Cosserat model incorporating anisotropy evolution and its application in numerical analysis of strain localization in clay

This paper deeply couples the exponential-type nonlinear strain softening with the anisotropic method of microstructure tensor combined stress invariants, proposing an effective strength formula that reflects the anisotropy evolution of soil. Furthermore, an expression for the anisotropy ratio k of strength as an equivalent plastic strain-related variable is derived. For natural clay, this evolution of strength anisotropy is incorporated into the Mohr–Coulomb-matched Drucker–Prager (MC-matched DP) yield criterion within the Cosserat continuum framework, resulting in a more refined soil constitutive model. The main strength parameters required for this model can be conveniently obtained based on conventional soil tests, and the model functionality can be degraded through parameter adjustments. The detailed procedure of stress updating algorithm and the elastoplastic tangent modulus matrix are provided for the constitutive integration. Through the finite element implementation, the superiority of the model is demonstrated compared with existing literature. Also, a biaxial compression example is systematically analyzed to prove that the model can effectively reflect the sensitivity of soil to loading direction. Moreover, the evolution of the shear band morphology, particle rotation in the shear band, and the anisotropy degree presented by the model are consistent with previous experimental studies and discrete element method (DEM)-related literature results. Furthermore, the proposed model effectively addresses numerical convergence issues and mesh size dependence usually encountered in classical models during the simulation of strain localization occurred in the soil.