近场动力学理论在脆性材料波散射与裂纹扩展问题的数值模拟
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摘要
近场动力学(peridynamics,PD)是一个物质点具有通用积分运动方程的连续介质理论,其非局部思想能够很好地处理和解决传统连续介质力学在裂纹尖端解的奇异性问题,也弥补了有限元法(FEM)在断裂问题上网格重构的缺陷,在研究材料的断裂与损伤方面有着独特的优势。基于固体力学和断裂力学理论在应力波传播的研究基础上,通过对比传统波动理论和PD理论中P波的传递速度、传递半径及受载出现的波反射和绕射现象,提出近场力波的概念,从本质上分析了近场力波与应力波传递的区别。用PD理论对含预制缺陷的脆性材料(混凝土)动态断裂过程进行数值模拟,通过分析C15混凝土受冲击载荷断裂过程的能量释放速率,得出近场力波的传递会对裂纹的萌生和扩展产生影响。
Peridynamics( PDs) is a continuous medium theory that material points have a general integral vibration equation,whose non-local thought can deal with the singular problem of traditional continuous media mechanics in crack tip solution. In PD theory,the defect of mesh reconstruction when the finite element method( FEM) was used to solve the fracture problem is compensated. There is a unique advantage in studying the fracture and damage of materials when using PD theory. Based on traditional solid mechanics and fracture mechanics in the study of stress wave,some characteristics of P wave were compared and analyzed,such as velocity,transmission radius,wave reflection and diffraction phenomenon. Then the concept of peridynamic force wave is proposed. Essentially,the difference between peridynamic force wave and stress wave was analyzed. The numerical simulation of wave scattering during the fracture process of the brittle material( concrete) with prefabricated defect was implemented and the energy release rate of C15 concrete during fracture process was analyzed,and the transmission of peridynamic force wave can affect the crack initiation and propagation was found.
Peridynamics( PDs) is a continuous medium theory that material points have a general integral vibration equation,whose non-local thought can deal with the singular problem of traditional continuous media mechanics in crack tip solution. In PD theory,the defect of mesh reconstruction when the finite element method( FEM) was used to solve the fracture problem is compensated. There is a unique advantage in studying the fracture and damage of materials when using PD theory. Based on traditional solid mechanics and fracture mechanics in the study of stress wave,some characteristics of P wave were compared and analyzed,such as velocity,transmission radius,wave reflection and diffraction phenomenon. Then the concept of peridynamic force wave is proposed. Essentially,the difference between peridynamic force wave and stress wave was analyzed. The numerical simulation of wave scattering during the fracture process of the brittle material( concrete) with prefabricated defect was implemented and the energy release rate of C15 concrete during fracture process was analyzed,and the transmission of peridynamic force wave can affect the crack initiation and propagation was found.
引文
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19 Leslie J R,Cheeseman W J.An ultrasonic method for studying deterioration and cracking in concrete structures[J].American Concrete Institute Proceedings,1949,46(1):208-210
20吕小彬,吴佳晔.冲击弹性波理论与应用[M].北京:中国水利水电出版社,2016Lv Xiaobin,Wu Jiaye.Impact elastic wave theory and application[M].Beijing:China Water Conservancy and Hydropower Press,2016
21 Yu K B.Enhanced integration method for the peridynamic theory[D].Manhattan:Kansas State University,2011
22杨立云,许鹏,郭东明,等.新型数字激光动光弹性实验技术在爆炸力学中的应用[J].科技导报,2013,31(15):27-30Yang Liyun,Xu Peng,Guo Dongming,et al.Dynamic photo elasticity method combined with laser and digital ultra high-speed camera and its applications in blasting mechanics[J].Science and Technology Review,2013,31(15):27-30
2 Narendar S.Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory[J].Applied Mathematical Modelling,2012,36(9):4529-4538
3曾新吾,韩开锋,张光莹.含裂缝介质中的弹性波传播特性[M].北京:科学出版社,2013:7-8Zeng Xinwu,Han Kaifeng,Zhang Guangying.Elastic wave propagation in fractured media[M].Beijing:Science Press,2013:7-8
4 Alterman Z S,Loewenthal D.Seismic wave in a quarter and three quarter plane[J].Geophysical Journal of the Royal Astronomical Society,1970,20:101-126
5张光莹,曾新吾.伪谱法模拟各向异性/非均匀介质中弹性波的传播[J].国防科技大学学报,2002,24(3):18-22Zhang Guangying,Zeng Xinwu.Numerical modeling of elastic waves propagating in the anisotropic/heterogeneous media by the pseudospectral method[J].Journal of National University of Defense Technology,2002,24(3):18-22
6韩开锋,尹梓安.间接边界元法模拟含裂纹介质中弹性波的传播[J].国防科技大学学报,2005,27(3):92-95Han Kaifeng,Yin Zian.Numerical modeling of elastic waves propagating in cracked media by the indirect BEM[J].Journal of National University of Defense Technology,2005,27(3):92-95
7白象元,张永彬,钟波波.应力波作用下含颗粒脆性材料裂纹扩展数值模拟[J].地下空间与工程学报,2015,11(2):469-497Bai Xiangyuan,Zhang Yongbin,Zhong Bobo.Numerical simulation of crack propagation in brittle material with granule under dynamic loading[J].Chinese Journal of Underground Space and Engineering,2015,11(2):469-497
8杨仁树,许鹏.节理岩体中爆炸应力波传播规律的研究[J].金属矿山,2016,480(6):49-54Yang Renshu,Xu Peng.Study of regularity of explosive stress wave propagation in jointed rock mass[J].Metal Mine,2016,480(6):49-54
9赵跃堂,梁晖,范斌.饱和土中爆炸波传播问题的数值模拟[J].爆炸与冲击,2007,27(4):352-357Zhao Yuetang,Liang Hui,Fan Bin.Numerical simulation of explosion wave propagation in the saturated soil[J].Explosion and Shock Waves,2007,27(4):352-357
10 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
11 Silling S A,Eption M,Weckner.Peridynamics states and constitutive modeling[J].Journal of Elasticity,2007,88(2):151-184
12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):448-459Huang Dan,Zhang Qing,Qiao Pizhong,et al.A review on peridynamics(PD)method and its applications[J].Advances in Mechanics,2010,40(4):448-459
13 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
14石宏顺,钱松荣,原群盛,等.基于近场动力学理论的准脆性材料的本构力函数的构建[J].计算力学学报,2017,34(4):422-427Shi Hongshun,Qian Songrong,Yuan Qunsheng,et al.Construction of the constitutive force function of quasi-brittle material based on the peridynamic theory[J].Journal of Computational Mechanics,2017,34(4):422-427
15胡祎乐.基于近场动力学的FRP层压板建模与分析[D].上海:上海交通大学,2013Hu Yile.Peridynamic modeling and analysis of FRP laminates[D].Shanghai:Shanghai Jiaotong University,2013
16谷新保.近场动力学理论及其在岩石类材料变形破坏过程的数值模拟[D].重庆:重庆大学,2015Gu Xinbao.Peridynamic theory and its numerical simulation in the deformation and damage process of the rock-like materials[D].Chongqing:Chongqing University,2015
17 Silling S A,Askari E.Peridynamic modeling of impact damage[J].ASME/JSME 2004 Pressure Vessels and Piping Conference,2004,489:197-205
18 Silling S A,Askari E.A meshfree method based on the peridynamic model of solid mechanics[J].Computers and Structures,2005,83(17-18):1526-1535
19 Leslie J R,Cheeseman W J.An ultrasonic method for studying deterioration and cracking in concrete structures[J].American Concrete Institute Proceedings,1949,46(1):208-210
20吕小彬,吴佳晔.冲击弹性波理论与应用[M].北京:中国水利水电出版社,2016Lv Xiaobin,Wu Jiaye.Impact elastic wave theory and application[M].Beijing:China Water Conservancy and Hydropower Press,2016
21 Yu K B.Enhanced integration method for the peridynamic theory[D].Manhattan:Kansas State University,2011
22杨立云,许鹏,郭东明,等.新型数字激光动光弹性实验技术在爆炸力学中的应用[J].科技导报,2013,31(15):27-30Yang Liyun,Xu Peng,Guo Dongming,et al.Dynamic photo elasticity method combined with laser and digital ultra high-speed camera and its applications in blasting mechanics[J].Science and Technology Review,2013,31(15):27-30