Nonlinear Continuum Mechanics And Physics
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Nonlinear Continuum Mechanics Of Solids
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Author : Yavuz Basar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Nonlinear Continuum Mechanics Of Solids written by Yavuz Basar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
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
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Author : Donald Charles Leigh
language : en
Publisher:
Release Date : 1968
Nonlinear Continuum Mechanics written by Donald Charles Leigh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Science categories.
Nonlinear Continuum Mechanics And Large Inelastic Deformations
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Author : Yuriy I. Dimitrienko
language : en
Publisher: Springer
Release Date : 2011-04-08
Nonlinear Continuum Mechanics And Large Inelastic Deformations written by Yuriy I. Dimitrienko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-08 with Technology & Engineering categories.
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.
Spatial And Material Forces In Nonlinear Continuum Mechanics
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Author : Paul Steinmann
language : en
Publisher: Springer Nature
Release Date : 2022-03-28
Spatial And Material Forces In Nonlinear Continuum Mechanics written by Paul Steinmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-28 with Science categories.
This monograph details spatial and material vistas on non-linear continuum mechanics in a dissipation-consistent approach. Thereby, the spatial vista renders the common approach to nonlinear continuum mechanics and corresponding spatial forces, whereas the material vista elaborates on configurational mechanics and corresponding material or rather configurational forces. Fundamental to configurational mechanics is the concept of force. In analytical mechanics, force is a derived object that is power conjugate to changes of generalised coordinates. For a continuum body, these are typically the spatial positions of its continuum points. However, if in agreement with the second law, continuum points, e.g. on the boundary, may also change their material positions. Configurational forces are then power conjugate to these configurational changes. A paradigm is a crack tip, i.e. a singular part of the boundary changing its position during crack propagation, with the related configurational force, typically the J-integral, driving its evolution, thereby consuming power, typically expressed as the energy release rate. Taken together, configurational mechanics is an unconventional branch of continuum physics rationalising and unifying the tendency of a continuum body to change its material configuration. It is thus the ideal formulation to tackle sophisticated problems in continuum defect mechanics. Configurational mechanics is entirely free of restrictions regarding geometrical and constitutive nonlinearities and offers an accompanying versatile computational approach to continuum defect mechanics. In this monograph, I present a detailed summary account of my approach towards configurational mechanics, thereby fostering my view that configurational forces are indeed dissipation-consistent to configurational changes.
Nonlinear Continuum Mechanics And Physics
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Author : Shaofan Li
language : en
Publisher: Academic Press
Release Date : 2029-01-15
Nonlinear Continuum Mechanics And Physics written by Shaofan Li and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2029-01-15 with Technology & Engineering categories.
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
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Author : R. S. Rivlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-07
Non Linear Continuum Theories In Mechanics And Physics And Their Applications written by R. S. Rivlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-07 with Mathematics categories.
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.
The Non Linear Field Theories Of Mechanics
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Author : C. Truesdell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Non Linear Field Theories Of Mechanics written by C. Truesdell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monograph`s genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also has greatly contributed to the unification and standardization of the concepts, terms and notations in the field.
The Non Linear Field Theories Of Mechanics Die Nicht Linearen Feldtheorien Der Mechanik
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Non Linear Field Theories Of Mechanics Die Nicht Linearen Feldtheorien Der Mechanik written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
Nonlinear Solid Mechanics
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Author : Gerhard A. Holzapfel
language : en
Publisher:
Release Date : 2000-04-06
Nonlinear Solid Mechanics written by Gerhard A. Holzapfel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-06 with Mathematics categories.
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.
Nonlinear Mechanics Of Structures
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Author : M. Kleiber
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Mechanics Of Structures written by M. Kleiber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.