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.

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One of the purposes in this study is to develop a modified micromorphic continuum model for granular materials on the basis of a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor is derived conjugating the symmetric curvature tensor. In addition, a correct derivation is presented to obtain the symmetric stress tensor conjugated with the symmetric strain tensor. The modified model provides a complete deformation mode for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the modified micromorphic model. By considering the extended Drucker-Prager yield criterion, the micromorphic elastoplastic model is developed. Another purpose of this study is to derive the finite element formulation for the developed micromorphic elastoplastic model. Based on the ABAQUS user element (UEL) interface, numerical simulations investigated the load-displacement relationship and the strain localization behavior of granular materials and investigated the influence of microscopic parameters in the micromorphic model on these macroscopic mechanical responses. Numerical results illustrate the presented model's capability of simulating the strain-softening and strain localization behaviors, and the capability of considering the influence of microstructural information on the macroscopic mechanical behaviors of granular materials. K E Y W O R D Selasto-plasticity, failure behaviors, granular materials, micromechanics, modified micromorphic model 1 | INTRODUCTION Granular materials are composed of solid particles and voids between particles with a high degree of heterogeneity and complex mechanical behaviors such as multi-scale behaviors, crushability, anisotropy. 1-4 These macroscopic behaviors of granular materials are closely related to the microstructure and the interaction between particles. Chang and Ma 5 believed that a microstructural continuum approach can consider the effect of the microstructure and the interaction. Therefore, the microstructural continuum approach can be used to describe the macroscopic measures reflecting

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