Mechanics Of Mixtures
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Author | : Kumbakonam R Rajagopal |
Publisher | : World Scientific |
Total Pages | : 220 |
Release | : 1995-10-18 |
Genre | : Science |
ISBN | : 9814502596 |
This book presents a unified treatment of the mechanics of mixtures of several constituents within the context of continuum mechanics. After an introduction to the basic theory in the first few chapters, the book deals with a detailed exposition of the mechanics of a mixture of a fluid and an elastic solid, which is either isotropic or anisotropic and is capable of undergoing large deformations. Issues regarding the specification of boundary conditions for mixtures are discussed in detail and several boundary value and initial-boundary value problems are solved. The status of some special theories like those of Darcy and Biot are discussed. Such a study has relevance to several technologically significant problems in geomechanics, biomechanics, diffusion of contaminants and the swelling and absorption of fluids in polymers and polymer composites, to mention a few.
Author | : Kumbakonam Ramamani Rajagopal |
Publisher | : World Scientific |
Total Pages | : 220 |
Release | : 1995 |
Genre | : Science |
ISBN | : 9810215851 |
This book presents a unified treatment of the mechanics of mixtures of several constituents within the context of continuum mechanics. After an introduction to the basic theory in the first few chapters, the book deals with a detailed exposition of the mechanics of a mixture of a fluid and an elastic solid, which is either isotropic or anisotropic and is capable of undergoing large deformations. Issues regarding the specification of boundary conditions for mixtures are discussed in detail and several boundary value and initial-boundary value problems are solved. The status of some special theories like those of Darcy and Biot are discussed. Such a study has relevance to several technologically significant problems in geomechanics, biomechanics, diffusion of contaminants and the swelling and absorption of fluids in polymers and polymer composites, to mention a few.
Author | : A Eringen |
Publisher | : Elsevier |
Total Pages | : 332 |
Release | : 2012-12-02 |
Genre | : Science |
ISBN | : 0323155561 |
Continuum Physics, Volume III: Mixtures and EM Field Theories discusses the field theories for bodies composed of different substances, such as mixtures and interaction of electromagnetic effects with the deformable bodies. This book aims to present the mathematical foundations of nonlinear mechanical, electrical, and magnetic phenomena that take place in mixtures and materially uniform bodies. This volume consists of three parts. Part I is devoted to the development of the theory of mixtures, including kinematics, balance laws, and constitutive equations for bodies consisting of several different substances. Part II is concerned with the mechanics of deformable bodies interacted by electromagnetic fields. The deformation produced by EM fields, EM fields resulting from the deformation of bodies, and plethora of other physical phenomena arising from mechanical and EM interactions are also covered. Micromagnetism is covered in Part III, including considerations arising from the interaction of strong magnetic fields with the inner structure of the body. This publication is valuable to students and researchers interested in mixtures and EM field theories.
Author | : Lukas Schneider |
Publisher | : Springer Science & Business Media |
Total Pages | : 264 |
Release | : 2009-07-25 |
Genre | : Science |
ISBN | : 364202968X |
Mixture concepts are nowadays used in a great number of subjects of the - ological, chemical, engineering, natural and physical sciences (to name these alphabetically) and the theory of mixtures has attained in all these dis- plines a high level of expertise and specialisation. The digression in their development has on occasion led to di?erences in the denotation of special formulations as ‘multi-phase systems’ or ‘non-classical mixtures’, ‘structured mixtures’, etc. , and their representatives or defenders often emphasise the di?erences of these rather than their common properties. Thismonographisanattempttoviewtheoreticalformulationsofprocesses which take place as interactions among various substances that are spatially intermixedandcanbeviewedtocontinuously?llthespacewhichtheyoccupy as mixtures. Moreover, we shall assume that the processes can be regarded to becharacterisedbyvariableswhichobeyacertaindegreeofcontinuityintheir evolution, so that the relevant processes can be described mathematically by balance laws, in global or local form, eventually leading to di?erential and/or integralequations,towhichtheusualtechniquesoftheoreticalandnumerical analysis can be applied. Mixtures are generally called non-classical, if, apart from the physical laws (e. g. balances of mass, momenta, energy and entropy), also further laws are postulated,whicharelessfundamental,butmaydescribesomefeaturesofthe micro-structure on the macroscopic level. In a mixture of ?uids and solids – thesearesometimescalledparticleladensystems–thefractionofthevolume that is occupied by each constituent is a signi?cant characterisation of the micro-structure that exerts some in?uence on the macro-level at which the equations governing the processes are formulated. For solid-?uid mixtures at high solids fraction where particle contact is essential, friction between the particles gives rise to internal stresses, which turn out to be best described by an internal symmetric tensor valued variable.
Author | : Anthony Bedford |
Publisher | : Springer Nature |
Total Pages | : 114 |
Release | : 2021-12-14 |
Genre | : Science |
ISBN | : 3030903060 |
This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.
Author | : Pierre Duhem |
Publisher | : Springer Science & Business Media |
Total Pages | : 364 |
Release | : 2002-01-31 |
Genre | : History |
ISBN | : 9781402002328 |
In addition to lecturing in physics, Duhem began to publish articles on philosophical and historical topics related to his scientific interests in the late 19th century, many of which appeared in the Catholic journal Revue des questions scientifiques. The present volume focuses on chemistry, and includes the book, Le mixte et la combinaison chimique (1902), as well as several related articles from Revue des questions scientifiques and other sources, appearing here in English translation for the first time. Translated by Paul Needham (U. of Stockholm). For Duhem scholars, philosophers of science and chemists with an interest in philosophy. Annotation copyrighted by Book News, Inc., Portland, OR.
Author | : A. Ian Murdoch |
Publisher | : Cambridge University Press |
Total Pages | : 439 |
Release | : 2012-10-22 |
Genre | : Science |
ISBN | : 1139788787 |
Ian Murdoch's Physical Foundations of Continuum Mechanics will interest engineers, mathematicians, and physicists who study the macroscopic behaviour of solids and fluids or engage in molecular dynamical simulations. In contrast to standard works on the subject, Murdoch's book examines physical assumptions implicit in continuum modelling from a molecular perspective. In so doing, physical interpretations of concepts and fields are clarified by emphasising both their microscopic origin and sensitivity to scales of length and time. Murdoch expertly applies this approach to theories of mixtures, generalised continua, fluid flow through porous media, and systems whose molecular content changes with time. Elements of statistical mechanics are included, for comparison, and two extensive appendices address relevant mathematical concepts and results. This unique and thorough work is an authoritative reference for both students and experts in the field.
Author | : Yehuda Klausner |
Publisher | : Springer Science & Business Media |
Total Pages | : 638 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1447116771 |
Fundamentals of Continuum Mechanics of Soils provides a long-needed general scheme for the study of the important yet problematic material of soil. It closes the gap between two disciplines, soil mechanics and con- tinuum mechanics, showing that the familiar concepts of soil mechanics evolve directly from continuum mechanics. It confirms concepts such as pore pressures, cohesion and dependence of the shear stress on consolidation, and rejects the view that continuum mechanics cannot be applied to a material such as soil. The general concepts of continuum mechanics, field equations and constitutive equations are discussed. It is shown how the theory of mixtures evolves from these equations and how, along with energetics and irrevers- ible thermodynamics, it can be applied to soils. The discussion also sheds light on some aspects of mechanics of materials, especially compressible materials. Examples are the introduction of the Hencky measure of strain, the requirement of dual constitutive equations, and the dependence of the spent internal energy on the stored internal energy. Researchers in engineering mechanics and material sciences may find that the results of experiments on soils can be generalized and extended to other materials. The book is a reference text for students familiar with the fundamentals of mechanics, for scholars of soil engineering, and for soil scientists. It is also suitable as an advanced undergraduate course in soil mechanics.
Author | : Arieh Ben-Naim |
Publisher | : Oxford University Press |
Total Pages | : 399 |
Release | : 2006-07-27 |
Genre | : Science |
ISBN | : 0199299692 |
This book presents new and updated developments in the molecular theory of mixtures and solutions. It is based on the theory of Kirkwood and Buff which was published more than fifty years ago. This theory has been dormant for almost two decades. It has recently become a very powerful and general tool to analyze, study and understand any type of mixtures from the molecular, or the microscopic point of view. The traditional approach to mixture has been, for many years, based on the study of excess thermodynamic quantities. This provides a kind of global information on the system. The new approach provides information on the local properties of the same system. Thus, the new approach supplements and enriches our information on mixtures and solutions.
Author | : Kolumban Hutter |
Publisher | : Springer Science & Business Media |
Total Pages | : 645 |
Release | : 2013-11-11 |
Genre | : Science |
ISBN | : 3662064022 |
The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.