A consistent return mapping algorithm for pressure-dependent elastoplastic Cosserat continua and modelling of strain localisation

A pressure-dependent elastoplastic Cosserat continuum model is presented in this paper. Splitting the scalar product of the stress rate and the strain rate into their deviatoric and spherical parts, the consistent algorithm, particularly the closed form of the consistent elastoplastic tangent modulus matrix, of the model is formulated in the framework of Cosserat continuum theory. The matrix inverse operation usually required in the calculation of elastoplastic tangent constitutive modulus matrix is avoided, that enhances computational efficiency of the model in numerical solution procedure with the second order convergence rate ensured. Numerical results illustrate the capability and performance of the present model in modelling strain localization phenomena due to strain softening.