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浙江大学学报(工学版)  2017, Vol. 51 Issue (7): 1324-1330    DOI: 10.3785/j.issn.1008-973X.2017.07.008
土木工程     
近场动力学与有限单元法的混合模型与隐式求解格式
郁杨天, 章青, 顾鑫
河海大学 工程力学系, 江苏 南京 210098
Hybrid model of peridynamics and finite element method under implicit schemes
YU Yang-tian, ZHANG Qing, GU Xin
Department of Engineering Mechanics, Hohai University, Nanjing 210098, China
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摘要:

利用近场动力学方法(PD)在模拟不连续变形问题的独特优势和有限单元法(FEM)的计算效率,提出近场动力学与有限单元法混合建模的方法,并用于求解断裂力学问题.裂纹出现的区域采用改进的近场动力学微观弹脆性(PMB)模型进行离散,其他区域采用有限元离散,通过杆单元连接不同的子区域.在隐式求解体系下实现了两种方法的混合建模,该模型在求解静力学问题时无需引入阻尼项,有效提高了计算效率和计算精度.通过模拟计算简支梁的弹性变形和三点弯曲梁I型裂纹的扩展过程,与理论解吻合良好,验证了提出的混合模型和求解方法的准确性和有效性.

Abstract:

A hybrid model of peridynamics (PD) and finite element method (FEM) was proposed and applied to solve problems of fracture mechanics in order to combine the unique advantage of PD in solving discontinuities and the computational efficiency of FEM. The improved prototype microelastic brittle (PMB) model of peridynamics was utilized for the regions where material failure was expected. The region without failure was discretized by FEM. The truss element was introduced to bridge peridynamic subregions and finite element subregions. The hybrid model is based on the implicit schemes, and it need not consider a fictitious damping term in solving static problems. The computational efficiency and accuracy of the model were improved. The static elastic deformation of a simply supported beam and the propagation process of mode I fracture in a three points bend beam were simulated to verify the accuracy and utility of the presented model. Results obtained by the model agreed well with the theoretical solutions.

收稿日期: 2016-04-09 出版日期: 2017-07-08
CLC:  TU375  
基金资助:

国家自然科学基金资助项目(11372099,11132003);江苏省自然科学基金资助项目(BK20151493)

通讯作者: 章青,男,教授.ORCID:0000-0002-2819-5976.     E-mail: lxzhangqing@hhu.edu.cn
作者简介: 郁杨天(1992—),男,硕士生,从事灾变破坏力学的研究.ORCID:0000-0002-6397-4158.E-mail:yuyangtian@hhu.edu.cn
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引用本文:

郁杨天, 章青, 顾鑫. 近场动力学与有限单元法的混合模型与隐式求解格式[J]. 浙江大学学报(工学版), 2017, 51(7): 1324-1330.

YU Yang-tian, ZHANG Qing, GU Xin. Hybrid model of peridynamics and finite element method under implicit schemes. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2017, 51(7): 1324-1330.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2017.07.008        http://www.zjujournals.com/eng/CN/Y2017/V51/I7/1324

[1] MUROTANI K, YAGAWA G, CHOI J B. Adaptivefinite elements using hierarchical mesh and its application to crack propagation analysis [J]. Computer Methods in Applied Mechanics and Engineering, 2013, 253: 1-14.
[2] CAMACHO G T, ORTIZ M. Computational modeling of impact damage in brittle materials [J]. International Journal of Solids and Structures, 1996, 33(20):2899-2938.
[3] XU X P, NEEDLEMAN A. Numerical simulations of fast crack growth in brittle solids [J]. Journal of the Mechanics and Physics of Solids, 1994, 42(9):1397-1434.
[4] 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.
[5] SILLING S A, EPTON M, WECKNER O, et al. Peridynamic states and constitutive modeling [J]. Journal of Elasticity, 2007, 88(2): 151-184.
[6] SILLING S A. Linearized theory of peridynamic states [J]. Journal of Elasticity, 2010, 99(1): 85-111.
[7] SILLING S A, BOBARU F. Peridynamic modeling of membranes and fibers [J]. International Journal of Nonlinear Mechanics, 2005, 40(2): 395-409.
[8] GERSTLE W, SAU N, SILLING S. Peridynamic modeling of concrete structures [J]. Nuclear Engineering and Design, 2007, 237(12): 1250-1258.
[9] ASKARI E, BOBARU F, LEHOUCQ R B, et al. Peridynamics for multiscale materials modeling [C]//Journal of Physics: Conference Series. [S. l.]: IOP Publishing, 2008, 125(1): 012078.
[10] XU J, ASKARI A, WECKNER O, et al. Peridynamic analysis of impact damage in composite laminates [J]. Journal of Aerospace Engineering, 2008, 21(3):187-194.
[11] 沈峰,章青,黄丹,等.冲击荷载作用下混凝土结构破坏过程的近场动力学模拟[J].工程力学,2012(增1): 12-15. SHEN Feng, ZHANG Qing, HUANG Dan, et al. Peridynamics modeling of failure process of concrete structure subjected to impact loading [J]. Engineering Mechanics, 2012(supple.1): 12-15.
[12] 胡祎乐,余音,汪海.基于近场动力学理论的层压板损伤分析方法[J].力学学报,2013,45(4): 624-628. HU Yi-le, YU Yin, WANG Hai. Damage analysis method for laminates based on peridynamic theory [J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(4): 624-628.
[13] 谷新保,周小平. 含圆孔拉伸板的近场动力学数值模拟[J]. 固体力学学报, 2015, 36(5): 376-383. GU Xin-bao, ZHOU Xiao-ping. The numerical simulation of tensile plate with circular hole using peridynamic theory [J]. Chinese Journal of Solid Mechanics, 2015, 36(5): 376-383.
[14] 郁杨天,章青,顾鑫.含单边缺口混凝土梁破坏的近场动力学模拟[J].工程力学,2016,33(12):80-85. YV Yang-tian, ZHANG Qing, GU Xin. Impact failure simulation of a single-edged notched concrete beam based on peridynamics [J]. Engineering Mechanics, 2016, 33(12): 80-85.
[15] LAI X, REN B, FAN H, et al. Peridynamics simulations of geomaterial fragmentation by impulse loads [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2015, 39(12): 1304-1330.
[16] LAI X, LIU L S, LIU Q W, et al. Slope stabilityanalysis by peridynamic theory [C]//Applied Mechanics and Materials. [S. l.]: Trans Tech Publications, 2015, 744: 584-588.
[17] ZHOU X P, GU X B, WANG Y T. Numerical simulations of propagation, bifurcation and coalescence of cracks in rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2015, 80: 241-254.
[18] REN B, FAN H, BERGEL G L, et al. A peridynamics-SPH coupling approach to simulate soil fragmentation induced by shock waves [J]. Computational Mechanics, 2015, 55(2): 287-302.
[19] FAN H, BERGEL G L, LI S. A hybrid peridynamics-SPH simulation of soil fragmentation by blast loads of buried explosive [J]. International Journal of Impact Engineering, 2016, 87: 14-27.
[20] MACEK R W, SILLING S A. Peridynamics via finite element analysis [J]. Finite Elements in Analysis and Design, 2007, 43(15): 1169-1178.
[21] KILIC B, MADENCI E. Coupling of peridynamic theory and the finite element method [J]. Journal of Mechanics of Materials and Structures, 2010, 5(5):707-733.
[22] LIU W, HONG J W. A coupling approach of discretized peridynamics with finite element method [J]. Computer Methods in Applied Mechanics and Engineering, 2012, 245: 163-175.
[23] HUANG D, LU G, QIAO P. An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis [J]. International Journal of Mechanical Sciences, 2015, 94: 111-122.
[24] AZIZI M A B. The peridynamic model of viscoelastic creep and recovery [J]. Multidiscipline Modeling in Materials and Structures, 2015, 11(4):579-597.
[25] MADENCI E, OTERKUS S. Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening [J]. Journal of the Mechanics and Physics of Solids, 2015, 86: 192-219.
[26] GHAJARI M, IANNUCCI L, CURTIS P. A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media [J]. Computer Methods in Applied Mechanics and Engineering, 2014,276(7): 431-452.
[27] SILLING S A, ASKARI E. A meshfree method based on the peridynamic model of solid mechanics [J]. Computers and Structures, 2005, 83(17): 1526-1535.
[28] HUANG D, LU G, WANG C, et al. An extended peridynamic approach for deformation and fractureanalysis [J]. Engineering Fracture Mechanics, 2015, 141: 196-211.
[29] 铁摩辛柯.弹性理论[M].北京:高等教育出版社,1990: 100-107.
[30] JENQ Y S, SHAH S P. Mixed-mode fracture of concrete [J]. International Journal of Fracture, 1988,38(2): 123-142.
[31] JOHN R, SHAH S P. Mixed-mode fracture of concrete subjected to impact loading [J]. Journal of Structural Engineering, 1990, 116(3): 585-602.

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