Polar extension of a hypoplastic model for granular materials with shear localization

A new formulation for polar extension of hypoplastic model is presented for cohesionless granular materials. The formulation is proposed based on the analysis of stationary states, which is a generalization of the concept of critical state in soil mechanics. The model includes stress, couple stress and void ratio as state variables and takes into account the mean grain diameter and inter-granular friction resistance to grain sliding and rotation. A coupled limit condition embedded in the model is derived from the analysis for stationary states and the physical interpretation of frictional parameters are provided. The performance of the model is studied by modeling the plane shearing of an infinite granular layer, which shows the capability of the model in capturing the phenomenon of shear localization with a finite thickness. Numerical results are presented to show the evolution of a localized zone and of the state variables. Parametric studies are performed to investigate the dependence of the thickness of shear bands on various factors. A correlation is proposed to correlate the thickness of shear bands with grain size, frictional parameters and pressure-dependent relative density.