Continuum Mechanics of Single-Substance Bodies
Continuum Mechanics of Single-Substance Bodies

Author: A. Cemal Eringen

Publisher: Academic Press

Published: 2013-10-22

Total Pages: 635

ISBN-13: 1483276678

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Continuum Physics, Volume II: Continuum Mechanics of Single-Substance Bodies discusses the continuum mechanics of bodies constituted by a single substance, providing a thorough and precise presentation of exact theories that have evolved during the past years. This book consists of three parts—basic principles, constitutive equations for simple materials, and methods of solution. Part I of this publication is devoted to a discussion of basic principles irrespective of material geometry and constitution that are valid for all kinds of substances, including composites. The geometrical notions, kinematics, balance laws, and thermodynamics of continua are also deliberated. Part II focuses on materials consisting of a single substance, followed by a general theory of constitutive equations and special types of bodies. The thermoelastic solids, thermoviscous fluids, and memory-dependent materials are likewise considered. Part III is devoted to a discussion of a variety of nonlinear and linear problems, as well as nonlinear deformations of elastic solids, viscometric fluids, singular surfaces and waves, and complex function technique. This volume is a good source for researchers and students conducting work on the continuum mechanics of single-substance bodies.

Continuum Mechanics
Continuum Mechanics

Author: Fridtjov Irgens

Publisher: Springer Science & Business Media

Published: 2008-01-10

Total Pages: 667

ISBN-13: 3540742980

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This book presents an introduction into the entire science of Continuum Mechanics in three parts. The presentation is modern and comprehensive. Its introduction into tensors is very gentle. The book contains many examples and exercises, and is intended for scientists, practitioners and students of mechanics.

The Thermodynamics of Linear Fluids and Fluid Mixtures
The Thermodynamics of Linear Fluids and Fluid Mixtures

Author: Miloslav Pekař

Publisher: Springer Science & Business Media

Published: 2013-11-19

Total Pages: 315

ISBN-13: 3319025147

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In this book, Samohýl and Pekař offer a consistent and general non-equilibrium thermodynamic description for a model of chemically reacting mixtures. This type of model is frequently encountered in practice and up until now, chemically reacting systems (out of equilibrium) have rarely been described in books on non-equilibrium thermodynamics. Readers of this book benefit from the systematic development of the theory; this starts with general principles, going through the applications to single component fluid systems, and finishing with the theory of mixtures, including chemical reactions. The authors describe the simplest mixture model – the linear fluid – and highlight many practical and thermodynamically consistent equations for describing transport properties and reaction kinetics for this model. Further on in the book, the authors also describe more complex models. Samohýl and Pekař take special care to clearly explain all methodology and starting axioms and they also describe in detail applied assumptions and simplifications. This book is suitable for graduate students in chemistry, materials science and chemical engineering as well as professionals working in these and related areas.

Material Substructures in Complex Bodies
Material Substructures in Complex Bodies

Author: Gianfranco Capriz

Publisher: Elsevier

Published: 2007-05-24

Total Pages: 363

ISBN-13: 0080445357

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Stringent industrial requirements of sophisticated performances and of circumstantial control for micro-devices or nanotechnology manufactures, and other types of machinery at multiple scales, can be satisfied often only by resort to or allowance for complex materials. The adjective 'complex' beckons to the fact that the substructure influences gross mechanical behaviour in a prominent way and interactions due to substructural changes are represented directly. The description of the mechanical behaviour of complex bodies proposes a wide class of challenging problems from macroscopic-to-nano-world. The collection of chapters composing this book aims to explore some aspects of these problems, proposing also new matter of discussion together with specific solutions. Contributors are Carlo Cercignani, Gianfranco Capriz, Pierre Degond, Antonio Fasano, Harley T. Johnson, Sukky Jun, Krishna Kannan, Wing Kam Liu, Alberto Mancini, Paolo Maria Mariano, Ingo Müller, Kumbakonan R. Rajagopal, Jan Jerzy Slawianowski. The book can be a useful tool for Scholars and PhD students addressing their research activity toward basic mathematical and physical problems accruing from the mechanics of materials.

The Catalogue of Computational Material Models
The Catalogue of Computational Material Models

Author: Paul Steinmann

Publisher: Springer Nature

Published: 2021-03-20

Total Pages: 402

ISBN-13: 3030636844

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This book gives a comprehensive account of the formulation and computational treatment of basic geometrically linear models in 1D. To set the stage, it assembles some preliminaries regarding necessary modelling, computational and mathematical tools. Thereafter, the remaining parts are concerned with the actual catalogue of computational material models. To this end, after starting out with elasticity as a reference, further 15 different basic variants of material models (5 x each of {visco-elasticity, plasticity, visco-plasticity}, respectively) are systematically explored. The presentation for each of these basic material models is a stand-alone account and follows in each case the same structure. On the one hand, this allows, in the true sense of a catalogue, to consult each of the basic material models separately without the need to refer to other basic material models. On the other hand, even though this somewhat repetitious concept may seem tedious, it allows to compare the formulation and resulting algorithmic setting of the various basic material models and thereby to uncover, in detail, similarities and differences. In particular, the response of each basic material model is analysed for the identical histories (Zig-Zag, Sine, Ramp) of prescribed strain and stress so as to clearly showcase and to contrast to each other the characteristics of the various modelling options.

Tensor Calculus and Differential Geometry for Engineers
Tensor Calculus and Differential Geometry for Engineers

Author: Shahab Sahraee

Publisher: Springer Nature

Published: 2023-12-12

Total Pages: 684

ISBN-13: 3031339533

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The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.

The Finite Element Method for Three-Dimensional Thermomechanical Applications
The Finite Element Method for Three-Dimensional Thermomechanical Applications

Author: Guido Dhondt

Publisher: John Wiley & Sons

Published: 2004-11-19

Total Pages: 362

ISBN-13: 0470857625

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Though many 'finite element' books exist, this book provides a unique focus on developing the method for three-dimensional, industrial problems. This is significant as many methods which work well for small applications fail for large scale problems, which generally: are not so well posed introduce stringent computer time conditions require robust solution techniques. Starting from sound continuum mechanics principles, derivation in this book focuses only on proven methods. Coverage of all different aspects of linear and nonlinear thermal mechanical problems in solids are described, thereby avoiding distracting the reader with extraneous solutions paths. Emphasis is put on consistent representation and includes the examination of topics which are not frequently found in other texts, such as cyclic symmetry, rigid body motion and nonlinear multiple point constraints. Advanced material formulations include anisotropic hyperelasticity, large strain multiplicative viscoplasticity and single crystal viscoplasticity. Finally, the methods described in the book are implemented in the finite element software CalculiX, which is freely available (www.calculix.de; the GNU General Public License applies). Suited to industry practitioners and academic researchers alike, The Finite Element Method for Three-Dimensional Thermomechanical Applications expertly bridges the gap between continuum mechanics and the finite element method.

Continuum Physics
Continuum Physics

Author: A Eringen

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 332

ISBN-13: 0323155561

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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.

Mathematical Foundations of Elasticity
Mathematical Foundations of Elasticity

Author: Jerrold E. Marsden

Publisher: Courier Corporation

Published: 2012-10-25

Total Pages: 578

ISBN-13: 0486142272

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Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.