Doctor of Philosophy (PhD)


Civil and Environmental Engineering

Document Type



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 was 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. 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 the classical continuum with the incorporation of the couple stress effect. 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. 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 study findings were consistent with the experimental results and the physical understanding of the phenomenon. The surface roughness of the particles was found to affect the shear band thickness and present model was able to feel such effects. The shape of the particles was found to significantly affect the shear band thickness as well. The effect of the initial void ratio, confining pressure, particle size, surface roughness and shape of particles is discussed in this dissertation. At the end, the material properties spatial distribution was mapped into the finite element mesh and the material heterogeneity effect on strain localization is shown accordingly.



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Committee Chair

Khalid Alshibli