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Nonlinear Continuum Mechanics and Physics

Nonlinear Continuum Mechanics and Physics
A Book

by Shaofan Li

  • Publisher : Academic Press
  • Release : 2019-04
  • Pages : 500
  • ISBN : 9780128115428
  • Language : En, Es, Fr & De
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Nonlinear Continuum Mechanics and Physics provides a differential geometry approach to nonlinear continuum mechanics that will appeal to both engineers and material scientists. It includes heuristic and rigorous expositions of crucial concepts like finite deformation compatibility conditions, the Lie-derivative, frame-indifference and material symmetry principles. With exercises at the end of each chapter to emphasize concepts, readers will be able to further understand the latest techniques and research. This book is designed to support postgraduates and researchers in the areas of mechanical engineering, nano-mechanics, biomechanics and computational mechanics. Systematically uses a differential geometric approach Provides new developments in convex analysis and variational calculus in finite deformation Investigates applications in biomechanics and soft matter mechanics Explains the atomistic interpretation of stress

Exam Prep for: Nonlinear Continuum Mechanics and Physics

Exam Prep for: Nonlinear Continuum Mechanics and Physics
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2021
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Nonlinear Continuum Mechanics

Nonlinear Continuum Mechanics
An Introduction to the Continuum Physics and Mathematical Theory of the Nonlinear Mechanical Behavior of Materials

by Donald Charles Leigh

  • Publisher : Unknown Publisher
  • Release : 1968
  • Pages : 240
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Non-linear Continuum Theories in Mechanics and Physics and their Applications

Non-linear Continuum Theories in Mechanics and Physics and their Applications
Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Bressanone (Bolzano), Italy, September 3-11, 1969

by R. S. Rivlin

  • Publisher : Springer Science & Business Media
  • Release : 2011-06-07
  • Pages : 356
  • ISBN : 3642110908
  • Language : En, Es, Fr & De
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P.A. Blythe: Non-linear far-field theories in relaxing gas flows.- Meixner: Thermodynamics of deformable materials.- A.C. Pipkin: Non-linear phenomena in continua.- R.S. Rivlin: An introduction to non-linear continuum mechanics.- G.F. Smith: The generation of integrity bases.

Nonlinear Continuum Mechanics of Solids

Nonlinear Continuum Mechanics of Solids
Fundamental Mathematical and Physical Concepts

by Yavuz Basar,Dieter Weichert

  • Publisher : Springer Science & Business Media
  • Release : 2013-11-11
  • Pages : 193
  • ISBN : 3662042991
  • Language : En, Es, Fr & De
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The aim of the book is the presentation of the fundamental mathematical and physical concepts of continuum mechanics of solids in a unified description so as to bring young researchers rapidly close to their research area. Accordingly, emphasis is given to concepts of permanent interest, and details of minor importance are omitted. The formulation is achieved systematically in absolute tensor notation, which is almost exclusively used in modern literature. This mathematical tool is presented such that study of the book is possible without permanent reference to other works.

Nonlinear Continuum Mechanics and Large Inelastic Deformations

Nonlinear Continuum Mechanics and Large Inelastic Deformations
A Book

by Yuriy I. Dimitrienko

  • Publisher : Springer Science & Business Media
  • Release : 2010-12-25
  • Pages : 721
  • ISBN : 9789400700345
  • Language : En, Es, Fr & De
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The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics
A Continuum Approach for Engineering

by Gerhard A. Holzapfel

  • Publisher : Wiley
  • Release : 2000-04-07
  • Pages : 470
  • ISBN : 9780471823193
  • Language : En, Es, Fr & De
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Nonlinear Solid Mechanics a Continuum Approach for Engineering Gerhard A. Holzapfel Graz University of Technology, Austria With a modern, comprehensive approach directed towards computational mechanics, this book covers a unique combination of subjects at present unavailable in any other text. It includes vital information on 'variational principles' constituting the cornerstone of the finite element method. In fact this is the only method by which Nonlinear Solid Mechanics is utilized in engineering practice. The book opens with a fundamental chapter on vectors and tensors. The following chapters are based on nonlinear continuum mechanics - an inevitable prerequisite for computational mechanicians. In addition, continuum field theory (applied to a representative sample of hyperelastic materials currently used in nonlinear computations such as incompressible and compressible materials) is presented, as are transversely isotropic materials, composite materials, viscoelastic materials and hyperelastic materials with isotropic damage. Another central chapter is devoted to the thermodynamics of materials, covering both finite thermoelasticity and finite thermoviscoelasticity. Also included are: * an up-to-date list of almost 300 references and a comprehensive index * useful examples and exercises for the student * selected topics of statistical and continuum thermodynamics. Furthermore, the principle of virtual work (in both the material and spatial descriptions) is compared with two and three-field variational principles particularly designed to capture kinematic constraints such as incompressibility. All of the features combined result in an essential text for final year undergraduates, postgraduates and researchers in mechanical, civil and aerospace engineering and applied maths and physics.

Continuum Mechanics

Continuum Mechanics
A Book

by Anthony James Merrill Spencer

  • Publisher : Courier Corporation
  • Release : 2004-01-01
  • Pages : 183
  • ISBN : 9780486435947
  • Language : En, Es, Fr & De
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Undergraduate text opens with introductory chapters on matrix algebra, vectors and Cartesian tensors, and an analysis of deformation and stress; succeeding chapters examine laws of conservation of mass, momentum, and energy as well as the formulation of mechanical constitutive equations. 1992 edition.

Mathematical Modeling in Continuum Mechanics

Mathematical Modeling in Continuum Mechanics
A Book

by Roger Temam,Alain Miranville

  • Publisher : Cambridge University Press
  • Release : 2005-05-19
  • Pages : 329
  • ISBN : 9781139443210
  • Language : En, Es, Fr & De
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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.

Continuum Mechanics

Continuum Mechanics
A Book

by C. S. Jog

  • Publisher : Cambridge University Press
  • Release : 2015-06-25
  • Pages : 873
  • ISBN : 1107091357
  • Language : En, Es, Fr & De
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"Presents several advanced topics including fourth-order tensors, differentiation of tensors, exponential and logarithmic tensors, and their application to nonlinear elasticity"--

Continuum Mechanics Via Problems and Exercises: Theory and problems

Continuum Mechanics Via Problems and Exercises: Theory and problems
A Book

by Margarita E. Eglit,Dewey H. Hodges

  • Publisher : World Scientific
  • Release : 1996
  • Pages : 523
  • ISBN : 9789810229627
  • Language : En, Es, Fr & De
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Nonlinear Analysis and Continuum Mechanics

Nonlinear Analysis and Continuum Mechanics
Papers for the 65th Birthday of James Serrin

by Giuseppe Butazzo,Giovanni Paolo Galdi,Ermanno Lanconelli,Patrizia Pucci

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 148
  • ISBN : 146122196X
  • Language : En, Es, Fr & De
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The chapters in this volume deal with four fields with deep historical roots that remain active areas reasearch: partial differential equations, variational methods, fluid mechanics, and thermodynamics. The collection is intended to serve two purposes: First, to honor James Serrin, in whose work the four fields frequently interacted; and second, to bring together work in fields that are usually pursued independently but that remain remarkably interrelated. Serrin's contributions to mathematical analysis and its applications are fundamental and include such theorems and methods as the Gilbarg- Serrin theorem on isoated singularities, the Serrin symmetry theorem, the Alexandrov-Serrin moving-plane technique, The Peletier-Serrin uniqueness theorem, and the Serrin integal of the calculus of variations. Serrin has also been noted for the elegance of his mathematical work and for the effectiveness of his teaching and collaborations.

Elementary Continuum Mechanics for Everyone

Elementary Continuum Mechanics for Everyone
With Applications to Structural Mechanics

by Esben Byskov

  • Publisher : Springer Science & Business Media
  • Release : 2013-02-03
  • Pages : 593
  • ISBN : 9400757662
  • Language : En, Es, Fr & De
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The book opens with a derivation of kinematically nonlinear 3-D continuum mechanics for solids. Then the principle of virtual work is utilized to derive the simpler, kinematically linear 3-D theory and to provide the foundation for developing consistent theories of kinematic nonlinearity and linearity for specialized continua, such as beams and plates, and finite element methods for these structures. A formulation in terms of the versatile Budiansky-Hutchinson notation is used as basis for the theories for these structures and structural elements, as well as for an in-depth treatment of structural instability.

Applied Continuum Mechanics

Applied Continuum Mechanics
A Book

by T. J. Chung

  • Publisher : Cambridge University Press
  • Release : 1996-01-26
  • Pages : 252
  • ISBN : 9780521482974
  • Language : En, Es, Fr & De
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A concise, applications-oriented introduction to continuum mechanics.

Elements of Continuum Mechanics

Elements of Continuum Mechanics
A Book

by R. C. Batra

  • Publisher : AIAA
  • Release : 2006
  • Pages : 325
  • ISBN : 9781600860485
  • Language : En, Es, Fr & De
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The Mechanics and Thermodynamics of Continua

The Mechanics and Thermodynamics of Continua
A Book

by Morton E. Gurtin,Eliot Fried,Lallit Anand

  • Publisher : Cambridge University Press
  • Release : 2010-04-19
  • Pages : 329
  • ISBN : 1139482157
  • Language : En, Es, Fr & De
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The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics
Theoretical Formulations and Finite Element Solution Methods

by Adnan Ibrahimbegovic

  • Publisher : Springer Science & Business Media
  • Release : 2009-04-02
  • Pages : 574
  • ISBN : 9048123313
  • Language : En, Es, Fr & De
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This book offers a recipe for constructing the numerical models for representing the complex nonlinear behavior of structures and their components, represented as deformable solid bodies. Its appeal extends to those interested in linear problems of mechanics.

Continuum Mechanics of Electromagnetic Solids

Continuum Mechanics of Electromagnetic Solids
A Book

by G.A. Maugin

  • Publisher : Elsevier
  • Release : 2013-10-22
  • Pages : 621
  • ISBN : 1483290107
  • Language : En, Es, Fr & De
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This volume is a rigorous cross-disciplinary theoretical treatment of electromechanical and magnetomechanical interactions in elastic solids. Using the modern style of continuum thermomechanics (but without excessive formalism) it starts from basic principles of mechanics and electromagnetism, and goes on to unify these two fields in a common framework. It treats linear and nonlinear static and dynamic problems in a variety of elastic solids such as piezoelectrics, electricity conductors, ferromagnets, ferroelectrics, ionic crystals and ceramics. Chapters 1-3 are introductory, describing the essential properties of electromagnetic solids, the essentials of the thermomechanics of continua, and the general equations that govern the electrodynamics of nonlinear continua in the nonrelativistic framework (e.g. Maxwell's equations, the fundamental balance laws of continuum mechanics, basic thermodynamical inequalities for electromagnetic continua, jump relations for studying the propagation of shock waves, nonlinear constitutive equations for large classes of materials). The remainder of the text presents in detail special cases, applications, solved problems, and more complex schemes of electromagnetic matter. Chapters 4 and 5 examine material schemes whose description relies on the above-mentioned equations. Chapters 6 and 7 are more advanced, reporting on recent progress in the field. Suitable for graduate teaching, the volume will also be useful to research workers and engineers in the field of electromagnetomechanical interactions, and to those interested in the basic principles, mathematical developments and applications of electroelasticity and magnetoelasticity in a variety of solid materials, such as crystals, polycrystals, compounds and alloys.

Nonlinear Mechanics of Structures

Nonlinear Mechanics of Structures
A Book

by M. Kleiber,C. Wozniak

  • Publisher : Springer Science & Business Media
  • Release : 2012-12-06
  • Pages : 472
  • ISBN : 9400905777
  • Language : En, Es, Fr & De
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The aim of this book is to provide a unified presentation of modern mechanics of structures in a form which is suitable for graduate students as well as for engineers and scientists working in the field of applied mechanics. Traditionally, students at technical universities have been taught subjects such as continuum mechanics, elasticity, plates and shells, frames or finite element techniques in an entirely separate manner. The authors' teaching experience clearly suggests that this situation frequently tends to create in students' minds an incomplete and inconsistent picture of the contemporary structural mechanics. Thus, it is very common that the fundamental laws of physics appear to students hardly related to simplified equations of different "technical" theories of structures, numerical solution techniques are studied independently of the essence of mechanical models they describe, and so on. The book is intended to combine in a reasonably connected and unified manner all these problems starting with the very fundamental postulates of nonlinear continuum mechanics via different structural models of "engineer ing" accuracy to numerical solution methods which can effectively be used for solving boundary-value problems of technological importance. The authors have tried to restrict the mathematical background required to that which is normally familiar to a mathematically minded engineering graduate.

Finite Elasticity and Viscoelasticity

Finite Elasticity and Viscoelasticity
A Course in the Nonlinear Mechanics of Solids

by A D Drozdov

  • Publisher : World Scientific
  • Release : 1996-01-11
  • Pages : 456
  • ISBN : 9814499757
  • Language : En, Es, Fr & De
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This book provides a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory. The objective is to expose the most intriguing aspects of elasticity and viscoelasticity with finite strains in such a way as to ensure mathematical correctness, on the one hand, and to demonstrate a wide spectrum of physical phenomena typical only of nonlinear mechanics, on the other. A novel aspect of the book is that it contains a number of examples illustrating surprising behaviour in materials with finite strains, as well as comparisons between theoretical predictions and experimental data for rubber-like polymers and elastomers. The book aims to fill a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics. The book has been developed from a graduate course in applied mathematics which the author has given for a number of years. Contents:Tensor CalculusMechanics of ContinuaConstitutive Equations in Finite ElasticityBoundary Problems in Finite ElasticityVariational Principles in ElasticityConstitutive Models in Finite ViscoelasticityBoundary Problems in Finite Viscoelasticity Readership: Applied mathematicians. keywords:Cauchy Elasticity;Strain Energy Density;Tensor Calculus;Kinematics of Continua;Constitutive Theory;Green Elasticity;Hyperelasticity;Elastic Potentials;Existence;Uniqueness;Boundary Value Problems;Lagrange Principle;Stability;First Order “… a systematic and self-consistent introduction to the nonlinear continuum mechanics of solids, from the main axioms to comprehensive aspects of the theory … fills a gap between mathematicians specializing in nonlinear continuum mechanics, and physicists and engineers who apply the methods of solid mechanics to a wide range of problems in civil and mechanical engineering, materials science, and polymer physics.” Lavoisier-Technique et Documentation “The text should be effective in its intended role as a graduate-level introduction, as well as providing a source of applications and giving a basis for finding some details about the foundations of mechanics. Since there are few, if any, texts having attempted quite the aim of this book … Finite Elasticity and Viscoelasticity can be considered a useful addition to many libraries.” Appl Mech Rev “The textbook includes many exercises of different levels of complexity, which makes the lecture very attractive. The book can be recommended to researchers and students interested in modelling and mathematical problems of nonlinear mechanics of solids.” Mathematical Reviews