Shear band evolution and accumulated microstructural development in Cosserat media

This paper prepares the ground for the continuum analysis of shear band evolution using a Cosserat/micropolar constitutive equation derived from micromechanical considerations. The nature of the constitutive response offers two key advantages over other existing models. Firstly, its non-local character obviates the mathematical difficulties of traditional analyses, and facilitates an investigation of the shear band evolution (i.e. the regime beyond the onset of localization). Secondly, the constitutive model parameters are physical properties of particles and their interactions (e.g. particle stiffness coefficients, coefficients of inter-particle rolling friction and sliding friction), as opposed to poorly understood fitting parameters. In this regard, the model is based on the same material properties used as model inputs to a discrete element (DEM) analysis, therefore, the micromechanics approach provides the vehicle for incorporating results not only from physical experiments but also from DEM simulations. Although the capabilities of such constitutive models are still limited, much can be discerned from their general rate form. In this paper, an attempt is made to distinguish between those aspects of the continuum theory of localization that are independent of the constitutive model, and those that require significant advances in the understanding of micromechanics