A micromechanics-based micromorphic model for granular materials and prediction on dispersion behaviors

Abstract

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.