The Mechanics of Constitutive Modeling

The Mechanics of Constitutive Modeling
Author: Niels Saabye Ottosen,Matti Ristinmaa
Publsiher: Elsevier
Total Pages: 700
Release: 2005-09-28
ISBN 10: 9780080525693
ISBN 13: 0080525695
Language: EN, FR, DE, ES & NL

The Mechanics of Constitutive Modeling Book Review:

Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. Topics covered include: Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The thermodynamic framework for constitutive modelling – Thermoplasticity - Uniqueness and discontinuous bifurcations • More comprehensive in scope than competitive titles, with detailed discussion of thermodynamics and numerical methods. • Offers appropriate strategies for numerical solution, illustrated by discussion of specific models. • Demonstrates each topic in a complete and self-contained framework, with extensive referencing.

Continuum Mechanics

Continuum Mechanics
Author: Franco M. Capaldi
Publsiher: Cambridge University Press
Total Pages: 343
Release: 2012-06-18
ISBN 10: 1107011817
ISBN 13: 9781107011816
Language: EN, FR, DE, ES & NL

Continuum Mechanics Book Review:

Designed for continuum mechanics courses and features both the theoretical framework and numerical methods required to model continuous material behaviour.

Continuum Mechanics Modeling of Material Behavior

Continuum Mechanics Modeling of Material Behavior
Author: Martin H. Sadd
Publsiher: Academic Press
Total Pages: 432
Release: 2018-03-31
ISBN 10: 0128116498
ISBN 13: 9780128116494
Language: EN, FR, DE, ES & NL

Continuum Mechanics Modeling of Material Behavior Book Review:

Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries; kinematics of motion and deformation; force and stress measures; and mass, momentum and energy balance principles. The book then moves beyond other books by dedicating the last chapter to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity, as well as linear and nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Offers a thorough, concise and organized presentation of continuum mechanics formulation Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study Features extensive use of exercises, providing more material for student engagement and instructor presentation

Continuum Mechanics and Plasticity

Continuum Mechanics and Plasticity
Author: Han-Chin Wu
Publsiher: CRC Press
Total Pages: 704
Release: 2004-12-20
ISBN 10: 0203491998
ISBN 13: 9780203491997
Language: EN, FR, DE, ES & NL

Continuum Mechanics and Plasticity Book Review:

Tremendous advances in computer technologies and methods have precipitated a great demand for refinements in the constitutive models of plasticity. Such refinements include the development of a model that would account for material anisotropy and produces results that compare well with experimental data. Key to developing such models-and to meeting

Constitutive Modelling of Solid Continua

Constitutive Modelling of Solid Continua
Author: José Merodio,Raymond Ogden
Publsiher: Springer Nature
Total Pages: 389
Release: 2019-11-14
ISBN 10: 3030315479
ISBN 13: 9783030315474
Language: EN, FR, DE, ES & NL

Constitutive Modelling of Solid Continua Book Review:

This volume consists of a collection of chapters by recognized experts to provide a comprehensive fundamental theoretical continuum treatment of constitutive laws used for modelling the mechanical and coupled-field properties of various types of solid materials. It covers the main types of solid material behaviour, including isotropic and anisotropic nonlinear elasticity, implicit theories, viscoelasticity, plasticity, electro- and magneto-mechanical interactions, growth, damage, thermomechanics, poroelasticity, composites and homogenization. The volume provides a general framework for research in a wide range of applications involving the deformation of solid materials. It will be of considerable benefit to both established and early career researchers concerned with fundamental theory in solid mechanics and its applications by collecting diverse material in a single volume. The readership ranges from beginning graduate students to senior researchers in academia and industry.

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials
Author: Peter Haupt
Publsiher: Springer Science & Business Media
Total Pages: 643
Release: 2013-03-14
ISBN 10: 3662047756
ISBN 13: 9783662047750
Language: EN, FR, DE, ES & NL

Continuum Mechanics and Theory of Materials Book Review:

The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

Mathematical Modeling in Continuum Mechanics

Mathematical Modeling in Continuum Mechanics
Author: Roger Temam,Alain Miranville
Publsiher: Cambridge University Press
Total Pages: 329
Release: 2005-05-19
ISBN 10: 9781139443210
ISBN 13: 1139443216
Language: EN, FR, DE, ES & NL

Mathematical Modeling in Continuum Mechanics Book Review:

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Nonlinear Continuum Mechanics for Finite Elasticity Plasticity

Nonlinear Continuum Mechanics for Finite Elasticity Plasticity
Author: Koichi Hashiguchi
Publsiher: Elsevier
Total Pages: 420
Release: 2020-06-19
ISBN 10: 0128194294
ISBN 13: 9780128194294
Language: EN, FR, DE, ES & NL

Nonlinear Continuum Mechanics for Finite Elasticity Plasticity Book Review:

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity empowers readers to fully understand the constitutive equation of finite strain, an essential piece in assessing the deformation/strength of materials and safety of structures. The book starts by providing a foundational overview of continuum mechanics, elasticity and plasticity, then segues into more sophisticated topics such as multiplicative decomposition of deformation gradient tensor with the isoclinic concept and the underlying subloading surface concept. The subloading surface concept insists that the plastic strain rate is not induced suddenly at the moment when the stress reaches the yield surface but it develops continuously as the stress approaches the yield surface, which is crucially important for the precise description of cyclic loading behavior. Then, the exact formulations of the elastoplastic and viscoplastic constitutive equations based on the multiplicative decomposition are expounded in great detail. The book concludes with examples of these concepts and modeling techniques being deployed in real-world applications. Table of Contents: 1. Mathematical Basics 2. General (Curvilinear) Coordinate System 3. Description of Deformation/Rotation in Convected Coordinate System 4. Deformation/Rotation (Rate) Tensors 5. Conservation Laws and Stress Tensors 6. Hyperelastic Equations 7. Development of Elastoplastic Constitutive Equations 8. Multiplicative Decomposition of Deformation Gradient Tensor 9. Multiplicative Hyperelastic-based Plastic and Viscoplastic Constitutive Equations 10. Friction Model: Finite Sliding Theory Covers both the fundamentals of continuum mechanics and elastoplasticity while also introducing readers to more advanced topics such as the subloading surface model and the multiplicative decomposition among others Approaches finite elastoplasticity and viscoplasticty theory based on multiplicative decomposition and the subloading surface model Provides a thorough introduction to the general tensor formulation details for the embedded curvilinear coordinate system and the multiplicative decomposition of the deformation gradient

Continuum Mechanics and Thermodynamics

Continuum Mechanics and Thermodynamics
Author: Ellad B. Tadmor,Ronald E. Miller,Ryan S. Elliott
Publsiher: Cambridge University Press
Total Pages: 329
Release: 2011-12-15
ISBN 10: 1139504827
ISBN 13: 9781139504829
Language: EN, FR, DE, ES & NL

Continuum Mechanics and Thermodynamics Book Review:

Continuum mechanics and thermodynamics are foundational theories of many fields of science and engineering. This book presents a fresh perspective on these fundamental topics, connecting micro- and nanoscopic theories and emphasizing topics relevant to understanding solid-state thermo-mechanical behavior. Providing clear, in-depth coverage, the book gives a self-contained treatment of topics directly related to nonlinear materials modeling. It starts with vectors and tensors, finite deformation kinematics, the fundamental balance and conservation laws, and classical thermodynamics. It then discusses the principles of constitutive theory and examples of constitutive models, presents a foundational treatment of energy principles and stability theory, and concludes with example closed-form solutions and the essentials of finite elements. Together with its companion book, Modeling Materials, (Cambridge University Press, 2011), this work presents the fundamentals of multiscale materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.

Multiscale Biomechanics

Multiscale Biomechanics
Author: Jean-Francois Ganghoffer
Publsiher: Elsevier
Total Pages: 582
Release: 2018-02-03
ISBN 10: 0081021151
ISBN 13: 9780081021156
Language: EN, FR, DE, ES & NL

Multiscale Biomechanics Book Review:

Multiscale Biomechanics provides new insights on multiscale static and dynamic behavior of both soft and hard biological tissues, including bone, the intervertebral disk, biological membranes and tendons. The physiological aspects of bones and biological membranes are introduced, along with micromechanical models used to compute mechanical response. A modern account of continuum mechanics of growth and remodeling, generalized continuum models to capture internal lengths scales, and dedicated homogenization methods are provided to help the reader with the necessary theoretical foundations. Topics discussed include multiscale methods for fibrous media based on discrete homogenization, generalized continua constitutive models for bone, and a presentation of recent theoretical and numerical advances. In addition, a refresher on continuum mechanics and more advanced background related to differential geometry, configurational mechanics, mechanics of growth, thermodynamics of open systems and homogenization methods is given in separate chapters. Numerical aspects are treated in detail, and simulations are presented to illustrate models. This book is intended for graduate students and researchers in biomechanics interested in the latest research developments, as well as those who wish to gain insight into the field of biomechanics. Provides a clear exposition of multiscale methods for fibrous media based on discrete homogenization and the consideration of generalized continua constitutive models for bone Presents recent theoretical and numerical advances for bone remodeling and growth Includes the necessary theoretical background that is exposed in a clear and self-contained manner Covers continuum mechanics and more advanced background related to differential geometry, configurational mechanics, mechanics of growth, thermodynamics of open systems and homogenization methods

Introduction to Continuum Mechanics

Introduction to Continuum Mechanics
Author: W Michael Lai,David H. Rubin,David Rubin,Erhard Krempl
Publsiher: Butterworth-Heinemann
Total Pages: 536
Release: 2009-07-23
ISBN 10: 0080942520
ISBN 13: 9780080942520
Language: EN, FR, DE, ES & NL

Introduction to Continuum Mechanics Book Review:

Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity, the tensor, introduced as a linear transformation. This is then followed by the formulation of the kinematics of deformation, large as well as very small, the description of stresses and the basic laws of continuum mechanics. As applications of these laws, the behaviors of certain material idealizations (models) including the elastic, viscous and viscoelastic materials, are presented. This new edition offers expanded coverage of the subject matter both in terms of details and contents, providing greater flexibility for either a one or two-semester course in either continuum mechanics or elasticity. Although this current edition has expanded the coverage of the subject matter, it nevertheless uses the same approach as that in the earlier editions - that one can cover advanced topics in an elementary way that go from simple to complex, using a wealth of illustrative examples and problems. It is, and will remain, one of the most accessible textbooks on this challenging engineering subject. Significantly expanded coverage of elasticity in Chapter 5, including solutions of some 3-D problems based on the fundamental potential functions approach. New section at the end of Chapter 4 devoted to the integral formulation of the field equations Seven new appendices appear at the end of the relevant chapters to help make each chapter more self-contained Expanded and improved problem sets providing both intellectual challenges and engineering applications

Basics of Continuum Plasticity

Basics of Continuum Plasticity
Author: Kwansoo Chung,Myoung-Gyu Lee
Publsiher: Springer
Total Pages: 360
Release: 2018-05-02
ISBN 10: 9811083061
ISBN 13: 9789811083068
Language: EN, FR, DE, ES & NL

Basics of Continuum Plasticity Book Review:

This book describes the basic principles of plasticity for students and engineers who wish to perform plasticity analyses in their professional lives, and provides an introduction to the application of plasticity theories and basic continuum mechanics in metal forming processes. This book consists of three parts. The first part deals with the characteristics of plasticity and instability under simple tension or compression and plasticity in beam bending and torsion. The second part is designed to provide the basic principles of continuum mechanics, and the last part presents an extension of one-dimensional plasticity to general three-dimensional laws based on the fundamentals of continuum mechanics. Though most parts of the book are written in the context of general plasticity, the last two chapters are specifically devoted to sheet metal forming applications. The homework problems included are designed to reinforce understanding of the concepts involved. This book may be used as a textbook for a one semester course lasting fourteen weeks or longer. This book is intended to be self-sufficient such that readers can study it independently without taking another formal course. However, there are some prerequisites before starting this book, which include a course on engineering mathematics and an introductory course on solid mechanics.

Continuum Mechanics

Continuum Mechanics
Author: Myron B. Allen
Publsiher: John Wiley & Sons
Total Pages: 304
Release: 2015-07-13
ISBN 10: 1118909348
ISBN 13: 9781118909348
Language: EN, FR, DE, ES & NL

Continuum Mechanics Book Review:

Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory Terminology that is aligned with standard courses in vector calculus and linear algebra The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting Over 200 exercises and problems with hints and solutions in an appendix Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an excellent reference for professional mathematicians, physical scientists, and engineers.

Constitutive Modelling of Solid Continua

Constitutive Modelling of Solid Continua
Author: José Merodio,Raymond Ogden
Publsiher: Springer Nature
Total Pages: 389
Release: 2019-11-14
ISBN 10: 3030315479
ISBN 13: 9783030315474
Language: EN, FR, DE, ES & NL

Constitutive Modelling of Solid Continua Book Review:

This volume consists of a collection of chapters by recognized experts to provide a comprehensive fundamental theoretical continuum treatment of constitutive laws used for modelling the mechanical and coupled-field properties of various types of solid materials. It covers the main types of solid material behaviour, including isotropic and anisotropic nonlinear elasticity, implicit theories, viscoelasticity, plasticity, electro- and magneto-mechanical interactions, growth, damage, thermomechanics, poroelasticity, composites and homogenization. The volume provides a general framework for research in a wide range of applications involving the deformation of solid materials. It will be of considerable benefit to both established and early career researchers concerned with fundamental theory in solid mechanics and its applications by collecting diverse material in a single volume. The readership ranges from beginning graduate students to senior researchers in academia and industry.

Continuum Mechanics

Continuum Mechanics
Author: Ellis H. Dill
Publsiher: CRC Press
Total Pages: 368
Release: 2006-11-10
ISBN 10: 1420009826
ISBN 13: 9781420009828
Language: EN, FR, DE, ES & NL

Continuum Mechanics Book Review:

Most books on continuum mechanics focus on elasticity and fluid mechanics. But whether student or practicing professional, modern engineers need a more thorough treatment to understand the behavior of the complex materials and systems in use today. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity offers a complete tour of the subject that includes not only elasticity and fluid mechanics but also covers plasticity, viscoelasticity, and the continuum model for fatigue and fracture mechanics. In addition to a broader scope, this book also supplies a review of the necessary mathematical tools and results for a self-contained treatment. The author provides finite element formulations of the equations encountered throughout the chapters and uses an approach with just the right amount of mathematical rigor without being too theoretical for practical use. Working systematically from the continuum model for the thermomechanics of materials, coverage moves through linear and nonlinear elasticity using both tensor and matrix notation, plasticity, viscoelasticity, and concludes by introducing the fundamentals of fracture mechanics and fatigue of metals. Requisite mathematical tools appear in the final chapter for easy reference. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity builds a strong understanding of the principles, equations, and finite element formulations needed to solve real engineering problems.

Computational Continuum Mechanics

Computational Continuum Mechanics
Author: Ahmed A. Shabana
Publsiher: John Wiley & Sons
Total Pages: 368
Release: 2018-01-30
ISBN 10: 1119293200
ISBN 13: 9781119293200
Language: EN, FR, DE, ES & NL

Computational Continuum Mechanics Book Review:

An updated and expanded edition of the popular guide to basic continuum mechanics and computational techniques This updated third edition of the popular reference covers state-of-the-art computational techniques for basic continuum mechanics modeling of both small and large deformations. Approaches to developing complex models are described in detail, and numerous examples are presented demonstrating how computational algorithms can be developed using basic continuum mechanics approaches. The integration of geometry and analysis for the study of the motion and behaviors of materials under varying conditions is an increasingly popular approach in continuum mechanics, and absolute nodal coordinate formulation (ANCF) is rapidly emerging as the best way to achieve that integration. At the same time, simulation software is undergoing significant changes which will lead to the seamless fusion of CAD, finite element, and multibody system computer codes in one computational environment. Computational Continuum Mechanics, Third Edition is the only book to provide in-depth coverage of the formulations required to achieve this integration. Provides detailed coverage of the absolute nodal coordinate formulation (ANCF), a popular new approach to the integration of geometry and analysis Provides detailed coverage of the floating frame of reference (FFR) formulation, a popular well-established approach for solving small deformation problems Supplies numerous examples of how complex models have been developed to solve an array of real-world problems Covers modeling of both small and large deformations in detail Demonstrates how to develop computational algorithms using basic continuum mechanics approaches Computational Continuum Mechanics, Third Edition is designed to function equally well as a text for advanced undergraduates and first-year graduate students and as a working reference for researchers, practicing engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.

Continuum Mechanics

Continuum Mechanics
Author: D. S. Chandrasekharaiah,Lokenath Debnath
Publsiher: Elsevier
Total Pages: 595
Release: 2014-05-19
ISBN 10: 1483294684
ISBN 13: 9781483294681
Language: EN, FR, DE, ES & NL

Continuum Mechanics Book Review:

A detailed and self-contained text written for beginners, Continuum Mechanics offers concise coverage of the basic concepts, general principles, and applications of continuum mechanics. Without sacrificing rigor, the clear and simple mathematical derivations are made accessible to a large number of students with little or no previous background in solid or fluid mechanics. With the inclusion of more than 250 fully worked-out examples and 500 worked exercises, this book is certain to become a standard introductory text for students as well as an indispensable reference for professionals. Key Features * Provides a clear and self-contained treatment of vectors, matrices, and tensors specifically tailored to the needs of continuum mechanics * Develops the concepts and principles common to all areas in solid and fluid mechanics with a common notation and terminology * Covers the fundamentals of elasticity theory and fluid mechanics

Notes on Continuum Mechanics

Notes on Continuum Mechanics
Author: Eduardo WV Chaves
Publsiher: Springer Science & Business Media
Total Pages: 700
Release: 2013-06-13
ISBN 10: 940075986X
ISBN 13: 9789400759862
Language: EN, FR, DE, ES & NL

Notes on Continuum Mechanics Book Review:

This publication is aimed at students, teachers, and researchers of Continuum Mechanics and focused extensively on stating and developing Initial Boundary Value equations used to solve physical problems. With respect to notation, the tensorial, indicial and Voigt notations have been used indiscriminately. The book is divided into twelve chapters with the following topics: Tensors, Continuum Kinematics, Stress, The Objectivity of Tensors, The Fundamental Equations of Continuum Mechanics, An Introduction to Constitutive Equations, Linear Elasticity, Hyperelasticity, Plasticity (small and large deformations), Thermoelasticity (small and large deformations), Damage Mechanics (small and large deformations), and An Introduction to Fluids. Moreover, the text is supplemented with over 280 figures, over 100 solved problems, and 130 references.

Advanced Mechanics of Continua

Advanced Mechanics of Continua
Author: Karan S. Surana
Publsiher: CRC Press
Total Pages: 786
Release: 2016-04-27
ISBN 10: 1498708110
ISBN 13: 9781498708111
Language: EN, FR, DE, ES & NL

Advanced Mechanics of Continua Book Review:

Explore the Computational Methods and Mathematical Models That Are Possible through Continuum Mechanics Formulations Mathematically demanding, but also rigorous, precise, and written using very clear language, Advanced Mechanics of Continua provides a thorough understanding of continuum mechanics. This book explores the foundation of continuum mechanics and constitutive theories of materials using understandable notations. It does not stick to one specific form, but instead provides a mix of notations that while in many instances are different than those used in current practice, are a natural choice for the information that they represent. The book places special emphasis on both matrix and vector notations, and presents material using these notations whenever possible. The author explores the development of mathematical descriptions and constitutive theories for deforming solids, fluids, and polymeric fluids—both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contravariant bases. He also establishes the tensorial nature of strain measures and influence of rotation of frames on various measures, illustrates the physical meaning of the components of strains, presents the polar decomposition of deformation, and provides the definitions and measures of stress. Comprised of 16 chapters, this text covers: Einstein’s notation Index notations Matrix and vector notations Basic definitions and concepts Mathematical preliminaries Tensor calculus and transformations using co- and contra-variant bases Differential calculus of tensors Development of mathematical descriptions and constitutive theories Advanced Mechanics of Continua prepares graduate students for fundamental and basic research work in engineering and sciences, provides detailed and consistent derivations with clarity, and can be used for self-study.

Tensor Analysis and Continuum Mechanics

Tensor Analysis and Continuum Mechanics
Author: Y.R. Talpaert
Publsiher: Springer Science & Business Media
Total Pages: 591
Release: 2013-03-14
ISBN 10: 9401599882
ISBN 13: 9789401599887
Language: EN, FR, DE, ES & NL

Tensor Analysis and Continuum Mechanics Book Review:

This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc ..