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## Nonlinear Continuum Mechanics and Physics

- Author : Shaofan Li
- Publisher :Unknown
- Release Date :2019-04
- Total pages :500
- ISBN : 0128115424

**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

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

- Author : R. S. Rivlin
- Publisher :Unknown
- Release Date :2010-11-30
- Total pages :356
- ISBN : 3642110894

**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 Continuum Mechanics of Solids

- Author : Yavuz Basar,Dieter Weichert
- Publisher :Unknown
- Release Date :2013-11-11
- Total pages :193
- ISBN : 9783662042991

**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 and Large Inelastic Deformations

- Author : Yuriy I. Dimitrienko
- Publisher :Unknown
- Release Date :2010-12-25
- Total pages :721
- ISBN : 9400700342

**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.

## Nonlinear Continuum Mechanics

- Author : Donald Charles Leigh
- Publisher :Unknown
- Release Date :1968
- Total pages :240
- ISBN : UOM:39015058912810

**Summary :**

## Nonlinear Solid Mechanics

- Author : Gerhard A. Holzapfel
- Publisher :Unknown
- Release Date :2000-04-07
- Total pages :470
- ISBN : 0471823198

**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.

## Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

- Author : Koichi Hashiguchi
- Publisher :Unknown
- Release Date :2020-06-19
- Total pages :420
- ISBN : 9780128194294

**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

## Continuum Mechanics

- Author : A. J. M. Spencer
- Publisher :Unknown
- Release Date :2012-06-08
- Total pages :192
- ISBN : 9780486139470

**Summary :** Undergraduate text offers an analysis of deformation and stress, covers laws of conservation of mass, momentum, and energy, and surveys the formulation of mechanical constitutive equations. 1992 edition.

## Continuum Mechanics and Theory of Materials

- Author : Peter Haupt
- Publisher :Unknown
- Release Date :2013-03-14
- Total pages :643
- ISBN : 9783662047750

**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

- Author : Javier Bonet,Antonio J. Gil,Richard D. Wood
- Publisher :Unknown
- Release Date :2012-08-02
- Total pages :229
- ISBN : 9781139561303

**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.

## Nonlinear Solid Mechanics

- Author : Davide Bigoni
- Publisher :Unknown
- Release Date :2012-07-30
- Total pages :532
- ISBN : 9781107025417

**Summary :** Addresses behaviour of materials under extreme mechanical conditions and of failure in terms of non-linear continuum mechanics and instability theory.

## Continuum Methods of Physical Modeling

- Author : Kolumban Hutter,Klaus Jöhnk
- Publisher :Unknown
- Release Date :2013-11-11
- Total pages :636
- ISBN : 9783662064023

**Summary :** 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.

## Mathematical Modeling in Continuum Mechanics

- Author : Roger Temam,Alain Miranville
- Publisher :Unknown
- Release Date :2005-05-19
- Total pages :229
- ISBN : 1139443216

**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 and Thermodynamics

- Author : Ellad B. Tadmor,Ronald E. Miller,Ryan S. Elliott
- Publisher :Unknown
- Release Date :2012
- Total pages :350
- ISBN : 9781107008267

**Summary :** Treats subjects directly related to nonlinear materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.

## Fundamentals of Continuum Mechanics

- Author : Stephen Bechtel,Robert Lowe
- Publisher :Unknown
- Release Date :2014-12-02
- Total pages :340
- ISBN : 9780123948342

**Summary :** Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study. Uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics Covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures Offers a unique approach to modeling incompressibility and thermal expansion, based on the authors’ own research

## Research in Non-Linear Continuum Mechanics

- Author : Bernard D. Coleman,CARNEGIE-MELLON UNIV PITTSBURGH PA MELLON INST OF SCIENCE.
- Publisher :Unknown
- Release Date :1971
- Total pages :8
- ISBN : OCLC:227638056

**Summary :** 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).

## A First Course in Continuum Mechanics

- Author : Oscar Gonzalez,Andrew M. Stuart
- Publisher :Unknown
- Release Date :2008-01-17
- Total pages :394
- ISBN : 9780521886802

**Summary :** A concise account of classic theories of fluids and solids, for graduate and advanced undergraduate courses in continuum mechanics.

## Continuum Mechanics

- Author : Antonio Romano,Addolorata Marasco
- Publisher :Unknown
- Release Date :2010-07-23
- Total pages :348
- ISBN : 9780817648701

**Summary :** This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.

## 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

**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.

## Nonlinear Mechanics of Structures

- Author : M. Kleiber,C. Wozniak
- Publisher :Unknown
- Release Date :2012-12-06
- Total pages :472
- ISBN : 9789400905771

**Summary :** 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.

## Tensor Analysis and Continuum Mechanics

- Author : Y.R. Talpaert
- Publisher :Unknown
- Release Date :2013-03-14
- Total pages :591
- ISBN : 9789401599887

**Summary :** 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 ..