ANALYSIS OF WAVE BEHAVIOR AND DEFORMATION CHARACTERISTICS OF GRANULAR MATERIALS IN PRO-BORDER ZONE UNDER IMPACT LOAD
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摘要: 研究颗粒材料中的波传播问题在超材料制造方面有重要意义, 如波传导超材料边界的设计需考虑应力波的反射和吸收等问题. 本文从一维颗粒链中的波传播行为出发, 根据距边界不同位置处颗粒能够得到的最大动能的不同, 给出了临边界区域的定义. 然后分析了多组二维颗粒样本在冲击载荷作用下应力波的传播行为, 主要考虑了不同边界形状及不同颗粒排列方式对应力波在临边界区域内传播行为的影响. 研究表明, 临边界区颗粒排列方式主要影响边界附近颗粒的相对位置和局部孔隙率; 经边界反射后的应力波直接以边界形状在临边界区内传播, 该结论在边界情况越复杂(高局部孔隙率, 颗粒无序随机排列)时越准确; 在临边界区域外(即材料中心区域), 波前形状主要由波速决定. 弧形边界对波反射的汇聚作用和临边界区域内颗粒的排列方式所引起的弥散作用是两个竞争因素, 共同决定临边界区域内波的反射过程. 最后分析了临边界区域内颗粒力链网络在反射前后的变化. 该研究将为超材料设计提供借鉴.Abstract: The study of wave propagation in granular materials is of great significance in metamaterial manufacturing. The boundary design of wave-conducting metamaterials needs to consider the reflection and absorption of stress waves. First, the wave propagation behavior in a one-dimensional particle chain has been studied. According to the difference in the maximum kinetic energy that the particles can obtain at different positions from the boundary, the definition of the boundary area is given. Then the stress wave propagation behaviors of multiple sets of two-dimensional particle samples under impact load are analyzed. The influences of different boundary shapes and particle arrangement on the propagation behavior of stress waves in the pro-border zone have been considered. The results show that the arrangement of particles in the pro-border zone mainly affects the relative position and local porosity of particles near the boundary. The stress wave reflected by the boundary propagates directly in the pro-border zone in the shape of the boundary line. The more complicated the boundary situation (high local porosity, random arrangement of particles), the more accurate the conclusion. The wave velocity mainly determines the shape of the wave-front outside the pro-border zone, i.e., in the material center area. The convergence effect of the arc boundary on the wave reflection and the dispersion effect caused by the arrangement of the particles in the pro-border zone are two competing factors, which together determine the reflection process of the wave in the pro-border zone. Finally, the changes of the force chain network in the pro-border zone before and after reflection are analyzed. The distribution of kinetic energy intuitively reflects the phenomenon of reflection hysteresis. The process of particle contact and rebound in the boundary area corresponds to the storage and release of energy. This research will provide reference for the handling of boundary problems in metamaterial design.
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Key words:
- granular materials /
- DEM /
- pro-border zone /
- stress wave reflection /
- wave-front shape
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图 1 颗粒速度随加载时间的变化(线性接触模型)
Figure 1. Particle velocity variation with loading time (linear contact model)
图 2 颗粒速度随加载时间的变化(赫兹接触模型)
Figure 2. Particle velocity variation with loading time (Hertz contact model)
图 11 随机排列样本中波前演化图. 上: 单粒径, 下: 均匀分布多粒径
Figure 11. Wavefront evolution in randomly arranged specimens. Top: single-size particles, bottom: uniform distribution of multi-size particles
图 12 波前形状随时间演化. 上: θ = 30°, 下: θ = 60°
Figure 12. Wavefront shape evolves over time. Top: θ = 30°, bottom: θ = 60°
图 13 B类边界θ = 30°波前形状分析示意图
Figure 13. Schematic diagram of wavefront shape analysis of type B boundary θ = 30°
图 15 单粒径随机排列样本波前形状图
Figure 15. Wavefront shape in randomly arranged samples of single-size particles
图 16 均匀分布多粒径随机排列样本波前形状图
Figure 16. Wavefront shape in randomly arranged samples of uniformly distributed multi-size particles
图 17 临边界区域力链随时间的演化
Figure 17. Evolution of force chain in the pro-border zone over time
图 18 应力波进入临边界区时力链网络
Figure 18. Force chain network when stress wave enters the pro-border zone
图 19 应力波反射后临边界区力链网络
Figure 19. Force chain network in the pro-border zone after stress wave reflection
图 20 应力波反射前后临边界区颗粒动能分布
Figure 20. Distribution of particle kinetic energy in the pro-border zone before and after stress wave reflection
表 1 计算参数
Table 1. Parameters used in the simulation
$\rho $
/(kg·m−3)${v_0}$
/(m·s−1)kn
/(N·m−1)ks
/(N·m−1)G
/Paν 2600 1.0 6.0 × 107 6.0 × 107 1.0 × 109 0.3 
下载: 导出CSV
表 2 二维样本尺寸参数
Table 2. Size parameters for 2-D specimen
Size/mm r/mm rlo/mm rhi/mm 75 × 150 0.5 0.25 0.75
下载: 导出CSV
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[1] Tichler AM, Gomez LR, Upadhyaya N, et al. Transmission and reflection of strongly nonlinear solitary waves at granular interfaces. Physical Review Letters, 2013, 111(4): 048001 doi: 10.1103/PhysRevLett.111.048001 [2] Sen S, Hong J, Bang J, et al. Solitary waves in the granular chain. Physics Reports, 2008, 462(2): 21-66 doi: 10.1016/j.physrep.2007.10.007 [3] Potekin R, Jayaprakash KR, Mcfarland DM, et al. Experimental study of strongly nonlinear resonances and anti-resonances in granular dimer chains. Experimental Mechanics, 2013, 53(5): 861-870 doi: 10.1007/s11340-012-9673-6 [4] Cheng H, Luding S, Saitoh K, et al. Elastic wave propagation in dry granular media: Effects of probing characteristics and stress history. International Journal of Solids and Structures, 2020, 187: 85-99 doi: 10.1016/j.ijsolstr.2019.03.030 [5] Wang J, Chu X. Impact energy distribution and wavefront shape in granular material assemblies. Granular Matter, 2019, 21(2): 23 doi: 10.1007/s10035-019-0880-z [6] Wang J, Chu X, Jiang Q, et al. Energy transfer and influence of excitation frequency in granular materials from the perspective of Fourier transform. Powder Technology, 2019, 356: 493-499 doi: 10.1016/j.powtec.2019.08.061 [7] Sadovskaya OV, Sadovskii VM. Elastoplastic waves in granular materials. Journal of Applied Mechanics & Technical Physics, 2003, 44(5): 741-747 [8] Pal RK, Awasthi AP, Geubelle PH. Characterization of wave propagation in elastic and elastoplastic granular chains. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2014, 89(1): 012204 [9] On T, Wang E, Lambros J. Plastic waves in one-dimensional heterogeneous granular chains under impact loading single intruders and dimer chains. International Journal of Solids & Structures, 2015, 62: 81-90 [10] Burgoyne HA, Newman JA, Jackson WC, et al. Guided impact mitigation in 2D and 3D granular crystals. Procedia Engineering, 2015, 103: 52-59 doi: 10.1016/j.proeng.2015.04.008 [11] Chong C, Porter MA, Kevrekidis PG, et al. Nonlinear coherent structures in granular crystals. Journal of Physics Condensed Matter An Institute of Physics Journal, 2017, 29(41): 413003 doi: 10.1088/1361-648X/aa7672 [12] Wang J, Chu X, Xiu C, et al. Stress wave in monosized bead string with various water contents. Advanced Powder Technology, 2020, 31(3): 993-1000 doi: 10.1016/j.apt.2019.12.027 [13] 孙锦山, 朱建士, 贾祥瑞. 颗粒材料中致密波结构研究. 力学学报, 1999, 31(4): 423-433 (Sun Jinshan, Zhu Jianshi, Jia Xiangrui. An analysis of compaction wave in granular material. Chinese Journal of Theoretical and Applied Mechanics, 1999, 31(4): 423-433 (in Chinese) doi: 10.3321/j.issn:0459-1879.1999.04.006 [14] 章青, 顾鑫郁, 杨天. 冲击载荷作用下颗粒材料动态力学响应的近场动力学模拟. 力学学报, 2016, 48(1): 56-63 (Zhang Qing, Gu Xinyu, Yang Tian. Peridynamics simulation for dynamic response of granular materials under impact loading. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 56-63 (in Chinese) doi: 10.6052/0459-1879-15-291 [15] 修晨曦, 楚锡华. 基于微形态模型的颗粒材料中波的频散现象研究. 力学学报, 2018, 50(2): 315-328 (Xiu Chenxi, Chu Xihua. Study on dispersion behavior and band gap in granular materials based on a micromorphic model. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 315-328 (in Chinese) doi: 10.6052/0459-1879-17-420 [16] Mouraille O, Mulder WA, Luding S. Sound wave acceleration in granular materials. Journal of Statistic Mechanics, 2006, 47(7): 1192-1197 [17] Awasthi AP, Smith KJ, Geubelle PH, et al. Propagation of solitary waves in 2D granular media: A numerical study. Mechanics of Materials, 2012, 54: 100-112 doi: 10.1016/j.mechmat.2012.07.005 [18] Chotiros NP, Isakson MJ. Shear and compressional wave speeds in Hertzian granular media. Journal of the Acoustical Society of America, 2011, 129(6): 3531 doi: 10.1121/1.3571421 [19] Huang B, Xia T, Qiu H, et al. Shear wave velocity in sand considering the effects of frequency based on particle contact theory. Wave Motion, 2017, 72: 173-186 doi: 10.1016/j.wavemoti.2017.02.006 [20] Yang J, Sutton M. Nonlinear wave propagation in a hexagonally packed granular channel under rotational dynamics. International Journal of Solids & Structures, 2015: 65-73 [21] Lisyansky A, Meimukhin D, Starosvetsky Y. Primary wave transmission in the hexagonally packed, damped granular crystal with a spatially varying cross section. Communications in Nonlinear Science & Numerical Simulation, 2015, 27(1-3): 193-205 [22] Keki A, Van Gorder R. Wave propagation across interfaces induced by different interaction exponents in ordered and disordered Hertz-like granular chains. Physica D: Nonlinear Phenomena, 2018, 384: 18-33 [23] Hua T, Van Gorder RA. Wave propagation and pattern formation in two-dimensional hexagonally-packed granular crystals under various configurations. Granular Matter, 2019, 21(1): 3 doi: 10.1007/s10035-018-0852-8 [24] Li LL, Yang XQ, Wei Z. Two interactional solitary waves propagating in two-dimensional hexagonal packing granular system. Granular Matter, 2018, 20(3): 49 doi: 10.1007/s10035-018-0810-5 [25] Leonard A, Fraternali F, Daraio C. Directional wave propagation in a highly nonlinear square packing of spheres. Experimental Mechanics, 2013, 53(3): 327-337 doi: 10.1007/s11340-011-9544-6 [26] Leonard A, Daraio C, Awasthi A. Effects of weak disorder on stress-wave anisotropy in centered square nonlinear granular crystals. Physical Review E: Statistical, 2012, 86(3): 1-10 [27] Leonard A, Daraio C. Stress wave anisotropy in centered square highly nonlinear granular systems. Physical Review Letters, 2012, 108(21): 214301-214301 doi: 10.1103/PhysRevLett.108.214301 [28] Leonard A, Ponson L, Daraio C. Wave mitigation in ordered networks of granular chains. Journal of the Mechanics & Physics of Solids, 2014, 73(4336): 103-117 [29] Xu J, Zheng B. Stress wave propagation in two-dimensional buckyball lattice. Scientific Reports, 2016, 6: 37692 doi: 10.1038/srep37692 [30] Galich PI, Fang NX, Boyce MC, et al. Elastic wave propagation in finitely deformed layered materials. Journal of the Mechanics and Physics of Solids, 2017, 98: 390-410 doi: 10.1016/j.jmps.2016.10.002 [31] Zhou XZ, Wang YS, Zhang C. Effects of material parameters on elastic band gaps of two-dimensional solid phononic crystals. Journal of Applied Physics, 2009, 106(1): 2022 [32] Wang J, Chu X, Zhang J, et al. The effects of microstructure on wave velocity and wavefront in granular assemblies with binary-sized particles. International Journal of Solids and Structures, 2018, 159(2): 156-162 [33] Wang J, Chu X. Compressive wave propagation in highly ordered granular media based on DEM. International Journal of Nonlinear Sciences and Numerical Simulation, 2018, 19(5): 545-552 doi: 10.1515/ijnsns-2017-0213 -
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