Regularization analysis of the strong discontinuity-Cosserat finite element method for modeling strain localization in cohesive-frictional materials by spectral theory

Abstract

An inappropriate numerical approach adopted for modeling the strain localization of geomaterials often leads to ill-posed boundary value problems (BVP). In this article, we apply spectral analysis to study the regularization mechanism of Cosserat finite element method (CFEM) and strong discontinuity-Cosserat FEM (SD-CFEM). The 1D shear layer model and 2D plane strain tests are modeled to conduct the diagnostic spectral analysis. A 2D slope problem is simulated to demonstrate the effectiveness of SD-CFEM in simulating the characteristics of progressive deformation in geomaterials. The numerical results show that CFEM and SD-CFEM not only maintain the eigenvalues as positive, but also make the dominant eigenvectors for different mesh densities possess the identical evolution pattern which is the fundemental regularization mechanism of both methods. The deformation patterns reflected by dominant eigenvectors indicate that SD-CFEM is more robust in modeling strain localization/shear band than CFEM and SD-FEM do because the former can reflect the energy dissipation both in the shear band with a constant width and on the slip line in the shear band. It can be concluded from the displacement evolution process in the shear band that SD-CFEM inheriting the merits of CFEM and SD-FEM can physically and mathematically better simulate the whole deformation process of geomaterials from weak discontinuity (strain localization) to strong discontinuity (slip).