Computational modeling of deformation bands in granular media. II. Numerical simulations Original Research Article

Development of accurate mathematical models of geomaterial behavior requires a more fundamental understanding of the localization phenomena; in particular, the important factors responsible for the inception and development of localized deformation. The objective of this paper is to implement and test the mathematical formulations presented in a companion paper to better understand the different failure processes in granular media, specifically the formation of deformation bands in geomaterials. Our approach revolves around the use of classical bifurcation theory combined with advanced constitutive modeling and state-of-the-art computation to capture the end members of the failures modes described in the companion paper, namely, simple shear, pure compaction, and pure dilation bands, as well as the combination modes described in the geological framework. The paper revisits the notion of the critical hardening modulus as it applies to the entire range of failure modes, elucidates the role of the third stress invariant and finite deformation effects on the localization properties, and describes some useful properties of the constitutive and algorithmic tangent operators as they relate to the capture of the onset of deformation bands in geomaterials.