# Download Ebook Free Nonlinear Continuum Mechanics And Physics

## Nonlinear Continuum Mechanics and Physics

Publisher : Academic Press

Release Date : 2019-04

Category : Technology & Engineering

Total pages :500

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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

## Nonlinear Continuum Mechanics of Solids

Publisher : Springer Science & Business Media

Release Date : 2013-11-11

Category : Technology & Engineering

Total pages :193

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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

Publisher : Springer Science & Business Media

Release Date : 2010-12-25

Category : Technology & Engineering

Total pages :721

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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

Publisher : Wiley

Release Date : 2000-04-07

Category : Technology & Engineering

Total pages :470

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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.

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

Publisher : Springer

Release Date : 2010-11-30

Category : Mathematics

Total pages :356

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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

Publisher : Unknown

Release Date : 1968

Category : Continuum mechanics

Total pages :240

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## Continuum Mechanics and Theory of Materials

Publisher : Springer Science & Business Media

Release Date : 2013-03-14

Category : Technology & Engineering

Total pages :643

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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.

## Continuum Methods of Physical Modeling

Publisher : Springer Science & Business Media

Release Date : 2013-11-11

Category : Science

Total pages :636

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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.

## Continuum Mechanics using Mathematica®

Publisher : Springer

Release Date : 2014-10-14

Category : Science

Total pages :480

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This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica® provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics and state changes (see A. Romano, A. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhäuser), 2010, ISBN 978-0-8176-4869-5). Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and one appendix * Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity. This second edition expands the key topics and features to include: * Two new applications of fluid dynamics: meteorology and navigation * New exercises at the end of the existing chapters * The packages are rewritten for Mathematica 9 Continuum Mechanics using Mathematica®: Fundamentals, Applications and Scientific Computing is aimed at advanced undergraduates, graduate students and researchers in applied mathematics, mathematical physics and engineering. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics.

## Nonlinear Continuum Mechanics

Publisher : Unknown

Release Date : 1968

Category : Continuum mechanics

Total pages :240

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## Research in Non-Linear Continuum Mechanics

Publisher : Unknown

Release Date : 1971

Category :

Total pages :8

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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 Applications in Geophysics and the Environment

Publisher : Springer Science & Business Media

Release Date : 2013-03-09

Category : Science

Total pages :394

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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.

## Nonlinear Mechanics of Structures

Publisher : Springer

Release Date : 2011-09-15

Category : Science

Total pages :472

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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 Solid Mechanics

Publisher : Springer Science & Business Media

Release Date : 2009-04-02

Category : Computers

Total pages :574

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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.

## Elementary Continuum Mechanics for Everyone

Publisher : Springer Science & Business Media

Release Date : 2013-02-03

Category : Science

Total pages :593

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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.