细观非连续介质的应力波传播研究

袁良柱 陈美多 谢雨珊 陆建华 王鹏飞 徐松林

袁良柱, 陈美多, 谢雨珊, 陆建华, 王鹏飞, 徐松林. 细观非连续介质的应力波传播研究[J]. 爆炸与冲击. doi: 10.11883/bzycj-2023-0365
引用本文: 袁良柱, 陈美多, 谢雨珊, 陆建华, 王鹏飞, 徐松林. 细观非连续介质的应力波传播研究[J]. 爆炸与冲击. doi: 10.11883/bzycj-2023-0365
YUAN Liangzhu, CHEN Meiduo, XIE Yushan, LU Jianhua, WANG Pengfei, XU Songlin. Investigation on stress wave propagation in mesoscopic discontinuous medium[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2023-0365
Citation: YUAN Liangzhu, CHEN Meiduo, XIE Yushan, LU Jianhua, WANG Pengfei, XU Songlin. Investigation on stress wave propagation in mesoscopic discontinuous medium[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2023-0365

细观非连续介质的应力波传播研究

doi: 10.11883/bzycj-2023-0365
基金项目: 国家自然科学基金 (11672286, 11872361);高压物理与地震科技联合实验室室开放基金 (2019HPPES01);中石油与中科院重大战略合作项目(2015A-4812);中央高校基本科研业务费专项资金(WK2480000008)
详细信息
    作者简介:

    袁良柱(1998- ),男,博士研究生,ylzustcedu@mail.ustc.edu.cn

    通讯作者:

    徐松林(1971- ),男,博士,研究员,博士生导师,slxu99@ustc.edu.cn

  • 中图分类号: O347.3

Investigation on stress wave propagation in mesoscopic discontinuous medium

  • 摘要: 固体介质,如岩石、混凝土、贝壳和多孔材料等均具有细观非连续、宏观连续的特性,揭示这种细观非连续性对材料动力学响应的影响规律,对于材料设计、安全防护等具有重要意义。本文从广义Taylor公式出发,推导了分数阶定义下的非连续介质的一维波动方程,引入等效分数阶简化了控制方程。利用有限差分法得到了控制方程的数值解,结果表明:当控制方程中的等效分数阶阶数越小,计算得到的波形衰减的程度越大。为了验证方程的可靠性,并进一步研究非连续介质的波传播规律,在考虑多孔材料、岩石等介质的结构特征的基础上,基于Abaqus软件建立了随机多孔介质模型。分析发现:多孔介质的波传播受到介质细观非连续程度、材料属性和输入波脉宽的影响,但对应的等效分数阶阶数只与介质细观非连续程度相关,因此其可以作为评价非连续介质动态响应的一个依据。等效分数阶阶数随着孔隙率的增加而减小,孔洞相对数量分布大致相同的情况下,其统计关系近似呈线性关系。研究结果可为研究多孔材料、贝壳等细观非连续介质的波动传播提供新思路。
  • 图  1  非连续介质微元体受力和变形的示意图

    Figure  1.  Schematic diagram of force and deformation of discontinuous medium

    图  2  非连续介质的非均质性

    Figure  2.  Heterogeneity of discontinuous medium

    图  3  不同分数阶阶数对应的波传播

    Figure  3.  Wave propagation with different fractional order

    图  4  细观多孔介质有限元模型及相应的波形

    Figure  4.  FEM of porous medium and corresponding wave form

    图  5  不同孔隙率的细观多孔介质的波传播及对应的分数阶阶数

    Figure  5.  Wave propagation of porous medium with different porosities and corresponding fractional order

    图  6  各孔隙率下不同孔洞分布的波形

    Figure  6.  Waveforms of different hole distribution under different porosity

    图  7  均匀分布的细观多孔介质的波传播及对应的分数阶阶数

    Figure  7.  Wave propagation of porous medium with uniformly distributed pores and corresponding fractional order

    图  8  等效分数阶阶数与细观多孔介质孔隙率之间的统计关系

    Figure  8.  The statistical relationship between the equivalent fractional order and the porosity of the porous medium

    图  9  材料属性对波传播的影响

    Figure  9.  Effect of material properties on wave propagation

    图  10  输入波脉宽对波传播的影响

    Figure  10.  Effect of pulse duration of input wave on wave propagation

    表  1  不同孔隙率的细观多孔介质对应的等效分数阶阶数

    Table  1.   The equivalent fractional order of porous medium with different porosity

    编号 孔隙率/% 等效分数阶阶数 编号 孔隙率/% 等效分数阶阶数 编号 孔隙率/% 等效分数阶阶数
    1 11.02 0.95 8 34.77 0.81 15 67.69 0.54
    2 17.37 0.95 9 43.46 0.70 16 73.8 0.50
    3 17.37 0.95 10 43.46 0.71 17 19.58 0.95
    4 26.06 0.85 11 52.13 0.68 18 30.83 0.90
    5 26.07 0.85 12 52.13 0.66 19 39.25 0.83
    6 34.76 0.78 13 60.83 0.60 20 43.27 0.83
    7 34.77 0.78 14 60.83 0.58 21 58.84 0.71
    下载: 导出CSV

    表  2  不同材料的物理参数

    Table  2.   Physical parameters of different materials

    材料密度/kg·m−3弹性模量/GPa波速/(m·s−1
    78002105189
    2700705092
    89601203660
    环氧树脂120031581
    下载: 导出CSV
  • [1] 王鹏飞, 徐松林, 胡时胜. 不同温度下泡沫铝压缩行为与变形机制探讨 [J]. 振动与冲击, 2013, 32(5): 16–19. DOI: 10.13465/j.cnki.jvs.2013.05.009.

    WANG P F, XU S L, HU S S. Compressive behavior and deformation mechanism of aluminum foam under different temperature [J]. Journal of Vibration and Shock, 2013, 32(5): 16–19. DOI: 10.13465/j.cnki.jvs.2013.05.009.
    [2] 王鹏飞, 徐松林, 李志斌, 等. 高温下轻质泡沫铝动态力学性能实验 [J]. 爆炸与冲击, 2014, 34(4): 433–438. DOI: 10.11883/1001-1455(2014)04-0433-06.

    WANG P F, XU S L, LI Z B, et al. An experimental study on dynamic mechanical property of ultra-light aluminum foam under high temperatures [J]. Explosion and Shock Waves, 2014, 34(4): 433–438. DOI: 10.11883/1001-1455(2014)04-0433-06.
    [3] WANG P F, XU S L, HU S S. Experimental and numerical study of the effect of micro-structure on the rate-sensitivity of cellular foam [J]. Mechanics of Advanced Materials and Structures, 2016, 23(8): 888–895. DOI: 10.1080/15376494.2015.1047477.
    [4] SHAN J F, XU S L, ZHOU L J, et al. Dynamic fracture of aramid paper honeycomb subjected to impact loading [J]. Composite Structures, 2019, 223: 110962. DOI: 10.1016/j.compstruct.2019.110962.
    [5] 刘永贵, 徐松林, 席道瑛, 等. 节理玄武岩体弹性波频散效应研究 [J]. 岩石力学与工程学报, 2010, 29(1): 3314–3320. DOI: CNKI:SUN:YSLX.0.2010-S1-106.

    LIU Y G, XU S L, XI D Y, et al. Dispersion effect of elastic wave in jointed basalts [J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(1): 3314–3320. DOI: CNKI:SUN:YSLX.0.2010-S1-106.
    [6] 席道瑛, 徐松林, 宛新林. 高孔隙岩石局部压缩屈服与帽盖模型 [J]. 地球物理进展, 2015, 30(4): 1926–1934. DOI: 10.6038/pg20150454.

    XI D Y, XU S L, WAN X L. The cap model and local compressive yield process of high porous rock [J]. Progress in Geophysics, 2015, 30(4): 1926–1934. DOI: 10.6038/pg20150454.
    [7] WEI X D, MOHAMMAD N, HORACIO D E. Optimal length scales emerging from shear load transfer in natural materials: Application to carbon-based nanocomposite design [J]. ACS Nano, 2012, 6(3): 2333–2344. DOI: 10.1021/nn204506d.
    [8] MENG X S, ZHOU L C, LEI L, et al. Deformable hard tissue with high fatigue resistance in the hinge of bivalve Cristaria plicata [J]. Science, 2023, 380(6651): 1252–1257. DOI: 10.1126/science.ade2038.
    [9] 胡亚峰, 刘建青, 顾文斌, 等. PVDF应力测试技术及其在多孔材料爆炸冲击实验中的应用 [J]. 爆炸与冲击, 2016, 36(5): 655–662. DOI: 10.11883/1001-1455(2016)05-0655-08.

    HU Y F, LIU J Q, GU W B, et al. Stress-testing method by PVDF gauge and its application in explosive test of porous material [J]. Explosion and Shock Waves, 2016, 36(5): 655–662. DOI: 10.11883/1001-1455(2016)05-0655-08.
    [10] 孙晓旺, 李永池, 叶中豹, 等. 新型空壳颗粒材料在人防工程中应用的实验研究 [J]. 爆炸与冲击, 2017, 37(4): 643–648. DOI: 10.11883/1001-1455(2017)04-0643-06.

    SUN X W, LI Y C, YE Z B, et al. Experimental study of a novel shelly cellular material used in civil defense engineering [J]. Explosion and Shock Waves, 2017, 37(4): 643–648. DOI: 10.11883/1001-1455(2017)04-0643-06.
    [11] YUAN L Z, MIAO C H, XU S L, et al. Stress-wave propagation in multilayered and density-graded viscoelastic medium [J]. International Journal of Impact Engineering, 2023, 173: 104415. DOI: 10.1016/j.ijimpeng.2022.104415.
    [12] REID S R, PENG C. Dynamic uniaxial crushing of wood. International Journal of Impact Engineering, 1997, 19(5–6): 531–570. DOI: 0.1016/S0734-743X(97)00016-X.
    [13] LOPATNIKOV S L, GAMA B A, JAHIRUL H M, et al. Dynamics of metal foam deformation during Taylor cylinder–Hopkinson bar impact experiment. Composite Structures, 2003, 61(1–2): 61–71. DOI: 10.1016/S0263-8223(03)00039-4.
    [14] HANSSEN A G, HOPPERSTAD O S, LANGSETH M, et al. Validation of constitutive models applicable to aluminium foams. International Journal of Mechanical Sciences, 2002, 44(2): 359–406. DOI: 10.1016/S0020-7403(01)00091-1.
    [15] ZHENG Z, WANG C, Yu J, et al. Dynamic stress–strain states for metal foams using a 3 D cellular model. Journal of the Mechanics and Physics of Solids, 2014, 72: 93–114. DOI: 10.1016/j.jmps.2014.07.013.
    [16] 徐松林, 刘永贵, 席道瑛, 等. 弹性波在含双裂纹岩体中的传播分析 [J]. 地球物理学报, 2012, 55(3): 944–952. DOI: 10.6038/j.issn.0001-5733.2012.03.024.

    XU S L, LIU Y G, XI D Y, et al. Analysis of propagation of elastic wave in rocks with double-crack model [J]. Chinese Journal of Geophysics, 2012, 55(3): 944–952. DOI: 10.6038/j.issn.0001-5733.2012.03.024.
    [17] 谭子翰, 徐松林, 刘永贵, 等. 含多种尺寸缺陷岩体中的弹性波散射 [J]. 应用数学和力学, 2013, 34(1): 38–48. DOI: 10.3879/j.issn.1000-0887.2013.01.005.

    TAN Z H, XU S L, LIU Y G, et al. Scattering of elastic waves by multi-size defects in rock mass [J]. Applied Mathematics and Mechanics, 2013, 34(1): 38–48. DOI: 10.3879/j.issn.1000-0887.2013.01.005.
    [18] 章超, 徐松林, 王鹏飞, 等. 不同冲击速度下泡沫铝变形和应力的不均匀性 [J]. 爆炸与冲击, 2015, 35(4): 567–575. DOI: 10.11883/1001-1455(2015)04-0567-09.

    ZHANG C, XU S L, WANG P F, et al. Deformation and stress nonuniformity of aluminum foam under different impact speeds [J]. Explosion and Shock Waves, 2015, 35(4): 567–575. DOI: 10.11883/1001-1455(2015)04-0567-09.
    [19] 刘冕, 旺根伟, 宋辉, 等. 负梯度泡沫金属中的局部密实化现象 [J]. 高压物理学报, 2020, 34(4): 044204. DOI: 10.11858/gywlxb.20190866.

    LIU M, WANG G W, SONG H, et al. Phenomenon of local densification in negative graded metal foam [J]. Chinese Journal of High Pressure Physics, 2020, 34(4): 044204. DOI: 10.11858/gywlxb.20190866.
    [20] 范东宇, 苏彬豪, 彭辉, 等. 多孔泡沫牺牲层的动态压溃及缓冲吸能机理研究 [J]. 力学学报, 2022, 54(6): 1630–1640. DOI: 10.6052/0459-1879-22-047.

    FAN D Y, SU B H, PENG H, et al. Research on dynamic crushing and mechanism of mitigation and energy absorption of cellular sacrificial layers [J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1630–1640. DOI: 10.6052/0459-1879-22-047.
    [21] 常白雪, 郑志军, 赵凯, 等. 具有恒定冲击荷载的梯度泡沫金属材料设计 [J]. 爆炸与冲击, 2019, 39(4): 041101. DOI: 10.11883/bzycj-2018-0431.

    CHANG B X, ZHENG Z J, ZHAO K, et al. Design of gradient foam metal materials with a constant impact load [J]. Explosion and Shock Waves, 2019, 39(4): 041101. DOI: 10.11883/bzycj-2018-0431.
    [22] CHANG B X, ZHENG Z J, ZHANG Y L, et al. Crashworthiness design of graded cellular materials: An asymptotic solution considering loading rate sensitivity [J]. International Journal of Impact Engineering, 2020, 143: 103611. DOI: 10.1016/j.ijimpeng.2020.103611.
    [23] 蔡正宇, 丁圆圆, 王士龙, 等. 梯度多胞牺牲层的抗爆炸分析 [J]. 爆炸与冲击, 2017, 37(3): 396–404. DOI: 10.11883/1001-1455(2017)03-0396-09.

    CAI Z Y, DING Y Y, WANG S L, et al. Anti-blast analysis of graded cellular sacrificial cladding [J]. Explosion and Shock Waves, 2017, 37(3): 396–404. DOI: 10.11883/1001-1455(2017)03-0396-09.
    [24] WANG D Y, WANG P F, WU Y F, et al. Temperature and rate-dependent plastic deformation mechanism of carbon nanotube fiber: Experiments and modeling [J]. Journal of the Mechanics and Physics of Solids, 2023, 173: 105241. DOI: 10.1016/j.jmps.2023.105241.
    [25] LIU J J, ZHU W Q, YU Z L, et al. Dynamic shear-lag model for understanding the role of matrix in energy dissipation in fiber-reinforced composites [J]. Acta Biomaterialia, 2018, 74: 270–279. DOI: 10.1016/j.actbio.2018.04.031.
    [26] 汪成贵, 束善治, 肖 杨, 等. 考虑钙质砂颗粒破碎的分数阶边界面本构模型 [J]. 岩土工程学报, 2023, 45(6): 162–1170. DOI: 10.11779/CJGE20220229.

    WANG C G, SHU S Z, XIAO Y, et al. Fractional-order bounding surface model considering breakage of calcareous sand [J]. Chinese Journal of Geotechnical Engineering, 2023, 45(6): 162–1170. DOI: 10.11779/CJGE20220229.
    [27] 刘泉声, 罗慈友, 彭星新, 等. 软岩现场流变试验及非线性分数阶蠕变模型 [J]. 煤炭学报, 2020, 45(4): 348–1356. DOI: 10.13225/j.cnki.jccs.2019.0479.

    LIU Q S, LUO C Y, PENG X X, et al. Research on field rheological test and nolinear fractional derivative creep model of weak rock mass [J]. Journal of China Coal Society, 2020, 45(4): 348–1356. DOI: 10.13225/j.cnki.jccs.2019.0479.
    [28] 孙逸飞, 沈 扬, 刘汉龙. 粗粒土的分数阶应变率及其与分形维度的关系 [J]. 岩土力学, 2018, 39(1): 97–317. DOI: 10.16285/j.rsm.2017.1320.

    SUN Y F, SHEN Y, LIU H L. Fractional strain rate and its relation with fractal dimension of granular soils [J]. Rock and Soil Mechanics, 2018, 39(1): 97–317. DOI: 10.16285/j.rsm.2017.1320.
    [29] 颜可珍, 杨胜丰, 黎国凯, 等. 沥青混合料动态黏弹性分数阶导数模型 [J]. 中国公路学报, 2022, 35(5): 12–22. DOI: 10.19721/j.cnki.1001-7372.2022.05.002.

    YAN K Z, YANG S F, LI G K, et al. Fractional derivative model for dynamic viscoelasticity of asphalt mixtures [J]. China Journal of Highway and Transport, 2022, 35(5): 12–22. DOI: 10.19721/j.cnki.1001-7372.2022.05.002.
    [30] 袁良柱, 陆建华, 苗春贺, 等. 基于分数阶模型的牡蛎壳动力学特性研究 [J]. 爆炸与冲击, 2023, 43(1): 011101. DOI: 10.11883/bzycj-2022-0318.

    YUAN L Z, LU J H, MIAO C H, et al. Dynamic properties of oyster shells based on a fractional-order model [J]. Explosion and Shock Waves, 2023, 43(1): 011101. DOI: 10.11883/bzycj-2022-0318.
    [31] ZAID M O, NABIL T S. Generalized Taylor’s formula [J]. Applied Mathematics and Computation, 2007, 186: 286–293. DOI: 10.1016/j.amc.2006.07.102.
    [32] GAO G H, SUN Z H, ZHANG H W. A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications [J]. Journal of Computational Physics, 2014, 259: 33–50. DOI: 10.1016/j.jcp.2013.11.017.
  • 加载中
图(10) / 表(2)
计量
  • 文章访问数:  133
  • HTML全文浏览量:  12
  • PDF下载量:  60
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-10-09
  • 修回日期:  2023-12-14
  • 网络出版日期:  2024-02-04

目录

    /

    返回文章
    返回