Abstract: Compared with the Cosserat theory, the complexity of the numerical framework can be reduced in the couple stress theory to some extent, and it has been gradually applied to the geotechnical strain localization analysis. However, the C¹ continuity should be satisfied in the straight-forward couple stress finite element method, that is, the continuity of the strain inside the elements and on the interface of the elements should be satisfied. To avoid developing more complicated C¹ couple stress elements, within the framework of Cosserat continuum theory, the approximate solution of the couple stress theory can be obtained by relaxing the C¹ continuity with the aid of the penalty function method, and the penalty-based couple stress finite element method (named PCS-FEM) is developed. The effectiveness of the PCS-FEM is verified by the stress concentration problem of an elastic circular hole under plane strain condition, and it is further applied to the strain localization analysis of soil mass. Based on the numerical simulation of the plane strain experiment of Ottawa sand, it is found that the stress-strain curve and the failure form of shear band obtained by the PCS-FEM method are basically consistent with the test results, and the ill-conditioned mesh sensitivity problem of the classical continuum theory can be avoided by the PCS-FEM so that the well-posedness of the strain localization problem can be ensured. Based on the strain localization analysis of the soil slope subject to the eccentric load, it is found that the mesh sensitivity problem in the strain-softening stage of the soil slope can also be avoided, and the progressive failure process of the slope can be captured by the PCS-FEM.

Key words: Cosserat theory, couple stress theory, penalty function, internal characteristic length, strain localization