Volume 44 Issue 4
Apr.  2023
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CHENG Jiahe, GU Xin, ZHANG Qing. Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond-Based Peridynamics[J]. Applied Mathematics and Mechanics, 2023, 44(4): 394-405. doi: 10.21656/1000-0887.430338
Citation: CHENG Jiahe, GU Xin, ZHANG Qing. Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond-Based Peridynamics[J]. Applied Mathematics and Mechanics, 2023, 44(4): 394-405. doi: 10.21656/1000-0887.430338

Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond-Based Peridynamics

doi: 10.21656/1000-0887.430338
  • Received Date: 2022-10-25
  • Rev Recd Date: 2023-01-07
  • Publish Date: 2023-04-01
  • The peridynamics (PD) as an integral non-local continuum mechanics theory, is widely used in the discontinuous deformation and failure analyses of solid materials and structures, mainly with the explicit dynamic solution method for meshless particles. In recent years, the discontinuous Galerlin finite element method for weak-form peridynamic equations has been developed. This method can not only describe the non-local action effects and discontinuous deformation characteristics of the investigated body, but also make full use of the finite element method. It has the advantages of efficient solution, direct application of local boundary conditions, and effective avoidance of the surface effects in peridynamics. The basic principle of the discontinuous Galerkin finite element method of bond-based peridynamics was expounded, the calculation formula was derived, the specific algorithm flowchart and details were given, and the dynamic cracking and bifurcation problems of brittle glass plates were simulated. The damage processes of concrete slabs under blast impact loads were calculated and analyzed. The research results show that, the proposed method can predict the complex rupture mode and the damage process of the structure under blast impact loads, with high computational efficiency, and makes an effective way to the simulation of the structural blast damage effects.
  • (Contributed by ZHANG Qing, M. AMM Editorial Board)
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  • [1]
    胡嘉辉, 吴昊, 方秦. 近区爆炸作用下砌体填充墙损伤破坏与动态响应的数值模拟[J]. 振动与冲击, 2021, 40(9): 1-11. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202109002.htm

    HU Jiahui, WU Hao, FANG Qin. Numerical simulation of damage and dynamic response of masonryinfilled wall under near zone explosion[J]. Journal of Vibration and Shock, 2021, 40(9): 1-11. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ202109002.htm
    师燕超, 李忠献, 郝洪. 爆炸荷载作用下钢筋混凝土框架结构的连续倒塌分析[J]. 解放军理工大学学报(自然科学版), 2007, 8(6): 652-658. https://www.cnki.com.cn/Article/CJFDTOTAL-JFJL200706018.htm

    SHI Yanchao, LI Zhongxian, HAO Hong. Numerical analysis of progressive collapse of reinforced concrete frame under blast loading[J]. Journal of PLA University of Science and Technology, 2007, 8(6): 652-658. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JFJL200706018.htm
    顾鑫, 章青. 爆炸荷载作用下大坝破坏分析的数值模拟研究进展[J]. 河海大学学报(自然科学版), 2017, 45(1): 45-55. https://www.cnki.com.cn/Article/CJFDTOTAL-HHDX201701007.htm

    GU Xin, ZHANG Qing. Progress in numerical simulation of dam failure under blast loading[J]. Journal of Hohai University(Natural Sciences), 2017, 45(1): 45-55. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HHDX201701007.htm
    宁建国, 王猛. 关于计算爆炸力学的进展与现状[J]. 力学与实践, 2012, 34(1): 10-19. https://www.cnki.com.cn/Article/CJFDTOTAL-LXYS201201006.htm

    NING Jianguo, WANG Meng. Review on computational explosion mechanics[J]. Mechanics in Engineering, 2012, 34(1): 10-19. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXYS201201006.htm
    RUWAN J, DAVID P T, NIMAL J P. Blast and residual capacity analysis of reinforced concrete framed buildings[J]. Engineering Structures, 2011, 33(12): 3483-3495. doi: 10.1016/j.engstruct.2011.07.011
    XU K, LU Y. Numerical simulation study of spallation in reinforced concrete plates subjected to blast loading[J]. Computers & Structures, 2006, 84(5/6): 431-438.
    朱劲松, 邢扬. 爆炸荷载作用下城市桥梁动态响应及其损伤过程分析[J]. 天津大学学报(自然科学与工程技术版), 2015, 48(6): 510-519. https://www.cnki.com.cn/Article/CJFDTOTAL-TJDX201506006.htm

    ZHU Jingsong, XING Yang. Dynamic response and damage process analysis of urban bridge subjected to blast load. [J]. Journal of Tianjin University(Science and Technology), 2015, 48(6): 510-519. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TJDX201506006.htm
    辛春亮, 薛再清. TrueGrid和LS-DYNA动力学数值计算详解[M]. 北京: 机械工业出版社, 2019.

    XIN Chunliang, XUE Zaiqing. TrueGrid and LS-DYNA Dynamics Numerical Calculation Details[M]. Beijing: China Machine Press, 2019. (in Chinese)
    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. doi: 10.1016/S0022-5096(99)00029-0
    SILLING S A, EPTON M, WECKNER O. Peridynamic states and constitutive modeling[J]. Journal of Elasticity. 2007, 88(2): 151-184. doi: 10.1007/s10659-007-9125-1
    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. https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201004007.htm

    HUANG Dan, ZHANG Qing, QIAO Pizhong, et al. A review on peridynamics(PD) method and its application[J]. Advances in Mechanics, 2010, 40(4): 448-459. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201004007.htm
    周保良, 李志远, 黄丹. 二维瞬态热传导的PDDO分析[J]. 应用数学和力学, 2022, 43(6): 660-668. doi: 10.21656/1000-0887.420150

    ZHOU Baoliang, LI Zhiyuan, HUANG Dan. PDDO analysis of 2D transient heat conduction problems[J]. Applied Mathematics and Mechanics, 2022, 43(6): 660-668. (in Chinese) doi: 10.21656/1000-0887.420150
    KILIC B, AGWAI A, MADENCI E. Peridynamic theory for progressive damage prediction in center-cracked composite laminates[J]. Composite Structures, 2009, 90(2): 141-151. doi: 10.1016/j.compstruct.2009.02.015
    章青, 顾鑫, 郁杨天. 冲击载荷作用下颗粒材料动态力学响应的近场动力学模拟[J]. 力学学报, 2016, 48(1): 64-71. doi: 10.3969/j.issn.1006-6616.2016.01.006

    ZHANG Qing, GU Xin, YU Yangtian. Peridynamics simulation for dynamic response of granular materials under impact loading[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 56-63. (in Chinese) doi: 10.3969/j.issn.1006-6616.2016.01.006
    张尚元, 聂玉峰, 李义强. RBF-PU方法求解二维非局部扩散问题和近场动力学问题[J]. 应用数学和力学, 2022, 43(6): 608-618. doi: 10.21656/1000-0887.420295

    ZHANG Shangyuan, NIE Yufeng, LI Yiqiang. The RBF-PU method for solving 2D nonlocal diffusion and peridynamic equations[J]. Applied Mathematics and Mechanics, 2022, 43(6): 608-618. (in Chinese) doi: 10.21656/1000-0887.420295
    HAN F, LUBINEAU G, AZDOUD Y. Adaptive coupling between damage mechanics and peridynamics: a route for objective simulation of material degradation up to complete failure[J]. Journal of the Mechanics and Physics of Solids, 2016, 94: 453-472. doi: 10.1016/j.jmps.2016.05.017
    DU Q, ZHOU K. Mathematical analysis for the peridynamic nonlocal continuum theory[J]. ESAIM: Mathematical Modelling and Numerical Analysis, 2011, 45(2): 217-234. doi: 10.1051/m2an/2010040
    XU F F, GUNZBURGER M, BURKARDT J. A multiscale method for nonlocal mechanics and diffusion and for the approximation of discontinuous functions[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 307: 117-143. doi: 10.1016/j.cma.2016.04.020
    AZDOUD Y. A hybrid local/non-local framework for the simulation of damage and fracture[D]. PhD Thesis. Thuwal: King Abdullah University of Science and Technology, 2014.
    CHEN X, GUNZBURGER M. Continuous and discontinuous finite element methods for a peridynamics model of mechanics[J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(9/12): 1237-1250.
    AKSOY H G, SENOCAK E. Discontinuous Galerkin method based on peridynamic theory for linear elasticity[J]. International Journal for Numerical Methods in Engineering, 2011, 88(7): 673-692. doi: 10.1002/nme.3196
    REN B, WU C T, ASKARI E. A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis[J]. International Journal of Impact Engineering, 2017, 99: 14-25. doi: 10.1016/j.ijimpeng.2016.09.003
    REN B, WU C T, SELESON P, et al. A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations[J]. International Journal of Fracture, 2018, 214(1): 49-68. doi: 10.1007/s10704-018-0317-4
    MADENCI E, OTERKUS E. Peridynamic theory and its applications[M]. New York: Springer, 2014.
    TIAN X C, DU Q. Nonconforming discontinuous Galerkin methods for nonlocal variational problems[J]. SIAM Journal on Numerical Analysis, 2015, 53(2): 762-781. doi: 10.1137/140978831
    HA D, BOBARU F. Studies of dynamic crack propagation and crack branching with peridynamics[J]. International Journal of Fracture, 2010, 162(1): 229-244.
    WANG W, ZHANG D, LU F Y, et al. Experimental study on scaling the explosion resistance of a one-way square reinforced concrete slab under a close-in blast loading[J]. International Journal of Impact Engineering, 2012, 49: 158-164.
    KINGERY C N, BULMASH G. Airblast parameters from TNT spherical air burst and hemispherical surface burst: ARBRL-TR-02555[R]. Maryland: Defence Technical Information Center, Ballistic Research Laboratory, Aberdeen Proving Ground, 1984.
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