Nonlinear softening Cosserat continuum model and its application in finite element analysis for strain localization of soils

An innovative approach is introduced to enhance the original soil nonlinear strain softening formula proposed by Ma et al. This formula is incorporated into the DP-MC yield criterion in the framework of Cosserat continuum, and the corresponding return mapping algorithm and consistent elastic-plastic tangent modulus matrix for the integration of constitutive equation are derived. The numerical implementation is realized through the user-defined element subroutine interface (UEL) in the ABAQUS finite element software. The proposed nonlinear softening DP-MC constitutive model for the Cosserat continuum is validated through the numerical modelling of the plane strain tests. The results demonstrate that the proposed model can effectively overcome the mesh-dependent issues of the classical finite element analysis for strain localization due to strain softening in soils. The model also captures the microscopic effects of particle rotation within the shear band. Additionally, the simulation for the plane compression tests highlights the significant impact of the softening coefficient ω and shape parameter η on the strength of soils.