动载作用下复合型裂纹扩展的近场动力学模拟
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摘要
构建改进的非局部近场动力学模型和粒子系统动力加载算法,开展复合型裂纹动力扩展过程模拟。在常规近场动力学微极模型中引入能反映非局部长程力尺寸效应的核函数修正项,以提高计算精度和收敛稳定性。通过模拟动载作用下含复合型裂纹混凝土三点弯梁的裂纹扩展与破坏过程并与试验结果对比,验证了本文模型和算法的可靠性。在此基础上,通过分组模拟分析了动载作用下,初始裂纹的位置、长度和方向对含复合型裂纹三点弯梁破坏模式、起裂时间与承载能力的影响规律。
An improved nonlocal peridynamic model and corresponding dynamic loading algorithms for a particle system have been proposed to simulate mixed-mode crack propagation subjected to dynamic load.A kernel function which could describe the internal length effect of long-range forces was introduced into the regular micropolar peridynamic model in order to improve the calculation accuracy and stability.The model was validated by analyzing the failure of a single-notched three-point bending concrete beam subjected to dynamic load and comparing the simulation results with experiments.A further investigation was taken into the effect of the location and orientation of the crack on the failure mode,cracking time and failure load of the three-point bending beam with pre-existing mixed-mode crack subjected to dynamic load.
An improved nonlocal peridynamic model and corresponding dynamic loading algorithms for a particle system have been proposed to simulate mixed-mode crack propagation subjected to dynamic load.A kernel function which could describe the internal length effect of long-range forces was introduced into the regular micropolar peridynamic model in order to improve the calculation accuracy and stability.The model was validated by analyzing the failure of a single-notched three-point bending concrete beam subjected to dynamic load and comparing the simulation results with experiments.A further investigation was taken into the effect of the location and orientation of the crack on the failure mode,cracking time and failure load of the three-point bending beam with pre-existing mixed-mode crack subjected to dynamic load.
引文
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[6]黄丹,章青,乔丕忠,等.近场动力学方法及其应用[J].力学进展,2010,40(4):448-459.(HUANG Dan,ZHANG Qing,QIAO Pi-zhong,et al.A review on peridynamics(pd)method and its applications[J].Advance in Mechanics,2010,40(4):448-459.(in Chinese))
[7] Silling S A.Reformulation of elasticity theory for discontinuities and long-range forces[J].Journal of the Mechanics and Physics of Solids,2000,48(1):175-209.
[8] Gerstle W H,Sau N,Sakhavand N.On peridynamic computational simulation of concrete structures[J].Special Publication,2009,265:245-264.
[9] Huang D,Lu G D,Wang C W,et al.An extended peridynamic approach for deformation and fracture analysis[J].Engineering Fracture Mechanics,2015,141:196-211.
[10]Kilic B.Peridynamic Theory for Progressive Failure Prediction in Homogeneous and Heterogeneous Materials[D].Tucson:The University of Arizona,2008.
[11]Kilic B,Madenci E.Structural stability and failure analysis using peridynamic theory[J].International Journal of Non-Linear Mechanics,2009,44(8):845-854.
[12]黄丹,卢广达,章青.准静态变形破坏的近场动力学分析[J].计算力学学报,2016,33(5):657-662.(HUANG Dan,LU Guang-da,ZHANG Qing.A peridynamic study on quasi-static deformation and failure[J].Chinese Journal of Computational Mechanics,2016,33(5):657-662.(in Chinese))
[13]Huang D,Zhang Q,Qiao P Z.Damage and progressive failure of concrete structures using non-local peridynamic modeling[J].Science China Technological Science,2011,54(3):591-596.
[14]Huang D,Lu G D,Qiao P Z.An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis[J].International Journal of Mechanical Sciences,2015,94-95:111-122.
[15]Silling S A,Askari E.A meshfree method based on the peridynamic model of solid mechanics[J].Computers&Structures,2005,83(17-18):1526-1535.
[16]Gerstle W,Sau N,Silling S A.Peridynamic modeling of plain and reinforced concrete structures[A].18th International Conference on Structural Mechanics in Reactor Technology(SMiRT18)[C].Beijing,China,2005.
[2] Carmona J R,Ruiz G,del Viso J R.Mixed-mode crack propagation through reinforced concrete[J].Engineering Fracture Mechanics,2007,74(17):2788-2809.
[3] Song J H,Areias P M A,Belytschko T.A method for dynamic crack and shear band propagation with phantom nodes[J].International Journal for Numerical Methods in Engineering,2006,67(6):868-893.
[4]章青,刘宽,夏晓舟,等.广义扩展有限元法及其在裂纹扩展分析中的应用[J].计算力学学报,2012,29(3):427-432.(ZHANG Qing,LIU Kuan,XIA Xiao-zhou,et al.Generalized extended finite element method and its application in crack growth analysis[J].Chinese Journal of Computational Mechanics,2012,29(3):427-432.(in Chinese))
[5] Zhang Z N,Chen Y X.Modeling nonlinear elastic solid with correlated lattice bond cell for dynamic fracture simulation[J].Computer Methods in Applied Mechanics and Engineering,2014,279:325-347.
[6]黄丹,章青,乔丕忠,等.近场动力学方法及其应用[J].力学进展,2010,40(4):448-459.(HUANG Dan,ZHANG Qing,QIAO Pi-zhong,et al.A review on peridynamics(pd)method and its applications[J].Advance in Mechanics,2010,40(4):448-459.(in Chinese))
[7] Silling S A.Reformulation of elasticity theory for discontinuities and long-range forces[J].Journal of the Mechanics and Physics of Solids,2000,48(1):175-209.
[8] Gerstle W H,Sau N,Sakhavand N.On peridynamic computational simulation of concrete structures[J].Special Publication,2009,265:245-264.
[9] Huang D,Lu G D,Wang C W,et al.An extended peridynamic approach for deformation and fracture analysis[J].Engineering Fracture Mechanics,2015,141:196-211.
[10]Kilic B.Peridynamic Theory for Progressive Failure Prediction in Homogeneous and Heterogeneous Materials[D].Tucson:The University of Arizona,2008.
[11]Kilic B,Madenci E.Structural stability and failure analysis using peridynamic theory[J].International Journal of Non-Linear Mechanics,2009,44(8):845-854.
[12]黄丹,卢广达,章青.准静态变形破坏的近场动力学分析[J].计算力学学报,2016,33(5):657-662.(HUANG Dan,LU Guang-da,ZHANG Qing.A peridynamic study on quasi-static deformation and failure[J].Chinese Journal of Computational Mechanics,2016,33(5):657-662.(in Chinese))
[13]Huang D,Zhang Q,Qiao P Z.Damage and progressive failure of concrete structures using non-local peridynamic modeling[J].Science China Technological Science,2011,54(3):591-596.
[14]Huang D,Lu G D,Qiao P Z.An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis[J].International Journal of Mechanical Sciences,2015,94-95:111-122.
[15]Silling S A,Askari E.A meshfree method based on the peridynamic model of solid mechanics[J].Computers&Structures,2005,83(17-18):1526-1535.
[16]Gerstle W,Sau N,Silling S A.Peridynamic modeling of plain and reinforced concrete structures[A].18th International Conference on Structural Mechanics in Reactor Technology(SMiRT18)[C].Beijing,China,2005.