Coupled wave propagation in meso-scale heterogeneous medium

LU Jianhua; YUAN Liangzhu; XIE Yushan; CHEN Meiduo; WANG Pengfei; XU Songlin

doi:10.11883/bzycj-2023-0438

Volume 44 Issue 9

Sep. 2024

Turn off MathJax

Article Contents

Article Navigation > Explosion And Shock Waves > 2024 > 44(9): 091423

LU Jianhua, YUAN Liangzhu, XIE Yushan, CHEN Meiduo, WANG Pengfei, XU Songlin. Coupled wave propagation in meso-scale heterogeneous medium[J]. Explosion And Shock Waves, 2024, 44(9): 091423. doi: 10.11883/bzycj-2023-0438

Citation:

LU Jianhua, YUAN Liangzhu, XIE Yushan, CHEN Meiduo, WANG Pengfei, XU Songlin. Coupled wave propagation in meso-scale heterogeneous medium[J]. Explosion And Shock Waves, 2024, 44(9): 091423. doi: 10.11883/bzycj-2023-0438

Citation:

PDF( 4971 KB)

Coupled wave propagation in meso-scale heterogeneous medium

doi: 10.11883/bzycj-2023-0438

1.
CAS Key Laboratory for Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230027, Anhui, China
2.
United Laboratory of High-Pressure Physics and Earthquake Science, Institute of Earthquake Forecasting, China Earthquake Administration, Beijing 100036, China

Received Date: 2023-12-12
Rev Recd Date: 2024-02-29

Available Online: 2024-03-12

Publish Date: 2024-09-20

Abstract

Abstract

Heterogeneous media are very common in nature. Due to the complex internal structure, the heterogeneous compressive shear coupled stress field is inside heterogeneous media, which leads to a mutual influence of compression and shear waves. The study of wave mechanics behavior and description of heterogeneity in heterogeneous media is of great significance and full of challenges. This article establishes a general constitutive relationship that reflects the compression shear coupling characteristics of heterogeneous materials, proposes coupling coefficients to describe material heterogeneity, combines momentum conservation law to establish a generalized wave equation, and provides a general method for solving the generalized wave equation. As an example, expressions for the three characteristic wave velocities of compression shear coupling under the first-order compression shear coupling constitutive relationship are provided, and the finite difference method is employed to obtain the propagation process of coupled compression and shear waves. The effects of four heterogeneous coupling coefficients on stress state, coupled wave velocity, and wave propagation process are studied. The positive and negative values of coupling parameters and their combinations reflect the structural characteristics of heterogeneous media and also determine the properties of compression shear coupling waves. For heterogeneous media with high-pressure effects, shear dilation effects, and shear weakening effects, the coupled compression wave velocity is lower than the elastic compression wave velocity corresponding to uniform media, and the coupled shear wave velocity is higher than the elastic shear wave velocity. The effect of shear on compression delays the propagation of compressive stress, while compression promotes the propagation of shear. Coupled compression wave velocity is the result of the competition between the coupling effect of shear on compression and the volume compaction effect. Coupled shear wave velocity is the result of the competition between the coupling effect of compression on shear and the shear weakening effect caused by continuous distortion of the medium. These mechanisms could be achieved through different combinations of compression shear coupling parameters. A true triaxial experimental testing system was used to measure the longitudinal wave velocity of granite, model materials made of mortar, and materials made of cement mortar with coarse aggregates under different compressive and shear stresses. The results indicate that for heterogeneous media, the longitudinal wave velocity decreases with the increase of static water pressure and equivalent shear stress, and the shear expansion and shear weakening effects dominate. The experimental results and theoretical results have the same trend. The conclusion of this study is expected to provide a physical mechanism explanation for the phenomenon of the variation of wave velocity with stress state in heterogeneous materials.
- heterogeneity,
- compression-shear coupling effect,
- generalized wave equation,
- constitutive relationship,
- wave velocity

FullText(HTML)

References(40)

References

[1]	LAN H X, MARTIN C D, HU B. Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading [J]. Journal of Geophysical Research: Solid Earth, 2010, 115(B1): B01202. DOI: 10.1029/2009JB006496.
[2]	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.
[3]	SHIROLE D, HEDAYAT A, WALTON G. Illumination of damage in intact rocks by ultrasonic transmission-reflection and digital image correlation [J]. Journal of Geophysical Research: Solid Earth, 2020, 125(7): e2020JB019526. DOI: 10.1029/2020JB019526.
[4]	SHIROLE D, WALTON G, HEDAYAT A. Experimental investigation of multi-scale strain-field heterogeneity in rocks [J]. International Journal of Rock Mechanics and Mining Sciences, 2020, 127: 104212. DOI: 10.1016/j.ijrmms.2020.104212.
[5]	徐松林, 周李姜, 黄俊宇, 等. 岩石类脆性材料动态压剪耦合特性研究 [J]. 振动与冲击, 2016, 35(10): 9–17, 23. DOI: 10.13465/j.cnki.jvs.2016.10.002. XU S L, ZHOU L J, HUANG J Y, et al. Investigation of dynamic coupled behavior of rock materials under combined compression and shear loading [J]. Journal of Vibration and Shock, 2016, 35(10): 9–17, 23. DOI: 10.13465/j.cnki.jvs.2016.10.002.
[6]	ZHOU L J, XU S L, SHAN J F, et al. Heterogeneity in deformation of granite under dynamic combined compression/shear loading [J]. Mechanics of Materials, 2018, 123: 1–18. DOI: 10.1016/j.mechmat.2018.04.013.
[7]	MIAO C H, XU S L, SONG Y P, et al. Influence of stress state on dynamic breakage of quartz glass spheres subjected to lower velocity impacting [J]. Powder Technology, 2022, 397: 11708. DOI: 10.1016/j.powtec.2021.117081.
[8]	CHEN M, XU S L, YUAN L Z, et al. Influence of stress state on dynamic behaviors of concrete under true triaxial confinements [J]. International Journal of Mechanical Sciences, 2023, 253: 108399. DOI: 10.1016/j.ijmecsci.2023.108399.
[9]	谢雨珊, 陆建华, 徐松林, 等. Mo-ZrC梯度金属陶瓷的冲击响应行为 [J]. 爆炸与冲击, 2023, 43(3): 033101. DOI: 10.11883/bzycj-2022-0374. XIE Y S, LU J H, XU S L, et al. On impact properties of Mo-ZrC gradient metal ceramics [J]. Explosion and Shock Waves, 2023, 43(3): 033101. DOI: 10.11883/bzycj-2022-0374.
[10]	HUANG J Y, LU L, FAN D, et al. Heterogeneity in deformation of granular ceramics under dynamic loading [J]. Scripta Materialia, 2016, 111: 114–118. DOI: 10.1016/j.scriptamat.2015.08.028.
[11]	HUANG J Y, XU S L, HU S S. Numerical investigations of the dynamic shear behavior of rough rock joints [J]. Rock Mechanics and Rock Engineering, 2014, 47(5): 1727–1743. DOI: 10.1007/s00603-013-0502-8.
[12]	MIAO C H, XU S L, YUAN L Z, et al. Experimental investigation of failure diffusion in brittle materials subjected to low-speed impact [J]. International Journal of Mechanical Sciences, 2023, 259: 108632. DOI: 10.1016/j.ijmecsci.2023.108632.
[13]	SHAN J F, XU S L, LIU Y G, et al. Dynamic breakage of glass sphere subjected to impact loading [J]. Powder Technology, 2018, 330: 317–329. DOI: 10.1016/j.powtec.2018.02.009.
[14]	TANG Z P, XU S L, DAI X Y, et al. S-wave tracing technique to investigate the damage and failure behavior of brittle materials subjected to shock loading [J]. International Journal of Impact Engineering, 2005, 31(9): 1172–1191. DOI: 10.1016/j.ijimpeng.2004.07.005.
[15]	TING T C T, NAN N. Plane waves due to combined compressive and shear stresses in a half space [J]. Journal of Applied Mechanics, 1969, 36(2): 189–197. DOI: 10.1115/1.3564606.
[16]	LI Y C, TING T C T. Plane waves in simple elastic solids and discontinuous dependence of solution on boundary conditions [J]. International Journal of Solids and Structures, 1983, 19(11): 989–1008. DOI: 10.1016/0020-7683(83)90024-0.
[17]	SONG Q Z, TANG Z P. Combined stress waves with phase transition in thin-walled tubes [J]. Applied Mathematics and Mechanics, 2014, 35(3): 285–296. DOI: 10.1007/s10483-014-1791-7.
[18]	WANG B, ZHANG K, CUI S T, et al. Mechanism of shear attenuation near the interface under combined compression and shear impact loading [J]. Wave Motion, 2017, 73: 96–103. DOI: 10.1016/j.wavemoti.2017.06.003.
[19]	RENAUD A, HEUZÉ T, STAINIER L. On loading paths followed inside plastic simple waves in two-dimensional elastic-plastic solids [J]. Journal of the Mechanics and Physics of Solids, 2020, 143: 104064. DOI: 10.1016/j.jmps.2020.104064.
[20]	PLONA T J. Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies [J]. Applied Physics Letters, 1980, 36(4): 259–261. DOI: 10.1063/1.91445.
[21]	LIU Q R, KATSUBE N. The discovery of a second kind of rotational wave in a fluid-filled porous material [J]. The Journal of the Acoustical Society of America, 1990, 88(2): 1045–1053. DOI: 10.1121/1.399853.
[22]	BEN-DAVID O, FINEBERG J. Static friction coefficient is not a material constant [J]. Physical Review Letters, 2011, 106(25): 254301. DOI: 10.1103/PhysRevLett.106.254301.
[23]	PASSELÈGUE F X, SCHUBNEL A, NIELSEN S, et al. From sub-Rayleigh to supershear ruptures during stick-slip experiments on crustal rocks [J]. Science, 2013, 340(6137): 1208–1211. DOI: 10.1126/science.1235637.
[24]	RUBINSTEIN S M, COHEN G, FINEBERG J. Detachment fronts and the onset of dynamic friction [J]. Nature, 2004, 430(7003): 1005–1009. DOI: 10.1038/nature02830.
[25]	RUBINSTEIN S M, COHEN G, FINEBERG J. Dynamics of precursors to frictional sliding [J]. Physical Review Letters, 2007, 98(22): 226103. DOI: 10.1103/PhysRevLett.98.226103.
[26]	XIA K W, ROSAKIS A J, KANAMORI H. Laboratory earthquakes: the sub-Rayleigh-to-supershear rupture transition [J]. Science, 2004, 303(5665): 1859–1861. DOI: 10.1126/science.1094022.
[27]	XIA K W, ROSAKIS A J, KANAMORI H, et al. Laboratory earthquakes along inhomogeneous faults: directionality and supershear [J]. Science, 2005, 308(5722): 681–684. DOI: 10.1126/science.110819.
[28]	ZOU Y T, ZHANG W, CHEN T, et al. Thermally induced anomaly in the shear behavior of magnetite at high pressure [J]. Physical Review Applied, 2018, 10(2): 024009. DOI: 10.1103/PhysRevApplied.10.024009.
[29]	WANG D J, LIU T, CHEN T, et al. Anomalous sound velocities of antigorite at high pressure and implications for detecting serpentinization at mantle wedges [J]. Geophysical Research Letters, 2019, 46(10): 5153–5160. DOI: 10.1029/2019GL082287.
[30]	LI B S, WOODY K, KUNG J. Elasticity of MgO to 11 GPa with an independent absolute pressure scale: implications for pressure calibration [J]. Journal of Geophysical Research: Solid Earth, 2006, 111(B11): B11206. DOI: 10.1029/2005jb004251.
[31]	ZOU Y T, LI M, DENG L W, et al. Acoustic velocities, elasticity, and pressure-induced elastic softening in compressed neodymium [J]. Mechanics of Materials, 2021, 155: 103776. DOI: 10.1016/j.mechmat.2021.103776.
[32]	CAI N, CHEN T, QI X T, et al. Sound velocities of the 23 Å phase at high pressure and implications for seismic velocities in subducted slabs [J]. Physics of the Earth and Planetary Interiors, 2019, 288: 1–8. DOI: 10.1016/j.pepi.2019.01.006.
[33]	CAI N, QI X T, CHEN T, et al. Enhanced visibility of subduction slabs by the formation of dense hydrous phase A [J]. Geophysical Research Letters, 2021, 48(19): e2021GL095487. DOI: 10.1029/2021GL095487.
[34]	LU J H, XU S L, MIAO C H, et al. The theory of compression-shear coupled composite wave propagation in rock [J]. Deep Underground Science and Engineering, 2022, 1(1): 77–86. DOI: 10.1002/dug2.12012.
[35]	LU J H, XU S L, LI Y, et al. Investigations on the compression-shear coupled stress waves propagating in heterogeneous rock [J]. Mechanics of Materials, 2023, 186: 104786. DOI: 10.1016/j.mechmat.2023.104786.
[36]	徐松林, 王鹏飞, 赵坚, 等. 基于三维Hopkinson杆的混凝土动态力学性能研究 [J]. 爆炸与冲击, 2017, 37(2): 180–185. DOI: 10.11883/1001-1455(2017)02-0180-06. XU S L, WANG P F, ZHAO J, et al. Dynamic behavior of concrete under static triaxial loading using 3D-Hopkinson bar [J]. Explosion and Shock Waves, 2017, 37(2): 180–185. DOI: 10.11883/1001-1455(2017)02-0180-06.
[37]	徐松林, 王鹏飞, 单俊芳, 等. 真三轴静载作用下混凝土的动态力学性能研究 [J]. 振动与冲击, 2018, 37(15): 59–67. DOI: 10.13465/j.cnki.jvs.2018.15.008. XU S L, WANG P F, SHAN J F, et al. Dynamic behavior of concrete under static tri-axial loadings [J]. Journal of Vibration and Shock, 2018, 37(15): 59–67. DOI: 10.13465/j.cnki.jvs.2018.15.008.
[38]	徐松林, 单俊芳, 王鹏飞, 等. 三轴应力状态下混凝土的侵彻性能研究 [J]. 爆炸与冲击, 2019, 39(7): 071101. DOI: 10.11883/bzycj-2019-0034. XU S L, SHAN J F, WANG P F, et al. Penetration performance of concrete under triaxial stress [J]. Explosion and Shock Waves, 2019, 39(7): 071101. DOI: 10.11883/bzycj-2019-0034.
[39]	XU S L, SHAN J F, ZHANG L, et al. Dynamic compression behaviors of concrete under true triaxial confinement: an experimental technique [J]. Mechanics of Materials, 2020, 140: 103220. DOI: 10.1016/j.mechmat.2019.103220.
[40]	ZHANG L, SHAN J F, MIAO C H, et al. The cratering performance of concrete target under true triaxial confinements [J]. International Journal of Mechanical Sciences, 2021, 210: 106714. DOI: 10.1016/j.ijmecsci.2021.106714.