A micromorphic elastoplastic model and finite element simulation on failure behaviors of granular materials

Abstract

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

Propagation Characteristics of Rotation Waves in Transversely Isotropic Granular Media Considering Microstructure Effect

“…Based on the work of Misra et al, Xiu et al. [30,31] proposed a simplified micromorphic model considering only the first-order gradient of particle displacement and rotation and then also analyzed the propagation characteristics of plane waves.…”

“…Furthermore, much research has shown that the fabric anisotropy has a significant impact on the macroscale and microscale mechanical properties of granular materials [32][33][34][35]. In addition, the relative displacement and rotation at contacts are considered as basic independent variables in these models [25][26][27]30,31]. However, particle displacement and rotation are interrelated.…”

Study on dispersion and wave velocity in 2D elliptic granular crystals by a micromechanics-based micromorphic model

“…Misra and Poorsolhjouy 33 first proposed a micromorphic model based on a micromechanical approach and applied the model to analyze dispersions in elastic granular media 20,33 and 1D granular crystal. 21,34 Following this method, Xiu and Chu 22,35 proposed a first-order micromechanics-based micromorphic model to predict dispersions and frequency band gaps of granular materials. 22 Furthermore, Xiu et al 31 derived macroscopic micromorphic constitutive modulus tensors for granular crystals with different specific 3D microstructures, instead of granular materials based on a hypothesis of isotropic contact density distribution in above models.…”

“…22 Furthermore, Xiu et al 31 derived macroscopic micromorphic constitutive modulus tensors for granular crystals with different specific 3D microstructures, instead of granular materials based on a hypothesis of isotropic contact density distribution in above models. 22,35 In this way, more microscopic information is considered by specific particle arrangements and sizes, void ratios, and coordination numbers. And dispersions predicted by the micromechanics-based micromorphic model are obtained for different granular crystals.…”

Numerical simulation of impulse waves in Cosserat media based on a time‐discontinuous Galerkin finite element method

“…However, limitations are found for the classical theory to solve dynamic problems as followings 12 . (1) The classical theory cannot give complete motion and wave modes for materials with inhomogeneous microstructures such as granular materials, porous media, layered materials, bones, and so forth 13,14 In fact, from the aspect of physics, these materials should have the rotation for each material point. Researchers have reported the experimental observation of coupled rotational‐translational wave modes 15,16 and the important role that rotations are playing in shear processes 17 .…”