This monograph contains original results in the field of mathematical and numerical modeling of mechanical behavior of granular materials and materials with different strengths. It proposes new models helping to define zones of the strain localization. The book shows how to analyze processes of the propagation of elastic and elastic-plastic waves in loosened materials, and constructs models of mixed type, describing the flow of granular materials in the presence of quasi-static deformation zones. In a last part, the book studies a numerical realization of the models on multiprocessor computer systems. The book is intended for scientific researchers, lecturers of universities, post-graduates and senior students, who specialize in the field of the deformable materials mechanics, mathematical modeling and adjacent fields of applied and calculus mathematics.

In view of its extreme complexity the mathematical description of the mechanical behaviour of granular materials is an extremely difficult task. Today many different models compete with each other. However, the complexity of the models hinders their comparison, and the potential users are confused and, often, disencouraged. This book is expected to serve as a milestone in the present situation, to evaluate the present methodes, to clear up the situation, to focus and encourage for further research activities.

This special issue collects selected contributions (excluding general lectures) of a Symposium on "Micro to MACRO Mathematical Modelling in Soil Mechanics", which took place at the University of Reggio Calabria, Italy, from May 29th to June 1st, 2018. The Symposium provided an opportunity to enhance the scientific debate on the construction of mathematical models for the description of the physical behaviour of soils, as well as on the suggestions provided by the micro-mechanical observation of the matter. The focus was on the comparison between the appropriateness of models and the need of mathematics to obtain rigorous results, which involves know-how from applied mathematical physics, geotechnical engineering and mechanics of solids. The contributions were selected by the Editors and the other Members of the Scientific Committee of the Symposium: Gianfranco Capriz (Pisa, Roma), Claudio di Prisco (Milan), Wolfgang Ehlers (Stuttgart), James T. Jenkins (Cornell), Stefan Luding (Twente), David Muir Wood (Dundee), Kenichi Soga (Berkeley).

The science of complex materials continues to engage researchers from a vast range of disciplines, including physics, mathematics, computational science, and virtually all domains of engineering.This volume presents a unique multidisciplinary panorama of the current research in complex materials. The contributions explore an array of problems reflecting recent developments in four main areas: characterization and modeling of disordered packings, micromechanics and continuum theory; discrete element method; statistical mechanics. The common theme is the quest to unravel the connection between the microscopic and macroscopic properties of complex materials.

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.

Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

Focussing on the basic mechanics and underlying physics of granular material, Mechanics of Granular Matter starts with an introduction to contact mechanics of individual particles before moving on to a discussion of the structure of force chain networks and the influence on bulk mechanical properties of granular solids and granular flows. Furthermore, a preliminary multi scale framework is proposed for the nonlinear mechanics and strain localization in granular materials.

This book brings together in a single volume various methods and skills for particle-scale or discrete-element numerical simulation of granular media. It covers a broad range of topics from basic concepts and methods towards more advanced aspects and technical details applicable to the current research on granular materials. Discrete-element simulations of granular materials are based on four basic models (molecular dynamics, contact dynamics, quasi-static and event driven) dealing with frictional contact interactions and integration schemes for the equations of dynamics. These models are presented in the first chapters of the book, followed by various methods for sample preparation and monitoring of boundary conditions, as well as dimensionless control parameters. Granular materials encountered in real life involve a variety of compositions (particle shapes and size distributions) and interactions (cohesive, hydrodynamic, thermal) that have been extensively covered by several chapters. The book ends with two applications in the field of geo-materials.

This book is devoted to the Discrete Element Method (DEM) technique, a discontinuum modelling approach that takes into account the fact that granular materials are composed of discrete particles which interact with each other at the microscale level. This numerical simulation technique can be used both for dispersed systems in which the particle-particle interactions are collisional and compact systems of particles with multiple enduring contacts. The book provides an extensive and detailed explanation of the theoretical background of DEM. Contact mechanics theories for elastic, elastic-plastic, adhesive elastic and adhesive elastic-plastic particle-particle interactions are presented. Other contact force models are also discussed, including corrections to some of these models as described in the literature, and important areas of further research are identified. A key issue in DEM simulations is whether or not a code can reliably simulate the simplest of systems, namely the single particle oblique impact with a wall. This is discussed using the output obtained from the contact force models described earlier, which are compared for elastic and inelastic collisions. In addition, further insight is provided for the impact of adhesive particles. The author then moves on to provide the results of selected DEM applications to agglomerate impacts, fluidised beds and quasi-static deformation, demonstrating that the DEM technique can be used (i) to mimic experiments, (ii) explore parameter sweeps, including limiting values, or (iii) identify new, previously unknown, phenomena at the microscale. In the DEM applications the emphasis is on discovering new information that enhances our rational understanding of particle systems, which may be more significant than developing a new continuum model that encompasses all microstructural aspects, which would most likely prove too complicated for practical implementation. The book will be of interest to academic and industrial researchers working in particle technology/process engineering and geomechanics, both experimentalists and theoreticians.

This book outlines the basic science underlying the prediction of stress and velocity distributions in granular materials. The nature of a rigid-plastic material is discussed and a comparison is made between the Coulomb and conical (extended Von Mises) models. The methods of measuring material properties are described and an interpretation of the experimental results is considered in the context of the Critical State Theory. Exercises and solutions are provided that will be particularly useful for the reader.