Download or read book Solution of Differential Equations in Mechanics of Granular Materials written by Adel M. Morad and published by LAP Lambert Academic Publishing. This book was released on 2014-11-03 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytical solutions of the nonlinear PDEs are presented to illustrate the wave propagation in granular materials. Theoretical investigations carried out for different values of the dispersion and microstructure parameters seem to show that the solutions of the models exhibit interesting features. Also, theoretical study of the two phase system of flow is presented to describe the fluid flow through porous granular matrix, and the various solutions of the magma equation are discussed to illustrate the evolution of porosity waves in the earth's interior. In addition, we consider the fluidization of granular materials by a vibrating wall. The system is studied in the case of viscous and inviscid model. Grains are modeled as smooth rigid disks and the collisions are characterized by a constant normal restitution coefficient. The solutions of the van der Waals model of a granular system, exhibit appearance of bubbles. The instability is caused by the energy dissipation at collisions. Painleve analysis is introduced to investigate the integrability. Dispersion properties are also discussed. This book is suitable and will be interesting for all researchers in related fields.
Download or read book Mathematical Modeling in Mechanics of Granular Materials written by Oxana Sadovskaya and published by Springer Science & Business Media. This book was released on 2012-06-08 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mechanics of Granular Materials written by James T. Jenkins and published by Elsevier. This book was released on 2017-05-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Applied Mechanics, Volume 7: Mechanics of Granular Materials: New Models and Constitutive Relations provides information pertinent to the fundamental aspects of the mechanics of granular materials. This book presents the theoretical and experimental studies of quasi-static deformations of granular materials. Organized into 30 chapters, this volume begins with an overview of the results on the description of a macroscopic stress measure and measures of the fabric of granular masses that support external loads through frictional contact. This text then introduces some quantities for the macroscopic description of mechanical and graphical characteristics of granular materials. Other chapters consider particle rolling, which appears to be a major microscopic deformation mechanism when interparticle friction is large. This book discusses as well the stress-induced anisotropy of granular materials that have initially strong anisotropic fabric. The final chapter deals with the interpretation of linear instabilities of voidage disturbances in fluidized beds. This book is a valuable resource for scientists, theoreticians, and experimentalists.
Download or read book Mathematics and Mechanics of Granular Materials written by James M. Hill and published by Springer Science & Business Media. This book was released on 2005-12-27 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mechanics of Granular Materials An Introduction written by K. Iwashita and published by CRC Press. This book was released on 2020-08-13 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook compiles reports written by about 35 internationally recognized authorities, and covers a range of interests for geotechnical engineers. Topics include: fundamentals for mechanics of granular materials; continuum theory of granular materials; and discrete element approaches.
Download or read book Understanding the Discrete Element Method written by Hans-Georg Matuttis and published by John Wiley & Sons. This book was released on 2014-05-12 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives readers a more thorough understanding of DEM and equips researchers for independent work and an ability to judge methods related to simulation of polygonal particles Introduces DEM from the fundamental concepts (theoretical mechanics and solidstate physics), with 2D and 3D simulation methods for polygonal particles Provides the fundamentals of coding discrete element method (DEM) requiring little advance knowledge of granular matter or numerical simulation Highlights the numerical tricks and pitfalls that are usually only realized after years of experience, with relevant simple experiments as applications Presents a logical approach starting withthe mechanical and physical bases,followed by a description of the techniques and finally their applications Written by a key author presenting ideas on how to model the dynamics of angular particles using polygons and polyhedral Accompanying website includes MATLAB-Programs providing the simulation code for two-dimensional polygons Recommended for researchers and graduate students who deal with particle models in areas such as fluid dynamics, multi-body engineering, finite-element methods, the geosciences, and multi-scale physics.
Download or read book Flow of Granular Materials Down an Inclined Plane written by and published by . This book was released on 1993 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mechanics of flowing granular materials such as coal, sand, fossil-fuel energy recovery, metal ores, etc., and their flow characteristics have received considerable attention in recent years because it has relevance to several technological problems. In a number of instances these materials are also heated prior to processing, or cooled after processing. The governing equations for the flow of granular materials taking into account the heat transfer mechanism are derived using the continuum model proposed by Rajagopal and Massoudi (1990). For a fully developed flow of granular materials down an inclined plane, these equations reduce to a system of coupled ordinary differential equations. The resulting boundary value problem is solved numerically and the results are presented. For a special case, it is possible to obtain an analytic solution; this is given in the Appendix A of this report.
Download or read book Granular Jumps Down an Inclined Plane written by M. C. Shen and published by . This book was released on 1983 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document studies granular jumps generated in the gravity flow of granular materials down an inclined plane. The equations governing the granular flow are reduced to a sequence of boundary value problems of linear ordinary differential equations by means of an asymptotic method. Their solutions are used to determine the Burgers equation, which possesses a progressive wave solution to describe a smooth granular jump. The wave speed and a criterion for the stability of the granular jump are also obtained. (Author).
Download or read book Theory of Dispersion in a Granular Medium written by Akio Ogata and published by . This book was released on 1970 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: A review of the theoretical aspects of dispersion of fluid flowing through a porous material.
Download or read book Symmetry Analysis of Differential Equations written by Daniel J. Arrigo and published by John Wiley & Sons. This book was released on 2015-01-30 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. Symmetry Analysis of Differential Equations: An Introduction also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations.
Download or read book Advances in Micromechanics of Granular Materials written by H.H. Shen and published by Elsevier. This book was released on 2013-10-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 45 papers presented in this volume all share the common goal of constructing continuum models based on the micro behaviours of granular materials. Computer simulations continue to provide observations to aid modelling, while new experimental works begin to show promise for increased understanding in this area. Theoretical studies have extended into transitions between the rapid and quasi-static regimes and the fluid and solid mixture flows. Exciting new topics discussed in this volume include: concepts of a measure for randomness in quasi-static granular materials, which is analogous to the granular temperature in a rapid flow; scaling effects in granular media and their implications in both physical and computer simulations; instability; and boundary effects on heterogeneous behavior in simple flow configurations, which are posing new challenges for mathematical modelling. The volume will prove indispensable reading for researchers interested in the current developments in the fundamental aspects of mechanics of granular materials.
Download or read book Micromechanics of Granular Materials written by Bernard Cambou and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nearly all solids are compised of grains. However most studies treat materials as a continious solid. The book applies analysis used on loose granular materials to dense grainular materials. This title’s main focus is devoted to static or dynamic loadings applied to dense materials, although rapid flows and widely dispersed media are also mentioned briefly. Three essential areas are covered: Local variable analysis: Contact forces, displacements and rotations, orientation of contacting particles and fabric tensors are all examples of local variables. Their statistical distributions, such as spatial distribution and possible localization, are analyzed, taking into account experimental results or numerical simulations. Change of scales procedures: Also known as “homogenization techniques”, these procedures make it possible to construct continuum laws to be used in a continuum mechanics approach or performing smaller scale analyses. Numerical modeling: Several methods designed to calculate approximate solutions of dynamical equations together with unilateral contact and frictional laws are presented, including molecular dynamics, the distinct element method and non-smooth contact dynamics. Numerical examples are given and the quality of numerical approximations is discussed.
Download or read book The Physics Of The Deformation Of Densely Packed Granular Materials written by Maarten Anton (Curt) Koenders and published by World Scientific. This book was released on 2020-03-10 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is of interest for those that are concerned professionally with granular materials: civil engineers, geologists and geophysicists, chemical engineers, pharmacists, food technologists, agriculturalists, biologists and astronomers.Granular materials play a role in nearly all human activities. For example, users of sand, from children in sandpits to sophisticated geotechnical engineers, know that it is a fascinating — and to some extent, unpredictable — material. In addition to sand, which itself may be of many compositions, there are various types of materials including gravel, fine-particle aggregates as employed in cosmetics, pharmaceuticals, dust, crushed rock and granules that occur in a domestic environment, such as breakfast cereals, sugar, salt and (instant or ground) coffee granules.The aim of the book is to present a theory that explains the physics behind the phenomena during the deformation of densely packed granular media. The physics that describes such features is rather subtle and is developed from the micro to macro level (the latter is the continuum mechanics level that is used in practical applications). It requires the analysis of anisotropy and the heterogeneity of the packing evaluated against the background of a frictional inter-particle interaction.
Download or read book Solving Ordinary Differential Equations II written by Ernst Hairer and published by Springer. This book was released on 2010-03-10 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including new numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes. From the reviews: "A superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." --MATHEMATICS TODAY
Download or read book Statics of Granular Media written by V. V. Sokolovskii and published by Elsevier. This book was released on 2016-12-05 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statics of Granular Media focuses on the theory of limiting equilibrium of a granular medium. The book first discusses the limiting of equilibrium of a granular medium, including limiting conditions, limiting equilibrium of foundations, and limiting plane equilibrium of a granular medium. The text also focuses on the stability of foundations and slopes. Topics include normal restraining pressure on foundations; normal failure pressure on foundations; stability of slopes; and shape of curvilinear curves. The selection also highlights pressure of a fill on retaining walls, including active and passive pressure of a fill on retaining walls, twin retaining walls, and limiting plane equilibrium of a lamellar medium. The text also underscores limiting equilibrium of a cohesive medium. Topics include stability of foundations; shape of curvilinear slopes; pressure of a fill on retaining walls; and limiting plane equilibrium of a cohesive medium. Limiting the equilibrium of wedges is also discussed. The book is a valuable source of data for readers interested in the theory of limiting equilibrium of a granular medium.
Download or read book Stochastic Methods in Mechanics of Granular Bodies written by J. Litwiniszyn and published by Springer. This book was released on 2014-05-04 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Equations And Asymptotic Theory In Mathematical Physics written by Hua Chen and published by World Scientific. This book was released on 2004-10-18 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
