IMPROVEMENT OF THE TOTAL LAGRANGIAN SPH AND ITS APPLICATION IN IMPACT PROBLEMS

Wang Lu; Xu Fei; Yang Yang

doi:10.6052/0459-1879-22-214

Volume 54 Issue 12

Dec. 2022

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Theoretical and Applied Mechanics > 2022 > 54(12): 3297-3309. > DOI: 10.6052/0459-1879-22-214 CSTR: 32045.14.0459-1879-22-214

Wang Lu, Xu Fei, Yang Yang. Improvement of the total Lagrangian SPH and its application in impact problemS. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3297-3309. DOI: 10.6052/0459-1879-22-214

Citation:

PDF (4360 KB)

IMPROVEMENT OF THE TOTAL LAGRANGIAN SPH AND ITS APPLICATION IN IMPACT PROBLEMS

Wang Lu^*,,
Xu Fei^†,
Yang Yang^†

*.
School of Civil Engineering, Chang’an University, Xi’an 710061, China
†.
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

Received Date: May 22, 2022
Accepted Date: August 09, 2022
Available Online: August 10, 2022

Graphical Abstract

Abstract

Abstract

SPH (smoothed particle hydrodynamics) has its natural advantages in dealing with the large deformation of the material, fracture and crack propagation due to the absence of mesh distortion. However, the tensile instability which is an inherent defect encountered in the conventional SPH, is an obstacle for further applying SPH in computational solid mechanics. TL-SPH (total Lagrangian-SPH) is an effective measure to improve the tensile instability, but it still faces some defects. For example, the accuracy may be not enough at the boundary region for the truncated supported domain of the particle. The interface conditions are difficult to be implemented strictly, and the crack propagation cannot be presented under the Total Lagrangian frame. So, first of all, TL-SPH is coupled with the high-order SPH method, which can achieve second-order accuracy. Moreover, the high-order method is simplified by reducing the number of neighbor particles to save the calculational cost, and TL-SFPM (TL-simplified finite particle method) method is proposed with a reasonable neighbor particles selection mode. Secondly, TL-SPH method is combined with the DFPM (discontinuous finite particle method), which can improve the accuracy of the interface. A contact algorithm based on the Riemann solution is proposed by establishing the Riemann model between two particles with different materials. Then the fluid-solid contact algorithm and the solid-solid contact algorithm are introduced, respectively. Moreover, to capture the damage form of the solid under external load, a particle damage model based on the total Lagrangian frame is proposed. Finally, the rationality and accuracy of the proposed TL-SFPM method, the contact algorithm and the damage model are verified by cases of the fluid-solid impact and solid-solid impact, which further extends the application of TL-SPH method in the calculation of solid impact problems. The results of the dam break with an elastic baffle and the bullet impacting target plate also demonstrate the algorithms proposed in this paper has a wide application prospect for simulation of fluid-solid interaction and solid impact problems.
- total Lagrangian SPH,
- tensile instability,
- Riemann contact,
- impact,
- simulation accuracy

FullText(HTML)

References (40)

References

[1]	杨秀峰, 刘谋斌. 光滑粒子动力学SPH方法应力不稳定性的一种改进方案. 物理学报, 2012, 61(22): 224701 (Yang Xiufeng, Liu Moubin. Improvement on stress instability in smoothed particle hydrodynamics. Acta Physica Sinica, 2012, 61(22): 224701 (in Chinese) doi: 10.7498/aps.61.224701
[2]	Salehizadeh AM, Shafiei AR. A coupled ISPH-TLSPH method for simulating fluid-elastic structure interaction problems. Journal of Marine Science and Application, 2022, 21: 15-36 doi: 10.1007/s11804-022-00260-3
[3]	Swegle JW, Hicks DL, Attaways SW. Smoothed Particle Hydrodynamics stability analysis. Journal of Computational Physics, 1995, 116: 123-134 doi: 10.1006/jcph.1995.1010
[4]	Chen JK, Beraun JE. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problem. Computer Methods in Applied Mechanics and Engineering, 2000, 190(1): 225-239
[5]	Liu MB, Liu GR. Restoring particle consistency in smoothed particle hydrodynamics. Applied Numerical Mathematics, 2006, 56(1): 19-36 doi: 10.1016/j.apnum.2005.02.012
[6]	Colagrossi A, Landrini M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics. Journal of Computational Physics, 2003, 191(2): 448-475 doi: 10.1016/S0021-9991(03)00324-3
[7]	张建伟, 主攀, 陈海舟等. 基于光滑粒子流体动力学方法的表中孔泄流模拟. 水电能源科学, 2022, 40(3): 136-139 (Zhang Jianwei, Zhu Pan, Chen Haizhou, et al. Simulation of discharge from middle surface hole based on Smoothed Particle Hydrodynamics method. Water Resources and Power, 2022, 40(3): 136-139 (in Chinese)
[8]	Zheng X, Tian ZZ, Xie ZG, et al. Numerical study of the ice breaking resistance of the icebreaker in the yellow river through smoothed-particle hydrodynamics. Journal of Marine Science and Application, 2022, 21: 1-14
[9]	杨波, 欧阳洁, 蒋涛. PTT黏弹性流体的光滑粒子动力学方法模拟. 力学学报, 2011, 43(4): 667-673 (Yang Bo, Ouyang Jie, Jiang Tao. Numerical simulation of the viscoelastic flows for PTT model by the SPH method. Chinese Journal of Theoretical and Applied Mechani, 2011, 43(4): 667-673 (in Chinese) doi: 10.6052/0459-1879-2011-4-lxxb2010-223
[10]	Belytschko T, Guo Y, Liu WK, et al. A unified stability analysis of meshless particle methods. International Journal for Numerical Methods in Engineering, 2000, 48: 1359-1400 doi: 10.1002/1097-0207(20000730)48:9<1359::AID-NME829>3.0.CO;2-U
[11]	Belytschko T, Xiao S. Stability analysis of particle methods with corrected derivatives. Computers & Mathematics with Applications, 2002, 43: 329-350
[12]	Daniel S, Mitsuteru A. Coupling total Lagrangian SPH−EISPH for fluid−structure interaction with large deformed hyperelastic solid bodies. Computer Methods in Applied Mechanics and Engineering, 2021, 381: 113832 doi: 10.1016/j.cma.2021.113832
[13]	Liu MB, Liu GR, Lam KY. A one-dimensional meshfree particle formulation for simulating shock waves. Shock Wave, 2003, 13: 201-211 doi: 10.1007/s00193-003-0207-0
[14]	Xu F, Zhao Y, Yan R, et al. Multi-dimensional Discontinuous SPH method and its application to metal penetration analysis. International Journal for Numerical Methods in Engineering, 2013, 93: 1125-1146 doi: 10.1002/nme.4414
[15]	王璐, 杨扬, 徐绯. 一种考虑界面不连续的改进FPM方法. 爆炸与冲击, 2019, 39(2): 024202 (Wang Lu, Yang Yang, Xu Fei. An improved finite particle method for discontinuous interface problems. Explosion and Shock Waves, 2019, 39(2): 024202 (in Chinese)
[16]	孔伟振, 陈占魁, 田强. 基于ISPH-TLSPH的充液多柔体动力学建模与计算. 中国科学: 物理学力学天文学, 2022, 52(4): 84-99 (Kong Weizhen, Chen Zhankui, Tian Qiang. Dynamic modeling and simulation of fluid-filled flexible multibody system based on ISPH-TLSPH method. Scientia Sinica:Physica,Mechanica &Astronomica, 2022, 52(4): 84-99 (in Chinese)
[17]	Liu MB, Shao JR, Chang JZ. On the treatment of solid boundary in smoothed particle hydrodynamics. Science China-Technological Sciences, 2012, 55: 244-254 doi: 10.1007/s11431-011-4663-y
[18]	韩亚伟, 强洪夫, 赵玖玲等. 光滑粒子流体动力学方法固壁处理的一种新型排斥力模型. 物理学报, 2013, 62(4): 044702 (Han Yawei, Qiang Hongfu, Zhao Jiuling, et al. A new repulsive model for solid boundary condition in smoothed particle hydrodynamics. Acta Physica Sinica, 2013, 62(4): 044702 (in Chinese) doi: 10.7498/aps.62.044702
[19]	陈飞国, 葛蔚. 多相流动的光滑粒子流体动力学方法研究综述. 力学学报, 2021, 53(9): 2357-2373 (Chen Feiguo, Ge Wei. A review of smoothed particle hydrodynamics family methods for multiphase flow. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2357-2373 (in Chinese) doi: 10.6052/0459-1879-21-270
[20]	张建伟, 杜宇, 陈海舟. 溃坝水流冲击水垫塘的SPH模拟. 水电能源科学, 2021, 39(3): 41-44 (Zhang Jianwei, Du Yu, Chen Haizhou. SPH simulation of dam break flow impacting plunge pool. Water Resources and Power, 2021, 39(3): 41-44 (in Chinese)
[21]	徐建于, 黄生洪. 圆柱形汇聚激波诱导 Richtmyer-Meshkov不稳定的 SPH 模拟. 力学学报, 2019, 51(4): 998-1011 (Xu Jianyu, Huang Shenghong. Numerical simulation of cylindrical converging shock induced richtmyer-meshkov instability with SPH. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 998-1011 (in Chinese) doi: 10.6052/0459-1879-19-041
[22]	孔祥振, 方秦. 基于SPH方法对强动载下混凝土结构损伤破坏的数值模拟研究. 中国科学: 物理学力学天文学, 2020, 50(2): 25-33 (Kong Xiangzhen, Fang Qin. Numerical predictions of failures in concrete structures subjected to intense dynamic loadings using the smooth particle hydrodynamics method. Scientia Sinica:Physica,Mechanica &Astronomica, 2020, 50(2): 25-33 (in Chinese)
[23]	徐帅, 黄君杰, 张纲等. 人下颌软硬组织爆炸伤光滑粒子流体动力学模型研究. 第三军医大学学报, 2020, 42(20): 1971-1977 (Xu Shuai, Huang Junjie, Zhang Gang, et, al. Smoothed particle hydrodynamics based simulation of blast injuries in human mandible. Journal of Third Military Medical University, 2020, 42(20): 1971-1977 (in Chinese)
[24]	周新超, 马小晶, 廖翔云等. 磨料水射流冲击孔隙岩体的SPH模拟研究. 岩土工程学报, 2022, 44(4): 731-739 (Zhou Xinchao, Ma Xiaojing, Liao Xiangyun, et al. Numerical simulation of abrasive water jet impacting porous rock based on SPH method. Chinese Journal of Geotechnical Engineering, 2022, 44(4): 731-739 (in Chinese)
[25]	吴思思, 董新龙, 俞鑫炉. 45钢柱壳爆炸膨胀断裂的SPH模拟分析. 爆炸与冲击, 2021, 41(10): 67-77 (Wu Sisi, Dong Xinlong, Yu Xinlu. An investigating on explosive expanding fracture of 45 steel cylinders by SPH method. Explosion and Shock Waves, 2021, 41(10): 67-77 (in Chinese)
[26]	Islam MRI, Peng C. A total Lagrangian SPH method for modelling damage and failure in solids. International Journal of Mechanical Sciences, 2019, 157-158: 498-511 doi: 10.1016/j.ijmecsci.2019.05.003
[27]	Islam MRI, Zhang W, Peng C. Large deformation analysis of geomaterials using stabilized total Lagrangian smoothed particle hydrodynamics. Engineering Analysis with Boundary Elements, 2022, 136: 252-265 doi: 10.1016/j.enganabound.2022.01.002
[28]	Wang L, Xu F, Yang Y. An improved total Lagrangian SPH method for modeling solid deformation and damage. Engineering Analysis with Boundary Elements, 2021, 133: 286-302 doi: 10.1016/j.enganabound.2021.09.010
[29]	Adami S, Hu XY, Adams NA. A transport-velocity formulation for smoothed particle hydrodynamics. Journal of Computational Physics, 2013, 241: 292-307 doi: 10.1016/j.jcp.2013.01.043
[30]	孙鹏楠. 物体与自由液面耦合作用的光滑粒子流体动力学方法研究. [博士论文]. 哈尔滨: 哈尔滨工程大学, 2018 Sun Pengnan. Study on SPH method for the simulation of object-free surface interactions. [PhD Thesis]. Harbin: Harbin Engineering University, 2018 (in Chinese))
[31]	Sugiura K, Inutsuka S. An extension of Godunov SPH II: Application to elastic dynamics. Journal of Computational Physics, 2017, 333: 78-103 doi: 10.1016/j.jcp.2016.12.026
[32]	杨秋足, 徐绯, 王璐等. 一种基于黎曼解处理大密度比多相流SPH的改进算法. 力学学报, 2019, 51(3): 730-742 (Yang Qiuzu, Xu Fei, Wang Lu, et al. An improved SPH algorithm for large density ratios multiphase flows based on riemann solution. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 730-742 (in Chinese)
[33]	强洪夫. 光滑粒子流体动力学新方法及应用. 北京: 科学出版社, 2017 Qiang Hongfu. New Method and Application of Smoothed Particle Hydrodynamics. Beijing: Science Press, 2017 (in Chinese))
[34]	Adami S, Hu XY, Adams NA. A generalized wall boundary condition for smoothed particle hydrodynamics. Journal of Computational Physics, 2012, 231: 7057-7075
[35]	Sun PN, Touzé D, Zhang A. Study of a complex fluid-structure dam-breaking benchmark problem using a multi-phase SPH method with APR. Engineering Analysis with Boundary Elements, 2019, 104: 240-258 doi: 10.1016/j.enganabound.2019.03.033
[36]	段兴锋, 任鸿翔, 神和龙. 基于CUDA的弱可压SPH流体建模与仿真. 计算机工程与科学, 2018, 40(8): 1375-1382 (Duan Xingfeng, Ren Hongxiang, Shen Helong. Fluid modeling and simulation using CUDA based weakly compressible SPH. Computer Engineering & Science, 2018, 40(8): 1375-1382 (in Chinese) doi: 10.3969/j.issn.1007-130X.2018.08.006
[37]	Zhang C, Hu XY, Adams NA. A weakly compressible SPH method based on a low-dissipation Riemann solver. Journal of Computational Physics, 2017, 335: 605-620 doi: 10.1016/j.jcp.2017.01.027
[38]	Wang L, Xu F, Yang Y. Improvement of the tensile instability in SPH scheme for the FEI (fluid-elastomer interaction) problem. Engineering Analysis with Boundary Elements, 2019, 106: 116-125 doi: 10.1016/j.enganabound.2019.04.032
[39]	Antoci C, Gallati M, Sibilla S. Numerical simulation of fluid–structure interaction by SPH. Computers and Structures, 2007, 85(11): 879-90
[40]	刘传雄, 郭伟国, 李玉龙. 不同结构形式加强蒙皮的抗弹性能研究. 科学技术与工程, 2008, 1: 21-25 (Liu Chuanxiong, Guo Weiguo, Li Yulong. Anti-penetration performance of different structural types of reinforced skin panels. Science Technology and Engineering, 2008, 1: 21-25 (in Chinese) doi: 10.3969/j.issn.1671-1815.2008.01.006

[1]	Wang Shuai, Xu Fei, Dai Zhen, Liu Xiaochuan, Li Xiaocheng, Yang leifeng, Xi Xulong. A DIRECT SCALING METHOD FOR THE DISTORTION PROBLEMS OF STRUCTURAL IMPACT[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(3): 774-786. DOI: 10.6052/0459-1879-19-327
[2]	Wang Nianhua, Li Ming, Zhang Laiping. ACCURACY ANALYSIS AND IMPROVEMENT OF VISCOUS FLUX SCHEMES IN UNSTRUCTURED SECOND-ORDER FINITE-VOLUME DISCRETIZATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 527-537. DOI: 10.6052/0459-1879-18-037
[3]	Z.Y. Gao, Tongxi Yu, D. Karagiozova. Finite element simulation on the mechanical properties of MHS materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(1): 65-75. DOI: 10.6052/0459-1879-2007-1-2006-198
[4]	EXPERIMENTAL STUDY ON PERMEABILITY AND SETTLEMENT OF SATURATED SAND UNDER IMPACT LOADING[J]. Chinese Journal of Theoretical and Applied Mechanics, 1999, 31(2): 230-237. DOI: 10.6052/0459-1879-1999-2-1995-023
[5]	THE CHARACTERISTICS OF TIMOSHENKO BEAM DURING THE PROCESS OF ELASTIC IMPACT AND CONTACT[J]. Chinese Journal of Theoretical and Applied Mechanics, 1999, 31(1): 68-74. DOI: 10.6052/0459-1879-1999-1-1995-006
[6]	THREE-DIMENSIONAL IMPACT OF A RIGID ELLIPSOID ON FIXED SURFACE WITH FRICTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(6): 726-732. DOI: 10.6052/0459-1879-1997-6-1995-290
[7]	混流式转轮内有旋流动的全三元反问题计算[J]. Chinese Journal of Theoretical and Applied Mechanics, 1995, 27(S): 30-36. DOI: 10.6052/0459-1879-1995-S-1995-500
[8]	NONLINEAR DYNAMIC RESPONSE OF THE CIRCULAR PLATES UNDER IMPACT OF A MASS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1990, 22(4): 420-428. DOI: 10.6052/0459-1879-1990-4-1995-965
[9]	AN EXPERIMENTAL STUDY OF DYNAMIC BEHAVIOR OF STRUCTURES UNDER IMPACT LOADS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1990, 22(3): 374-379. DOI: 10.6052/0459-1879-1990-3-1995-959
[10]	CONDITION FOR OCCURENCE OF CIRCULAR PENETRATION DURING IMPACT OF A FALLING DROPLET WITH A FLUID[J]. Chinese Journal of Theoretical and Applied Mechanics, 1990, 22(3): 337-340. DOI: 10.6052/0459-1879-1990-3-1995-952

Cited By

Cited by

Periodical cited type(3)

1.	周建，廖星川，刘福深，尚肖楠，沈君逸. 应用卷积近场动力学快速模拟随机裂纹扩展. 岩土力学. 2025(02): 625-639 .
2.	张德沧，毛佳，戴妙林，邵琳玉，赵兰浩. 圆化离散单元法的改进及其在岩体断裂过程中的应用. 岩土工程学报. 2024(09): 1974-1983 .
3.	许晓阳，赵雨婷，李家宇，余鹏. 非等温黏弹性复杂流动的改进SPH方法模拟. 力学学报. 2023(05): 1099-1112 . 本站查看

Other cited types(3)

Get Citation

PDF

XML

Article Metrics

Article views (1072) PDF downloads (201) Cited by(6)

IMPROVEMENT OF THE TOTAL LAGRANGIAN SPH AND ITS APPLICATION IN IMPACT PROBLEMS

Abstract

References

Related Articles

Cited by

Periodical cited type(3)

Other cited types(3)

Catalog

Article Metrics

Related

Download Center

Author Center

IMPROVEMENT OF THE TOTAL LAGRANGIAN SPH AND ITS APPLICATION IN IMPACT PROBLEMS

Abstract

References

Related Articles

Cited by

Periodical cited type(3)

Other cited types(3)

Catalog

Article Metrics

Related

Download Center

Author Center

Export File

Citation

Format

Content