersected by the extended crack or not,the extended crack is located in the model based on hypothesis of the direction of crack propagation perpendicular to the direction of the extended crack passing through the centroid of the triangle element.By simulating the marble plates with double parallel cracks subjected to uniaxial compressive loads,it is shown that the simulated results are in good agreement with the experimental results,so as to show that the present method is valid and feasible in rock crack propagation simulation.
It is difficult to describe the thickness of joint with a constant in practical engineering.In order to model the mechanical behaviors of joints conveniently,a non-thickness three-node joint element is proposed on the basis of the existed three-node joint element;and the stiffness matrix of non-thickness three-node element is deduced.For it shares the same nodes with original three-node triangle element,the non-thickness three-node joint element is adopted to model crack propagation without remeshing or adjustment of the original mesh.Another advantage is that the cracked body is meshed without considering its geometry integrity and the existence of joints or pre-existed crack in the procedure of mesh generation;and then the triangular element intersected by crack or joint is automatically transformed into the three-node joint element to represent pre-existed cracks.These make the numerical simulation of crack propagation highly convenient and efficient.After the maximum strain failure criterion is chosen to determine whether the element is intersected by the extended crack or not,the extended crack is located in the model based on hypothesis of the direction of crack propagation perpendicular to the direction of the extended crack passing through the centroid of the triangle element.By simulating the marble plates with double parallel cracks subjected to uniaxial compressive loads,it is shown that the simulated results are in good agreement with the experimental results,so as to show that the present method is valid and feasible in rock crack propagation simulation.
引文
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[15]周维垣,杨强.岩石力学数值计算方法[M].北京:中国电力出版社,2005.(ZHOU Weiyuan,YANG Qiang.Numerical computational methods for rock mechanics[M].Beijing:China Electric Power Press,2005.(in Chinese))
[16]陈枫.岩石压剪断裂的理论与试验研究[博士学位论文][D].长沙:中南大学,2002.(CHEN Feng.The theoretical and experimental investigation on rock fracture due to shear-compression loading[Ph.D.Thesis][D].Changsha:Central South University,2002.(in Chinese))
[2]CHOWDHURY S R,NARASIMHAN R.A cohesive finite element formulation for modelling fracture and delamination in solids[J].Sadhana,2000,25(6):561-587.
[3]杨庆生,杨卫.断裂过程的有限元模拟[J].计算力学学报,1997,14(4):407-412.(YANG Qingsheng,YANG Wei.Finite element simulation of fracture process[J].Chinese Journal of Computational Mechanics,1997,14(4):407-412.(in Chinese))
[4]邱峰,丁桦.具有单元分裂功能的间断有限元方法[J].力学与实践,2006,28(4):54-59.(QIU Feng,DING Hua.Element splittingtechnique in discontinuous finite element method[J].Mechanics and Engineering,2006,28(4):54-59.(in Chinese))
[5]SOUIYAH M,ALSHOAIBI A,MUCHTAR A,et al.Finite element model for linear-elastic mixed mode loading using adaptive mesh strategy[J].Journal of Zhejiang University(Science A),2008,9(1):32-37.
[6]BOUCHARD P O,BAY F,CHASTEL Y.Numerical modelling of crack propagation:automatic remeshing and comparison of different criteria[J].Computer Methods in Applied Mechanics and Engineering,2003,192(35/36):3887-3908.
[7]唐春安,黄明利,张国民,等.岩石介质中多裂纹扩展相互作用及其贯通机制的数值模拟[J].地震,2001,21(2):53-58.(TANG Chun′an,HUANG Mingli,ZHANG Guomin,et al.Numerical simulation on propagation,interaction and coalescence of multi-cracks in rocks[J].Earthquake,2001,21(2):53-58.(in Chinese))
[8]BELYTSCHKO T,BLACK T.Elastic crack growth in finite elements with minimal remeshing[J].International Journal for Numerical Methods in Engineering,1999,45(5):601-602.
[9]BELYTSCHKO T,MOES N,USUI S,et al.Arbitrary discontinuities in finite elements[J].International Journal for Numerical Methods in Engineering,2001,50(4):993-1013.
[10]BABUSKA I,MELENK J M.The partition of unity method[J].International Journal for Numerical Methods in Engineering,1997,40(4):727-758.
[11]ZHANG Z N,CHEN Y Q.Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds[J].International Journal of Rock Mechanics and Minging Sciences,2009,46(6):1010-1022.
[12]张振南,陈永泉.一种模拟节理岩体破坏的新方法:单元劈裂法[J].岩土工程学报,2009,31(12):1858-1865.(ZHANG Zhennan,CHEN Yongquan.Novel numerical approach to jointed rock mass simulation:element partition method[J].Chinese Journal of Geotechnical Engineering,2009,31(12):1858-1865.(in Chinese))
[13]张振南,葛修润.二点接触单元法及其数值验证[J].岩石力学与工程学报,2005,24(14):2560-2564.(ZHANG Zhennan,GE Xiurun.Two-node contact element method and its numerical validation[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(14):2560-2564.(in Chinese))
[14]葛修润,任建喜,蒲毅彬,等.岩土损伤力学宏细观试验研究[M].北京:科学出版社,2004.(GE Xiurun,REN Jianxi,PU Yibin,et al.Macro-and micro-scopic experimental studies on damage mechanics of rock and soil[M].Beijing:Science Press,2004.(in Chinese))
[15]周维垣,杨强.岩石力学数值计算方法[M].北京:中国电力出版社,2005.(ZHOU Weiyuan,YANG Qiang.Numerical computational methods for rock mechanics[M].Beijing:China Electric Power Press,2005.(in Chinese))
[16]陈枫.岩石压剪断裂的理论与试验研究[博士学位论文][D].长沙:中南大学,2002.(CHEN Feng.The theoretical and experimental investigation on rock fracture due to shear-compression loading[Ph.D.Thesis][D].Changsha:Central South University,2002.(in Chinese))
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