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Nonlinear Continuum Mechanics And Physics

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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 : 9400700342
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 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 Solid Mechanics

Nonlinear Solid Mechanics Book
Author : Gerhard A. Holzapfel
Publisher : John Wiley & Sons Incorporated
Release : 2000-04-06
ISBN : 0987650XXX
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.

Spatial and Material Forces in Nonlinear Continuum Mechanics

Spatial and Material Forces in Nonlinear Continuum Mechanics Book
Author : Paul Steinmann
Publisher : Springer
Release : 2022-02-15
ISBN : 9783030890698
Language : En, Es, Fr & De

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Book Description :

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 for Finite Elasticity Plasticity

Nonlinear Continuum Mechanics for Finite Elasticity Plasticity Book
Author : Koichi Hashiguchi
Publisher : Elsevier
Release : 2020-06-19
ISBN : 0128194294
Language : En, Es, Fr & De

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Book Description :

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

Collected Papers of R S Rivlin

Collected Papers of R S  Rivlin Book
Author : Grigory I. Barenblatt,Daniel D. Joseph
Publisher : Springer Science & Business Media
Release : 2013-12-14
ISBN : 1461224160
Language : En, Es, Fr & De

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Book Description :

R.S. Rivlin is one of the principal architects of nonlinear continuum mechanics: His work on the mechanics of rubber (in the 1940s and 50s) established the basis of finite elasticity theory. These volumes make most of his scientific papers available again and show the full scope and significance of his contributions.

Nonlinear Continuum Mechanics and Large Inelastic Deformations

Nonlinear Continuum Mechanics and Large Inelastic Deformations Book
Author : Yuriy I. Dimitrienko
Publisher : Springer
Release : 2010-11-11
ISBN : 9789400700338
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.

Spatial and Material Forces in Nonlinear Continuum Mechanics

Spatial and Material Forces in Nonlinear Continuum Mechanics Book
Author : Paul Steinmann
Publisher : Springer Nature
Release : 2022-03-28
ISBN : 3030890708
Language : En, Es, Fr & De

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Book Description :

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 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.

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 : 1139443216
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.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics Book
Author : Gerhard A. Holzapfel
Publisher : John Wiley & Sons Incorporated
Release : 2000-04-06
ISBN : 0987650XXX
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.

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.

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials Book
Author : Peter Haupt
Publisher : Springer Science & Business Media
Release : 2013-03-14
ISBN : 3662047756
Language : En, Es, Fr & De

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Book Description :

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.

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.

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials Book
Author : Peter Haupt
Publisher : Springer Science & Business Media
Release : 2002-03-12
ISBN : 9783540431114
Language : En, Es, Fr & De

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Book Description :

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.

Nonlinear Mechanics of Crystals

Nonlinear Mechanics of Crystals Book
Author : John D. Clayton
Publisher : Springer Science & Business Media
Release : 2010-11-01
ISBN : 9400703503
Language : En, Es, Fr & De

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Book Description :

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 Continuum Mechanics for Finite Element Analysis

Nonlinear Continuum Mechanics for Finite Element Analysis Book
Author : Javier Bonet,Richard D. Wood
Publisher : Cambridge University Press
Release : 2008-03-13
ISBN : 9781139467544
Language : En, Es, Fr & De

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Book Description :

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.

Developments and Novel Approaches in Nonlinear Solid Body Mechanics

Developments and Novel Approaches in Nonlinear Solid Body Mechanics Book
Author : Bilen Emek Abali,Ivan Giorgio
Publisher : Springer Nature
Release : 2020-07-18
ISBN : 3030504603
Language : En, Es, Fr & De

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Book Description :

This book features selected manuscripts presented at ICoNSoM 2019, exploring cutting-edge methods for developing novel models in nonlinear solid mechanics. Innovative methods like additive manufacturing—for example, 3D printing— and miniaturization mean that engineers need more accurate techniques for modeling solid body mechanics. The book focuses on the formulation of continuum and discrete models for complex materials and systems, particularly the design of metamaterials.

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.

Nonlinear Solid Mechanics for Finite Element Analysis Statics

Nonlinear Solid Mechanics for Finite Element Analysis  Statics Book
Author : Javier Bonet,Antonio J. Gil,Richard D. Wood
Publisher : Cambridge University Press
Release : 2016-06-23
ISBN : 1107115795
Language : En, Es, Fr & De

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Book Description :

A clear and complete postgraduate introduction to the theory and computer programming for the complex simulation of material behavior.