基于微形态模型的颗粒材料中波的频散现象研究

修晨曦; 楚锡华

doi:10.6052/0459-1879-17-420

基于微形态模型的颗粒材料中波的频散现象研究

doi: 10.6052/0459-1879-17-420

武汉大学土木建筑工程学院工程力学系,武汉 430072

基金项目: 国家自然科学基金资助项目(11772237，11472196).

详细信息

作者简介:
null

作者简介：楚锡华，教授，主要研究方向：计算固体力学，颗粒材料力学. E-mail: Chuxh@whu.edu.cn

中图分类号: O34;
计量
- 文章访问数: 1330
- HTML全文浏览量: 202
- PDF下载量: 485
- 被引次数: 0
出版历程
- 收稿日期: 2017-12-20
- 刊出日期: 2018-03-18

STUDY ON DISPERSION BEHAVIOR AND BAND GAP IN GRANULAR MATERIALS BASED ON A MICROMORPHIC MODEL

Department of Engineering Mechanics,School of Civil Engineering, Wuhan University,Wuhan 430072,China

摘要

摘要: 基于颗粒材料冲击与波动响应特性的调控波传播行为的超材料设计受到广泛关注,设计这类材料需要对颗粒材料的波传播机制及调控机理有深入认识. 波在颗粒材料中传播的频散现象及频率带隙等行为与材料的非均匀性密切相关,通常讨论频散现象是基于弹性理论框架建立微结构连续体或高阶梯度连续体等广义连续体模型来进行. 本研究基于细观力学给出了一个颗粒材料的微形态连续体模型. 在该模型中,考虑了颗粒的平动和转动,且颗粒间的相对运动分解为两部分：即宏观平均运动和细观真实运动. 基于此分解,提出了一个完备的变形模式,得到了对应于不同应变及颗粒间运动的宏细观本构关系. 结合宏观变形能的细观变形能求和表达式,获得了基于细观量表示的宏观本构模量. 应用所建议模型考察了波在弹性颗粒介质的传播行为,给出了不同形式的波的频散曲线,结果显示此模型具有预测频率带隙的能力.
- 颗粒材料 /
- 微形态模型 /
- 波传播 /
- 频散 /
- 频率带隙
Abstract: The design of metamaterials is paid more attention to control the behaviors of the wave propagation based on response characteristics of shock and wave in granular materials, and it requires in-depth understanding of the propagation mechanism and control mechanism of waves for granular materials. The dispersion behavior and frequency band gap of granular materials are closely related to the heterogeneity. Generally, the dispersion behavior and frequency band gap are based on the elastic theory framework to establish a generalized continuum model including the microstructural continuum or the high order gradient continuum. This study proposes a micromorphic continuum model based on micromechanics for granular materials. In this model, the translation and the rotation of particles are taken into consideration, and the relative motion between particles is decomposed into two parts: the macroscopic mean motion and the microscopic actual motion. Based on this decomposition, a complete pattern of deformation is obtained. The macroscopic deformation energy is defined by a summation of the microscopic deformation energy at each contact. As a result, the micromorphic constitutive relation can be derived, and the corresponding constitutive modulus can be derived by microscopic parameters in terms of contact stiffness parameters and microscopic geometric parameters. The proposed model investigates the propagation of waves in an elastic granular medium, give dispersion curves for different waves such as longitudinal, transverse and rotational waves and predict the frequency band gap. It proves that the proposed model has the ability to describe dispersion behaviors and predict the frequency band gap in granular materials.
- granular materials /
- micromorphic model /
- wave propagation /
- dispersion /
- frequency band gap

HTML全文

参考文献(1)

[1]	Li XK, Chu XH, Feng YT.A discrete particle model and numerical modeling of the failure modes of granular materials.Engineering Computations, 2005, 22(8): 894-920
[2]	Chu XH, Yu C, Xiu CX, et al.Two scale modeling of behaviors of granular structure: Size effects and displacement fluctuations of discrete particle assembly.Structural Engineering & Mechanics, 2015, 55(2): 315-334
[3]	冯春, 李世海, 刘晓宇. 基于颗粒离散元法的连接键应变软化模型及其应用. 力学学报, 2016, 48(1): 76-85
[3]	(Feng Chun, Li Shihai, Liu Xiaoyu.Particle-dem based linked bar strain softening model and its application.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 76-85(in Chinese))
[4]	季顺迎, 孙珊珊, 陈晓东. 颗粒材料剪切流动状态转变的环剪试验研究. 力学学报, 2016, 48(5): 1061-1072
[4]	(Ji Shunying, Sun Shanshan, Chen Xiaodong.Shear cell test on transition of shear flow states of granular materials.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5): 1061-1072(in Chinese))
[5]	白以龙, 汪海英, 夏蒙棼等. 固体的统计细观力学—连接多个耦合的时空尺度. 力学进展, 2006, 36(2): 286-305
[5]	(Bai Yilong, Wang Haiying, Xia Mengfen, et al.Statistical mesomechanics of solid, linking coupled multiple space and time scales.Advances in Mechanics, 2006, 58(6): 286-305 (in Chinese))
[6]	Torquato S, Haslach H.Random heterogeneous materials: Microstructure and macroscopic properties.Applied Mechanics Reviews, 2002, 55(4): B62
[7]	Chang CS, Ma L.Modeling of discrete granulates as micropolar continua.Journal of Engineering Mechanics, 1990, 116(12): 2703-2721
[8]	Eringen AC, Suhubi ES.Nonlinear theory of simple micro-elastic solids—I.International Journal of Engineering Science, 1964, 2(2): 189-203
[9]	Eringen AC, Suhubi ES.Nonlinear theory of simple micro-elastic solids—II.International Journal of Engineering Science, 1964, 2(4): 389-404
[10]	Stojanovi R. On the mechanics of materials with microstructure.Acta Mechanica, 1972, 15(3-4): 261-273
[11]	Mühlhaus HB.Application of Cosserat theory in numerical solutions of limit load problems.Archive of Applied Mechanics, 1989, 59(2): 124-137
[12]	Li XK, Tang HX.A consistent return mapping algorithm for pressure-dependent elastoplastic Cosserat continua and modelling of strain localisation.Computers & Structures, 2005, 83(1): 1-10
[13]	Granik VT, Ferrari M.Microstructural mechanics of granular media.Mechanics of Materials, 1993, 15(4): 301-322
[14]	Christoffersen J, Mehrabadi MM, Nematnasser S.A micromechanical description of granular material behavior.Journal of Applied Mechanics, 1981, 48(2): 339
[15]	Mehrabadi MM, Nemat-Nasser S.Stress, dilatancy and fabric in granular materials.Mechanics of Materials, 1983, 2(2): 155-161
[16]	唐洪祥, 李锡夔. Cosserat连续体模型中本构参数对应变局部化模拟结果影响的数值分析. 计算力学学报, 2008, 25(5): 676-681
[16]	(Tang Hongxiang, Li Xikui.Numerical analysis for the effects of constitutive parameters in Cosserat continuum model on the simulation results of the strain localization.Chinese Journal of Computational Mechanics, 2008, 25(5): 676-681 (in Chinese))
[17]	Li XK, Liu QP, Zhang JB.A micro-macro homogenization approach for discrete particle assembly-Cosserat continuum modeling of granular materials.International Journal of Solids and Structures, 2010, 47(2): 291-303
[18]	Chang JF, Chu XH, Xu YJ.Finite-element analysis of failure in transversely isotropic geomaterials. International Journal of Geomechanics, 2014, 15(6): 04014096
[19]	Gennes PG.Granular matter: A tentative view.Reviews of Modern Physics, 1999, 71(2): S374
[20]	Chang CS, Chang Y, Kabir MG.Micromechanics modeling for stress-strain behavior of granular soils I: Theory.Journal of Geotechnical Engineering, 1992, 118(12): 1959-1974
[21]	Chang CS, Kuhn MR.On virtual work and stress in granular media.International Journal of Solids & Structures, 2005, 42(13): 3773-3793
[22]	Saxcé GD, Fortin J, Millet O.About the numerical simulation of the dynamics of granular media and the definition of the mean stress tensor.Mechanics of Materials, 2004, 36(12): 1175-1184
[23]	Kruyt NP.Statics and kinematics of discrete Cosserat-type granular materials.International Journal of Solids & Structures, 2003, 40(3): 511-534
[24]	Bonelli S, Millet O, Nicot F, et al.On the definition of an average strain tensor for two-dimensional granular material assemblies.International Journal of Solids & Structures, 2012, 49(7-8): 947-958
[25]	Kruyt NP, Millet O, Nicot F.Macroscopic strains in granular materials accounting for grain rotations.Granular Matter, 2014, 16(6): 933-944
[26]	Chang CS, Liao CL.Constitutive relation for a particulate medium with the effect of particle rotation.International Journal of Solids & Structures, 1990, 26(4): 437-453
[27]	Chang CS, Gao J.Second-gradient constitutive theory for granular material with random packing structure.International Journal of Solids & Structures, 1995, 32(16): 2279-2293
[28]	Misra A, Poorsolhjouy P.Granular micromechanics based micromorphic model predicts frequency band gaps.Continuum Mechanics & Thermodynamics, 2016, 28(1-2): 215-234
[29]	Mindlin RD.Micro-structure in linear elasticity.Archive for Rational Mechanics and Analysis, 1964, 16(1): 51-78
[30]	Eringen AC.Microcontinuum Field Theories: Foundations and Solids. New York: Springer, 1999
[31]	Neff P, Ghiba ID, Madeo A, et al.A unifying perspective: the relaxed linear micromorphic continuum.Continuum Mechanics & Thermodynamics, 2014, 26(5): 639-681
[32]	Ghiba ID, Neff P, Madeo A, et al.The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics.Mathematics & Mechanics of Solids, 2015, 20(10): 1171-1197
[33]	Neff P, Ghiba ID, Lazar M, et al.The relaxed linear micromorphic continuum: Well-posedness of the static problem and relations to the gauge theory of dislocations.The Quarterly Journal of Mechanics and Applied Mathematics, 2015, 68(1): 53-84
[34]	Merkel A, Luding S.Enhanced micropolar model for wave propagation in ordered granular materials.International Journal of Solids & Structures, 2017, 106: 91-105
[35]	Maugin GA, Metrikine AV.Mechanics of Generalized Continua: One Hundred Years After the Cosserats. Berlin, Heidelerg: Springer-Verlag, 2010
[36]	Askes H, Aifantis EC.Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results.International Journal of Solids & Structures, 2011, 48: 1962-1990
[37]	Muhlhaus HB, Oka F.Dispersion and wave propagation in discrete and continuous models for granular materials.International Journal of Solids & Structures, 1996, 33: 2841-2858
[38]	Huang WX, Sloan SW, Sheng DC.Analysis of plane Couette shear test of granular media in a Cosserat continuum approach.Mechanics of Materials, 2014, 69: 106-115
[39]	Tordesillas A, Muthuswamy M, Walsh SDC.Mesoscale measures of nonaffine deformation in dense granular assemblies.Journal of Engineering Mechanics, 2008, 134: 1095-1113
[40]	Jiang MJ, Yu HS, Harris D.Kinematic variables bridging discrete and continuum granular mechanics.Mechanics Research Communications, 2006, 33: 651-666
[41]	Lee JD, Wang XQ.Generalized micromorphic solids and fluids.International Journal of Solids & Structures, 2011, 49: 1378-1387
[42]	Hutter G.Homogenization of a Cauchy continuum towards a micromorphic continuum.Journal of the Mechanics and Physics, 2017, 99: 394-408
[43]	Forest S.Nonlinear regularization operators as a derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage.Proceedings of the Royal Society A, 2016, 472: 20150755
[44]	马天雪, 苏晓星, 董浩文等. 声光子晶体带隙特性与声光耦合作用研究综述. 力学学报, 2017, 49(4): 743-757
[44]	(Ma Tianxue, Su Xiaoxing, Dong Haowen, et al.Review of bandgap characteristics and acousto-optical coupling in phoxonic crystals.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(4): 743-757(in Chinese))
[45]	Tordesillas A, Walsh DCS.Incorporating rolling resistance and contact anisotropy in micromechanical models of granular media.Powder Technology, 2002, 124(1-2): 106-111
[46]	Hicher PY, Chang CS.Elastic model for partially saturated granular materials.Journal of Engineering Mechanics, 2008, 134(6): 505-513
[47]	Chang CS, Lun M.Elastic material constants for isotropic granular solids with particle rotation.International Journal of Solids & Structures, 1992, 29(8): 1001-10
[48]	Merkel A, Tournat V, Gusev V.Dispersion of elastic waves in three-dimensional noncohesive granular phononic crystals: properties of rotational modes.Physical Review E, 2010, 82(3 Pt 1): 031305
[49]	Merkel A, Tournat V, Gusev V.Experimental evidence of rotational elastic waves in granular phononic crystals.Physical Review Letters, 2011, 107(22): 225502