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完全拉格朗日SPH在冲击问题中的改进和应用

王璐 徐绯 杨扬

王璐, 徐绯, 杨扬. 完全拉格朗日SPH在冲击问题中的改进和应用. 力学学报, 2022, 54(12): 3297-3309 doi: 10.6052/0459-1879-22-214
引用本文: 王璐, 徐绯, 杨扬. 完全拉格朗日SPH在冲击问题中的改进和应用. 力学学报, 2022, 54(12): 3297-3309 doi: 10.6052/0459-1879-22-214
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: 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

完全拉格朗日SPH在冲击问题中的改进和应用

doi: 10.6052/0459-1879-22-214
基金项目: 中央高校基本科研业务费资助项目(300102282105)和国家自然科学基金(11972309)项目资助
详细信息
    作者简介:

    王璐, 讲师, 主要研究方向: 无网格粒子法理论及应用. E-mail: lwang@chd.edu.cn

  • 中图分类号: O34

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

  • 摘要: 光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)在模拟固体大变形、破碎和裂纹扩展等问题中有天然的优势, 但SPH固有的拉伸不稳定缺陷是SPH在计算固体力学领域进一步应用的一大障碍. 完全拉格朗日SPH (total Lagrangian-SPH, TL-SPH)方法是一种有效的改善拉伸不稳定的措施, 但其仍面临边界区域精度低、界面条件难以施加、损伤裂纹难以模拟等缺陷. 因此, 首先将可达到二阶精度的高阶SPH方法与TL-SPH耦合, 为了节省高阶方法的计算量, 进一步简化粒子选取模式, 提出TL-SFPM (TL-simplified finite particle method)方法; 其次, 将可提高界面精度的DFPM (discontinuous finite particle method)方法与TL-SPH结合, 并提出一种基于黎曼解的界面接触算法, 通过在不同材料粒子间建立黎曼模型求解不同材料间的相互作用, 分别应用于流体−固体接触和固体−固体接触中; 再者, 为了捕捉固体受外载荷后的损伤程度及破坏模式, 提出一种完全拉格朗日框架下的粒子损伤破坏模型; 最后, 通过流−固冲击的带弹性挡板溃坝算例和固−固冲击的子弹撞击靶板算例验证提出的TL-SFPM方法、界面接触算法和损伤破坏模型的合理性和精确性, 进一步扩展TL-SPH方法在计算固体冲击问题中的应用.

     

  • 图  1  规则构型下不同区域粒子选取方式

    Figure  1.  Particles selection modes in different regions under regular configuration

    图  2  不同粒子间距下式(7)~式(9)计算三次函数∂f/X的均方误差

    Figure  2.  Mean square error of cubic function ∂f/X calculated byEqs. (7)~(9) under different particle spacings

    图  3  不规则计算域边界粒子选取方式

    Figure  3.  Particles selection mode in boundary region under irregular configuration

    图  4  二维情形下的不连续计算域示意图

    Figure  4.  Discontinuous computational domain in 2-D

    图  5  界面处TL-SFPM方法中四个粒子的选取方式

    Figure  5.  Particles selection mode at interface in TL-SFPM method

    图  6  SPH粒子间黎曼模型

    Figure  6.  Riemann model with SPH particles

    图  7  带弹性挡板溃坝模型

    Figure  7.  Model of the dam with elastic baffle

    图  8  不同粒子间距弹性挡板自由端竖直位移变化曲线

    Figure  8.  Vertical displacement of the free end of elastic baffle with different particle spacings

    图  9  弹性挡板和液面位置随时间变化曲线

    Figure  9.  Curves of the elastic baffle and the water surface positions

    图  10  TL-SFPM模拟结果和试验结果[39]对比图(自0~0.32 s, 每隔0.08 s)

    Figure  10.  Comparison of TL-SFPM simulation and experiment results[39] from 0 s to 0.32 s (at 0.08 s intervals)

    图  11  TL-SFPM和文献 [39] 模拟得到某时刻弹性挡板y方向应力分布云图

    Figure  11.  Stress distribution at y-direction of the baffle obtained by the TL-SFPM and Ref. [39]

    图  12  CSPM和TL-SFPM得到钢弹撞击铝合金板同一时刻速度分布云图

    Figure  12.  Velocity distribution obtained by the traditional SPH and high-order TL-SPH

    图  13  TL-SFPM和有限元模拟的不同时刻子弹和板的速度(m/s)云图

    Figure  13.  Velocity (m/s) distribution at different times obtained by TL-SFPM and FEM

    图  14  加入断裂模型后不同冲击速度下的失效粒子分布

    Figure  14.  Distribution of failure particles at different impact velocities with the fracture model

    图  15  钢弹冲击靶板计算结果与试验结果对比[40]

    Figure  15.  Comparison of the steel projectile impacting the aluminum alloy plate results between simulation and experiment[40]

    表  1  弹性挡板材料参数

    Table  1.   Material parameters of elastic baffle

    H/mh/mZ/ms/mρ/
    (kg·m−3)
    νE/
    MPa
    0.140.0790.10.00511000.412
    下载: 导出CSV

    表  2  TL-SPH和TL-SFPM模拟时间对比

    Table  2.   Computational time with TL-SPH and TL-SFPM methods

    MethodTL-SPHTL-SFPM
    Computational time/s95629403
    下载: 导出CSV

    表  3  钢和铝材料参数

    Table  3.   Material parameters of steel and aluminum

    Materialρ/(kg·m−3)Cs/(m·s−1)νE/GPaA/MPa
    steel780045960.3200335
    aluminum278553280.372265
    MaterialB/MPanCmTmelt/K
    steel2750.360.0221.01811
    aluminum4260.340.0151.0775
    下载: 导出CSV

    表  4  CSPM和TL-SFPM模拟时间对比

    Table  4.   Computational time with CSPM and TL-SFPM methods

    MethodCSPMTL-SFPM
    Computational time/s26533225
    下载: 导出CSV
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  • 收稿日期:  2022-05-23
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