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

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;
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出版历程
- 收稿日期: 2017-12-19
- 刊出日期: 2018-03-17

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

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