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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

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
  • Release : 2010-11-30
  • Pages : 356
  • ISBN : 9783642110894
  • 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

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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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.

Finite Elasticity and Viscoelasticity

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

by Aleksey D. Drozdov

  • Publisher : Unknown Publisher
  • Release : 1996
  • Pages : 434
  • ISBN : 9786613948342
  • 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.

Continuum Methods of Physical Modeling

Continuum Methods of Physical Modeling
Continuum Mechanics, Dimensional Analysis, Turbulence

by Kolumban Hutter,Klaus Jöhnk

  • Publisher : Springer Science & Business Media
  • Release : 2013-11-11
  • Pages : 636
  • ISBN : 3662064022
  • Language : En, Es, Fr & De
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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.

Research in Non-Linear Continuum Mechanics

Research in Non-Linear Continuum Mechanics
A Book

by Bernard D. Coleman,CARNEGIE-MELLON UNIV PITTSBURGH PA MELLON INST OF SCIENCE.

  • Publisher : Unknown Publisher
  • Release : 1971
  • Pages : 8
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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The research supported by this grant was concentrated in two areas: (I) the theory of functional-differential equations, and (II) continuum physics, with emphasis on the mechanics, thermodynamics, and optical behavior of nonlinear media with memory. For many dynamical problems involving non-linear viscoelastic materials, thermodynamical considerations supply Lyapunov functionals which can be used to investigate the stability of equilibrium points. The work done here on functional-differential equations was directed toward such dynamical problems. The research in continuum physics led to the development of a mathematical framework for the description of induced birefringence in materials with long-range memory. It was shown that for certain broad classes of motions in general isotropic materials, material symmetry and the principle of frame-indifference can be employed to simplify the relation between the history strain and dielectric properties, without invoking special hypotheses of smoothness. It was shown that for all motions of plane strain and for some motions of plane stress, general reduced formulae can be derived for quantities accessible to measurement with a plan polariscope, such as the birefringence and the inclination of the axes of refraction. A study was made of thermodynamical restrictions on electromagnetic constitutive equations. (Author).

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials
A Book

by Peter Haupt

  • Publisher : Springer Science & Business Media
  • Release : 2013-03-14
  • Pages : 643
  • ISBN : 3662047756
  • Language : En, Es, Fr & De
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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.

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.

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

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.

Continuum Mechanics and Applications in Geophysics and the Environment

Continuum Mechanics and Applications in Geophysics and the Environment
A Book

by Brian Straughan,Ralf Greve,Harald Ehrentraut,Yongqi Wang

  • Publisher : Springer Science & Business Media
  • Release : 2013-03-09
  • Pages : 394
  • ISBN : 3662044390
  • Language : En, Es, Fr & De
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The topics covered include soil mechanics and porous media, glacier and ice dynamics, climatology and lake physics, climate change as well as numerical algorithms. The book, written by well-known experts, addresses researchers and students interested in physical aspects of our environment.

Differential Geometry and Kinematics of Continua

Differential Geometry and Kinematics of Continua
A Book

by John D Clayton

  • Publisher : World Scientific
  • Release : 2014-07-31
  • Pages : 192
  • ISBN : 9814616052
  • Language : En, Es, Fr & De
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This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided. Contents: IntroductionGeometric FundamentalsKinematics of Integrable DeformationGeometry of Anholonomic DeformationKinematics of Anholonomic DeformationList of SymbolsBibliographyIndex Readership: Researchers in mathematical physics and engineering mechanics. Key Features:Presentation of mathematical operations and examples in anholonomic space associated with a multiplicative decomposition (e.g., of the gradient of motion) is more general and comprehensive than any given elsewhere and contains original ideas and new resultsLine-by-line derivations are frequent and exhaustive, to facilitate practice and enable verification of final resultsGeneral analysis is given in generic curvilinear coordinates; particular sections deal with applications and examples in Cartesian, cylindrical, spherical, and convected coordinates. Indicial and direct notations of tensor calculus enable connections with historic and modern literature, respectivelyKeywords:Differential Geometry;Tensor Analysis;Continuum Mechanics;Kinematics;Deformation;Anholonomic Coordinates

Nonlinear Mechanics of Structures

Nonlinear Mechanics of Structures
A Book

by M. Kleiber,C. Wozniak

  • Publisher : Springer
  • Release : 2011-09-15
  • Pages : 472
  • ISBN : 9789401067478
  • 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.

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.

Developments and Novel Approaches in Biomechanics and Metamaterials

Developments and Novel Approaches in Biomechanics and Metamaterials
A Book

by Bilen Emek Abali,Ivan Giorgio

  • Publisher : Springer Nature
  • Release : 2020-07-06
  • Pages : 484
  • ISBN : 3030504646
  • Language : En, Es, Fr & De
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This book presents a selection of cutting-edge methods that allow readers to obtain novel models for nonlinear solid mechanics. Today, engineers need more accurate techniques for modeling solid body mechanics, chiefly due to innovative methods like additive manufacturing—for example, 3D printing—but also due to miniaturization. This book focuses on the formulation of continuum and discrete models for complex materials and systems, and especially the design of metamaterials. It gathers outstanding papers from the international conference IcONSOM 2019

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.

Collected Papers of R.S. Rivlin

Collected Papers of R.S. Rivlin
Volume I and II

by Grigory I. Barenblatt,Daniel D. Joseph

  • Publisher : Springer Science & Business Media
  • Release : 2013-12-14
  • Pages : 2829
  • ISBN : 1461224160
  • Language : En, Es, Fr & De
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R.S. Rivlin is one of the principal architects of nonlinear continuum mechanics: His work on the mechanics of rubber (in the 1940s and 50s) established the basis of finite elasticity theory. These volumes make most of his scientific papers available again and show the full scope and significance of his contributions.