Elasto-Plastic FEM Analysis of Alternating Rock Mass Based by Cosserat Constitutive Model and Its Numerical Simulation

Classical yield criterions cannot be applied directly to Cosserat continua since the strain tensor and stress tensor in Cosserat continua are asymmetric. In this work, the strain tensor and stress tensor were decomposed into symmetric and anti-symmetric components, and the formulae of stress invariants were modified for Cosserat continua. Mohr-Coulomb yield criterion for Cosserat continua was established in detail, and the elasto-plastic FEM (Finite element method) based on the yield criterions was addressed as well. Then, the model was implemented into a Cosseart FEM program based on MATLAB platform. A numerical example on the underground cavern in inter-layered rock mass stability under gravity shows the superior behavior of the established Mohr-Coulomb yield criterion, and demonstrates that the Cosserat model incorporating an internal length scale can resolve the mesh-dependence that classical continua encounter in the strain localization problem. Moreover, it was shown that the FEM program based on MATLAB and Cosserat model was right and effective. The results reveal that, compared with the conventional continuum model, the proposed Cosserat model better reflects elasto-plastic FEM analysis of alternating rock mass, which is closer to the actual situation. The results aid in a better understanding of the mechanical properties of alternating rock masses.