Abstract：An elastoplastic Cosserat continuum model for CAP constitutive model with non-smooth multiplicative yield surfaces is presented. Splitting the scalar product of the stress rate and the strain rate into the deviatoric and the spherical parts，the consistent algorithm of the CAP elastoplastic model is derived according to one or two yielding surfaces being activated in the framework of Cosserat continuum theory，i.e. the return mapping algorithm for the integration of the rate constitutive equation and the closed form of the consistent elastoplastic tangent modulus matrix. The matrix inverse operation usually required in the calculation of elastoplastic tangent constitutive modulus matrix is avoided. The strain localization and progressive failure phenomena of the slope due to strain softening and the failure of the tunnel due to the excavation are numerically simulated using the developed model with corresponding finite element method. Numerical results of the plane strain examples illustrate the capability and good performance of the present model in keeping the well-posedness of the boundary value problems with strain softening behaviors and non-associated plasticity incorporation and ensuring the second order convergence rate and the computational efficiency of the model in numerical solution procedure.
