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

This paper introduces an innovative approach to enhance the original soil nonlinear strain softening formula proposed by Ma et al. 1. 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 Cosserat continuum is validated through the numerical modelling of the plane strain test. The results demonstrate that the proposed model can effectively overcome the mesh-dependent issues of 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 test highlights the significant impact of the softening coefficient ω and shape parameter η on the strength of soil: smaller ω and larger η result in lower ultimate bearing capacity factors. In the softening stage after the post-peak value, η primarily affects the rate at which the soil reaches the residual strength, while ω influences the magnitude of the residual strength.