Abstract：A pressure-dependent elasto-plastic Cosserat continuum model is presented. The non-associated Drucker-Prager yield criterion is particularly considered. The scalar product of the stress rate and the strain rate is decomposed into the deviatoric and the spherical parts，and the consistent algorithm，such as the return mapping algorithm for the integration of the rate constitutive equation and the closed form of the consistent elasto-plastic tangent modulus matrix，of the pressure-dependent elastoplastic model is derived in the framework of Cosserat continuum theory. The matrix inverse operation usually required in the calculation of elasto-plastic tangent constitutive modulus matrix is avoided，which ensures the second-order convergence rate and the computational efficiency of the model in numerical solution procedure. The strain localization phenomena due to the strain softening are numerically simulated by using the developed model with corresponding finite element method. Numerical results of the plane strain examples illustrate that the capability and performance of the developed model in keeping the well-posedness of the boundary value problems with strain softening behavior incorporated and in reproducing the characteristics of strain localization problems，i.e.，the problems of intense straining development of localization in narrow bands and decreasing load-bearing capacity of the media with developments of the plastic strains.
