A micromechanics-based elasto-plastic model for granular media combined with Cosserat continuum theory

This paper is devoted to the micromechanical model of granular materials based on the Cosserat continuum theory. The generalised stress–strain relationships of a representative element volume are closely related to the micro elasto-plastic force–displacement and moment–rotation laws. With the help of generalised micro–macro relations, a micromechanical model is presented by aggregating the generalised micro elasto-plastic inter-particle contact laws in each contact orientation. A corresponding implicit multiscale integration algorithm for integrating the micromechanical model is proposed. Furthermore, the micromechanical model and implicit multiscale integration algorithm are simplified to consider a two-dimensional condition, and the Romberg integration of the numerical quadrature formula is also introduced in this condition. Compared with the data of Hostun sand and the results of DEM simulations for different particle shapes, it is demonstrated that the proposed micromechanical model can describe both the macro and micro responses of granular materials relatively well, such as strain softening/hardening, volumetric compaction/dilatancy, particle rotation, and evolution of the coordination number.