One of the purposes in this study is to develop a micromorphic continuum model for granular materials based on a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor conjugated with the symmetric curvature tensor is derived. In addition, a symmetric stress tensor is obtained conjugating a symmetric strain tensor. The presented model provides a complete deformation pattern for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic elastic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the presented micromorphic model. The other purpose in this study is to predict the dispersion behaviors of granular materials using the micromechanics-based micromorphic model. Five wave modes are predicted based on the presented model, including coupled transverse–rotational transverse, longitudinal, rotational longitudinal, transverse shear and rotational transverse waves. Investigating the propagations of these waves in the elastic granular media, the dispersion behaviors are predicted for coupled transverse–rotational transverse, longitudinal, rotational longitudinal waves, and the corresponding frequency band gaps are obtained.

Graphical Abstract

中文翻译：

---

基于微力学的粒料微晶模型及分散行为预测

本研究的目的之一是基于微力学方法为颗粒材料开发微晶连续体模型。该模型提出了对称曲率张量，推导了与对称曲率张量共轭的对称耦合应力张量。另外，获得了对称应力张量与对称应变张量的共轭。通过考虑颗粒运动（位移和旋转）的分解，提出的模型为颗粒材料提供了完整的变形模式。因此，在微观结构信息的表达式中得出了宏观弹性本构关系和本构模量。此外，针对所提出的微晶模型获得了平衡方程和边界条件。本研究的另一个目的是使用基于微力学的微晶模型预测颗粒材料的分散行为。根据给出的模型预测了五种波模，包括横波-旋转横波，纵波，纵波，横切变波和横波。通过研究这些波在弹性颗粒介质中的传播，预测了横向-旋转横向，纵向，纵向旋转波的色散特性，并获得了相应的频带间隙。横向剪切和旋转横向波。通过研究这些波在弹性颗粒介质中的传播，预测了横向-旋转横向，纵向，纵向旋转波的色散特性，并获得了相应的频带间隙。横向剪切和旋转横向波。通过研究这些波在弹性颗粒介质中的传播，预测了横向-旋转横向，纵向，纵向旋转波的色散特性，并获得了相应的频带间隙。

图形概要