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

Abstract

SummaryOne 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.