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Nonlinear Continuum Mechanics And Physics

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Nonlinear Continuum Mechanics and Physics

Nonlinear Continuum Mechanics and Physics Book
Author : Shaofan Li
Publisher : Academic Press
Release : 2019-04
ISBN : 9780128115428
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : R. S. Rivlin
Publisher : Springer Science & Business Media
Release : 2011-06-07
ISBN : 3642110908
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Yavuz Basar,Dieter Weichert
Publisher : Springer Science & Business Media
Release : 2013-11-11
ISBN : 3662042991
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Yuriy I. Dimitrienko
Publisher : Springer Science & Business Media
Release : 2010-12-25
ISBN : 9789400700345
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Gerhard A. Holzapfel
Publisher : John Wiley & Sons Incorporated
Release : 2000-04-06
ISBN :
Language : En, Es, Fr & De

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Book Description :

Providing a modern and comprehensive coverage of continuum mechanics, this volume includes information on "variational principles"--Significant, as this is the only method by which such material is actually utilized in engineering practice.

Mathematical Modeling in Continuum Mechanics

Mathematical Modeling in Continuum Mechanics Book
Author : Roger Temam,Alain Miranville
Publisher : Cambridge University Press
Release : 2005-05-19
ISBN : 9781139443210
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Anthony James Merrill Spencer
Publisher : Courier Corporation
Release : 2004-01-01
ISBN : 9780486435947
Language : En, Es, Fr & De

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Book Description :

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 Solid Mechanics

Nonlinear Solid Mechanics Book
Author : Adnan Ibrahimbegovic
Publisher : Springer Science & Business Media
Release : 2009-04-02
ISBN : 9048123313
Language : En, Es, Fr & De

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Book Description :

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

Continuum Mechanics Book
Author : C. S. Jog
Publisher : Cambridge University Press
Release : 2015-06-25
ISBN : 1107091357
Language : En, Es, Fr & De

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Book Description :

"Presents several advanced topics including fourth-order tensors, differentiation of tensors, exponential and logarithmic tensors, and their application to nonlinear elasticity"--

Nonlinear Mechanics of Structures

Nonlinear Mechanics of Structures Book
Author : M. Kleiber,C. Wozniak
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9400905777
Language : En, Es, Fr & De

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Book Description :

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.

Geometric Continuum Mechanics and Induced Beam Theories

Geometric Continuum Mechanics and Induced Beam Theories Book
Author : Simon R. Eugster
Publisher : Springer
Release : 2015-03-19
ISBN : 3319164953
Language : En, Es, Fr & De

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Book Description :

This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.

Continuum Mechanics and Thermodynamics

Continuum Mechanics and Thermodynamics Book
Author : Ellad B. Tadmor,Ronald E. Miller,Ryan S. Elliott
Publisher : Cambridge University Press
Release : 2012
ISBN : 1107008263
Language : En, Es, Fr & De

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Book Description :

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

Finite Elasticity and Viscoelasticity

Finite Elasticity and Viscoelasticity Book
Author : Aleksey D. Drozdov
Publisher : World Scientific
Release : 1996-01-01
ISBN : 9789810224332
Language : En, Es, Fr & De

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Book Description :

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.

Elementary Continuum Mechanics for Everyone

Elementary Continuum Mechanics for Everyone Book
Author : Esben Byskov
Publisher : Springer Science & Business Media
Release : 2013-02-03
ISBN : 9400757662
Language : En, Es, Fr & De

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Book Description :

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.