Numerical modeling of strain localization in granular materials using Cosserat theory enhanced with microfabric properties

Finite element solution in the updated Lagrangian frame is used to investigate the strain localization phenomenon "shear bands" in granular materials. The micro-polar theory originally proposed by the Cosserat brothers is used as the mathematical foundation for the continuum formulations. A laboratory testing results are used for verification and comparison with the numerical simulation. Silica sand and glass beads with different shape indices, size and surface roughness were tested under biaxial and triaxial loading conditions to investigate the physics of the problem. Many researchers have investigated the phenomenon and the factors affecting its properties; namely, the thickness of the shear band and its inclination. In this study, additional factors were investigated and recommendations are provided accordingly. More precisely, the shape non-uniformity and the irregular surface roughness of the grains were studied carefully to evaluate their effect on shear band characteristics. To this end, attempts have been made to bring these additional micro-properties into the constitutive equations in this study. Elasto-plastic constitutive laws with a non-associated flow rule were used in order to capture the high deformations inside the localization zones. The Micropolar theory requires two independent kinematical fields; the first is the Cosserat objective strain tensor and the second is the curvature or the rotation gradient vector. The deviation in the kinematics is performed using Cosserat Continuum.; A single hardening yielding model, (Lade's model), with a different plastic potential function has been enhanced to account for the couple stresses and the rotations of the grains through the stress invariants. The constitutive model was first implemented into a FORTRAN subroutine and verified using triaxial and biaxial tests results (prediction of stress-strain and volumetric strain-axial strain curves). Thereafter those constitutive relations were implemented into a User Material Subroutine (UMAT) for ABAQUS and verified using axisymmetric and plane strain elements. Finally, the finite element formulations in the updated Lagrangian frame were obtained. These formulations have been implemented into the finite element program ABAQUS using the user element subroutine utility (UEL). The model was tested and verified using localizations results obtained from the literature for silica sand and glass beads.