Mathematics and mechanics of granular materials -- The incremental response of soils. An investigation using a discrete-element model -- Initial response of a micro-polar hypoplastic material under plane shearing -- Some theoretical results about second-order work, uniqueness, existence and controllability independent of the constitutive equation -- Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers -- Micromechanical constitutive modelling of granular media: Evolution and loss of contact in particle clusters -- A hyperbolic well-posed model for the flow of granular materials -- Towards a theory of granular plasticity -- Formulation of non-standard dissipative behavior of geomaterials -- Bifurcation analysis for shear localization in non-polar and micro-polar hypoplastic continua -- Large-strain dynamic cavity expansion in a granular material -- Generalised homogenisation procedures for granular materials -- Some fundamental aspects of the continuumization problem in granular Media -- Compression and shear of a layer of granular material -- An assessment of plasticity theories for modeling the incrementally nonlinear behavior of granular soils -- Incompressible granular flow from wedge-shaped hoppers -- Micromechanic modeling and analysis of unsteady-state granular flow in a cylindrical hopper.Granular or particulate materials arise in almost every aspect of our lives, including many familiar materials such as tea, coffee, sugar, sand, cement and powders. At some stage almost every industrial process involves a particulate material, and it is usually the cause of the disruption to the smooth running of the process. In the natural environment, understanding the behaviour of particulate materials is vital in many geophysical processes such as earthquakes, landslides and avalanches. This book is a collection of current research from some of the major contributors in the topic of modelling the behaviour of granular materials. Papers from every area of current activity are included, such as theoretical, numerical, engineering and computational approaches. This book illustrates the numerous diverse approaches to one of the outstanding problems of modern continuum mechanics.