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Nonlinear Continuum Mechanics and Physics

Nonlinear Continuum Mechanics and Physics
  • Author : Shaofan Li
  • Publisher :Unknown
  • Release Date :2019-04
  • Total pages :500
  • ISBN : 0128115424
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Summary : 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
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :2021
  • Total pages :229
  • ISBN : 1230987654XX
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Summary :

Nonlinear Continuum Mechanics of Solids

Nonlinear Continuum Mechanics of Solids
  • Author : Yavuz Basar,Dieter Weichert
  • Publisher :Unknown
  • Release Date :2013-11-11
  • Total pages :193
  • ISBN : 9783662042991
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Summary : 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
  • Author : Donald Charles Leigh
  • Publisher :Unknown
  • Release Date :1968
  • Total pages :240
  • ISBN : UOM:39015006412087
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Summary :

Nonlinear Continuum Mechanics and Large Inelastic Deformations

Nonlinear Continuum Mechanics and Large Inelastic Deformations
  • Author : Yuriy I. Dimitrienko
  • Publisher :Unknown
  • Release Date :2010-12-25
  • Total pages :721
  • ISBN : 9400700342
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Summary : 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.

Non-linear Continuum Theories in Mechanics and Physics and their Applications

Non-linear Continuum Theories in Mechanics and Physics and their Applications
  • Author : R. S. Rivlin
  • Publisher :Unknown
  • Release Date :2011-06-07
  • Total pages :356
  • ISBN : 9783642110900
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Summary : 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 Solid Mechanics

Nonlinear Solid Mechanics
  • Author : Gerhard A. Holzapfel
  • Publisher :Unknown
  • Release Date :2000-04-07
  • Total pages :470
  • ISBN : 0471823198
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Summary : 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
  • Author : Anthony James Merrill Spencer
  • Publisher :Unknown
  • Release Date :2004-01-01
  • Total pages :183
  • ISBN : 0486435946
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Summary : 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.

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity
  • Author : Koichi Hashiguchi
  • Publisher :Unknown
  • Release Date :2020-06-19
  • Total pages :420
  • ISBN : 9780128194294
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Summary : 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

Mathematical Modeling in Continuum Mechanics

Mathematical Modeling in Continuum Mechanics
  • Author : Roger Temam,Alain Miranville
  • Publisher :Unknown
  • Release Date :2005-05-19
  • Total pages :229
  • ISBN : 1139443216
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Summary : 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
  • Author : P. Chadwick
  • Publisher :Unknown
  • Release Date :2012-08-08
  • Total pages :200
  • ISBN : 9780486139142
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Summary : DIVComprehensive treatment offers 115 solved problems and exercises to promote understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. /div

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials
  • Author : Peter Haupt
  • Publisher :Unknown
  • Release Date :2013-03-14
  • Total pages :643
  • ISBN : 9783662047750
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Summary : 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.

Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis

Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis
  • Author : Javier Bonet,Antonio J. Gil,Richard D. Wood
  • Publisher :Unknown
  • Release Date :2012-08-02
  • Total pages :229
  • ISBN : 9781139561303
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Summary : Many processes in materials science and engineering, such as the load deformation behaviour of certain structures, exhibit nonlinear characteristics. The computer simulation of such processes therefore requires a deep understanding of both the theoretical aspects of nonlinearity and the associated computational techniques. This book provides a complete set of exercises and solutions in the field of theoretical and computational nonlinear continuum mechanics and is the perfect companion to Nonlinear Continuum Mechanics for Finite Element Analysis, where the authors set out the theoretical foundations of the subject. It employs notation consistent with the theory book and serves as a great resource to students, researchers and those in industry interested in gaining confidence by practising through examples. Instructors of the subject will also find the book indispensable in aiding student learning.

The Mechanics and Thermodynamics of Continua

The Mechanics and Thermodynamics of Continua
  • Author : Morton E. Gurtin,Eliot Fried,Lallit Anand
  • Publisher :Unknown
  • Release Date :2010-04-19
  • Total pages :229
  • ISBN : 9781139482158
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Summary : 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 Via Problems and Exercises: Theory and problems

Continuum Mechanics Via Problems and Exercises: Theory and problems
  • Author : Margarita E. Eglit,Dewey H. Hodges
  • Publisher :Unknown
  • Release Date :1996
  • Total pages :523
  • ISBN : 9810229623
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Summary :

Notes on Continuum Mechanics

Notes on Continuum Mechanics
  • Author : Eduardo WV Chaves
  • Publisher :Unknown
  • Release Date :2013-06-13
  • Total pages :700
  • ISBN : 9789400759862
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Summary : 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.

Continuum Mechanics

Continuum Mechanics
  • Author : C. S. Jog
  • Publisher :Unknown
  • Release Date :2015-06-25
  • Total pages :873
  • ISBN : 9781107091351
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Summary : "Presents several advanced topics including fourth-order tensors, differentiation of tensors, exponential and logarithmic tensors, and their application to nonlinear elasticity"--

Nonlinear Solid Mechanics for Finite Element Analysis: Dynamics

Nonlinear Solid Mechanics for Finite Element Analysis: Dynamics
  • Author : Javier Bonet,Antonio J. Gil,Richard D. Wood
  • Publisher :Unknown
  • Release Date :2021-03-31
  • Total pages :350
  • ISBN : 9781107115620
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Summary : The perfect introduction to the theory and computer programming for the dynamic simulation of nonlinear solid mechanics.

Nonlinear Mechanics of Crystals

Nonlinear Mechanics of Crystals
  • Author : John D. Clayton
  • Publisher :Unknown
  • Release Date :2010-11-01
  • Total pages :700
  • ISBN : 9789400703506
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Summary : This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics
  • Author : Davide Bigoni
  • Publisher :Unknown
  • Release Date :2012-07-30
  • Total pages :532
  • ISBN : 9781107025417
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Summary : Addresses behaviour of materials under extreme mechanical conditions and of failure in terms of non-linear continuum mechanics and instability theory.

Nonlinear Continuum Mechanics for Finite Element Analysis

Nonlinear Continuum Mechanics for Finite Element Analysis
  • Author : Javier Bonet,Richard D. Wood
  • Publisher :Unknown
  • Release Date :2008-03-13
  • Total pages :229
  • ISBN : 1139467549
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Summary : Designing engineering components that make optimal use of materials requires consideration of the nonlinear characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, and this requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both nonlinear continuum analysis and associated finite element techniques under one roof, Bonet and Wood provide, in this edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at www.flagshyp.com. Worked examples and exercises complete each chapter, making the text an essential resource for postgraduates studying nonlinear continuum mechanics. It is also ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.