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Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity
Multiplicative Decomposition with Subloading Surface Model

by Koichi Hashiguchi

  • Publisher : Elsevier
  • Release : 2020-06-19
  • Pages : 420
  • ISBN : 0128194294
  • Language : En, Es, Fr & De
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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

Continuum Mechanics
Elasticity, Plasticity, Viscoelasticity

by Ellis H. Dill

  • Publisher : CRC Press
  • Release : 2006-11-10
  • Pages : 368
  • ISBN : 9780849397790
  • Language : En, Es, Fr & De
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Most books on continuum mechanics focus on elasticity and fluid mechanics. But whether student or practicing professional, modern engineers need a more thorough treatment to understand the behavior of the complex materials and systems in use today. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity offers a complete tour of the subject that includes not only elasticity and fluid mechanics but also covers plasticity, viscoelasticity, and the continuum model for fatigue and fracture mechanics. In addition to a broader scope, this book also supplies a review of the necessary mathematical tools and results for a self-contained treatment. The author provides finite element formulations of the equations encountered throughout the chapters and uses an approach with just the right amount of mathematical rigor without being too theoretical for practical use. Working systematically from the continuum model for the thermomechanics of materials, coverage moves through linear and nonlinear elasticity using both tensor and matrix notation, plasticity, viscoelasticity, and concludes by introducing the fundamentals of fracture mechanics and fatigue of metals. Requisite mathematical tools appear in the final chapter for easy reference. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity builds a strong understanding of the principles, equations, and finite element formulations needed to solve real engineering problems.

The Mechanics of Constitutive Modeling

The Mechanics of Constitutive Modeling
A Book

by Niels Saabye Ottosen,Matti Ristinmaa

  • Publisher : Elsevier
  • Release : 2005-09-28
  • Pages : 700
  • ISBN : 9780080525693
  • Language : En, Es, Fr & De
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Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. Topics covered include: Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The thermodynamic framework for constitutive modelling – Thermoplasticity - Uniqueness and discontinuous bifurcations • More comprehensive in scope than competitive titles, with detailed discussion of thermodynamics and numerical methods. • Offers appropriate strategies for numerical solution, illustrated by discussion of specific models. • Demonstrates each topic in a complete and self-contained framework, with extensive referencing.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics
Theoretical Formulations and Finite Element Solution Methods

by Adnan Ibrahimbegovic

  • Publisher : Springer Science & Business Media
  • Release : 2009-06-02
  • Pages : 574
  • ISBN : 9048123305
  • Language : En, Es, Fr & De
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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.

Continuum Mechanics Modeling of Material Behavior

Continuum Mechanics Modeling of Material Behavior
A Book

by Martin H. Sadd

  • Publisher : Academic Press
  • Release : 2018-03-31
  • Pages : 432
  • ISBN : 0128116498
  • Language : En, Es, Fr & De
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Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries; kinematics of motion and deformation; force and stress measures; and mass, momentum and energy balance principles. The book then moves beyond other books by dedicating the last chapter to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity, as well as linear and nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Offers a thorough, concise and organized presentation of continuum mechanics formulation Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study Features extensive use of exercises, providing more material for student engagement and instructor presentation

Nonlinear Continuum Mechanics of Solids

Nonlinear Continuum Mechanics of Solids
Fundamental Mathematical and Physical Concepts

by Yavuz Basar,Dieter Weichert

  • Publisher : Springer Science & Business Media
  • Release : 2013-11-11
  • Pages : 193
  • ISBN : 3662042991
  • Language : En, Es, Fr & De
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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.

Computational Methods in Elasticity and Plasticity

Computational Methods in Elasticity and Plasticity
Solids and Porous Media

by A. Anandarajah

  • Publisher : Springer Science & Business Media
  • Release : 2011-01-04
  • Pages : 653
  • ISBN : 9781441963796
  • Language : En, Es, Fr & De
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Computational Methods in Elasticity and Plasticity: Solids and Porous Media presents the latest developments in the area of elastic and elasto-plastic finite element modeling of solids, porous media and pressure-dependent materials and structures. The book covers the following topics in depth: the mathematical foundations of solid mechanics, the finite element method for solids and porous media, the theory of plasticity and the finite element implementation of elasto-plastic constitutive models. The book also includes: -A detailed coverage of elasticity for isotropic and anisotropic solids. -A detailed treatment of nonlinear iterative methods that could be used for nonlinear elastic and elasto-plastic analyses. -A detailed treatment of a kinematic hardening von Mises model that could be used to simulate cyclic behavior of solids. -Discussion of recent advances in the analysis of porous media and pressure-dependent materials in more detail than other books currently available. Computational Methods in Elasticity and Plasticity: Solids and Porous Media also contains problem sets, worked examples and a solutions manual for instructors.

Continuum Theory of Plasticity

Continuum Theory of Plasticity
A Book

by Akhtar S. Khan,Sujian Huang

  • Publisher : John Wiley & Sons
  • Release : 1995-02-06
  • Pages : 440
  • ISBN : 9780471310433
  • Language : En, Es, Fr & De
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The only modern, up-to-date introduction to plasticity Despite phenomenal progress in plasticity research over the past fifty years, introductory books on plasticity have changed very little. To meet the need for an up-to-date introduction to the field, Akhtar S. Khan and Sujian Huang have written Continuum Theory of Plasticity--a truly modern text which offers a continuum mechanics approach as well as a lucid presentation of the essential classical contributions. The early chapters give the reader a review of elementary concepts of plasticity, the necessary background material on continuum mechanics, and a discussion of the classical theory of plasticity. Recent developments in the field are then explored in sections on the Mroz Multisurface model, the Dafalias and Popov Two Surface model, the non-linear kinematic hardening model, the endochronic theory of plasticity, and numerous topics in finite deformation plasticity theory and strain space formulation for plastic deformation. Final chapters introduce the fundamentals of the micromechanics of plastic deformation and the analytical coupling between deformation of individual crystals and macroscopic material response of the polycrystal aggregate. For graduate students and researchers in engineering mechanics, mechanical, civil, and aerospace engineering, Continuum Theory of Plasticity offers a modern, comprehensive introduction to the entire subject of plasticity.

Stanford Bulletin

Stanford Bulletin
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2003
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Basics of Continuum Plasticity

Basics of Continuum Plasticity
A Book

by Kwansoo Chung,Myoung-Gyu Lee

  • Publisher : Springer
  • Release : 2018-05-02
  • Pages : 360
  • ISBN : 9811083061
  • Language : En, Es, Fr & De
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This book describes the basic principles of plasticity for students and engineers who wish to perform plasticity analyses in their professional lives, and provides an introduction to the application of plasticity theories and basic continuum mechanics in metal forming processes. This book consists of three parts. The first part deals with the characteristics of plasticity and instability under simple tension or compression and plasticity in beam bending and torsion. The second part is designed to provide the basic principles of continuum mechanics, and the last part presents an extension of one-dimensional plasticity to general three-dimensional laws based on the fundamentals of continuum mechanics. Though most parts of the book are written in the context of general plasticity, the last two chapters are specifically devoted to sheet metal forming applications. The homework problems included are designed to reinforce understanding of the concepts involved. This book may be used as a textbook for a one semester course lasting fourteen weeks or longer. This book is intended to be self-sufficient such that readers can study it independently without taking another formal course. However, there are some prerequisites before starting this book, which include a course on engineering mathematics and an introductory course on solid mechanics.

The Mechanics and Thermodynamics of Continua

The Mechanics and Thermodynamics of Continua
A Book

by Morton E. Gurtin,Eliot Fried,Lallit Anand

  • Publisher : Cambridge University Press
  • Release : 2010-04-19
  • Pages : 329
  • ISBN : 1139482157
  • Language : En, Es, Fr & De
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The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Courses and Degrees

Courses and Degrees
A Book

by Stanford University

  • Publisher : Unknown Publisher
  • Release : 1992
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Classical and Computational Solid Mechanics

Classical and Computational Solid Mechanics
A Book

by Yuan-cheng Fung,Pin Tong

  • Publisher : World Scientific
  • Release : 2001
  • Pages : 930
  • ISBN : 9789810241247
  • Language : En, Es, Fr & De
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This invaluable book has been written for engineers and engineering scientists in a style that is readable, precise, concise, and practical. It gives first priority to the formulation of problems, presenting the classical results as the gold standard, and the numerical approach as a tool for obtaining solutions. The classical part is a revision of the well-known text Foundations of Solid Mechanics, with a much-expanded discussion on the theories of plasticity and large elastic deformation with finite strains. The computational part is all new and is aimed at solving many major linear and nonlinear boundary-value problems.

Nonlinear Mechanics of Crystals

Nonlinear Mechanics of Crystals
A Book

by John D. Clayton

  • Publisher : Springer Science & Business Media
  • Release : 2010-11-01
  • Pages : 700
  • ISBN : 9400703503
  • Language : En, Es, Fr & De
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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.

Continuum Mechanics

Continuum Mechanics
A Book

by Gyula Béda,Imre Kozák,József Verhás

  • Publisher : Akademiai Kiado
  • Release : 1995
  • Pages : 313
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Introduction to Finite Strain Theory for Continuum Elasto-Plasticity

Introduction to Finite Strain Theory for Continuum Elasto-Plasticity
A Book

by Koichi Hashiguchi,Yuki Yamakawa

  • Publisher : John Wiley & Sons
  • Release : 2012-10-09
  • Pages : 440
  • ISBN : 1118437721
  • Language : En, Es, Fr & De
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Comprehensive introduction to finite elastoplasticity,addressing various analytical and numerical analyses &including state-of-the-art theories Introduction to Finite Elastoplasticity presentsintroductory explanations that can be readily understood by readerswith only a basic knowledge of elastoplasticity, showing physicalbackgrounds of concepts in detail and derivation processes ofalmost all equations. The authors address various analytical andnumerical finite strain analyses, including new theories developedin recent years, and explain fundamentals including thepush-forward and pull-back operations and the Lie derivatives oftensors. As a foundation to finite strain theory, the authors begin byaddressing the advanced mathematical and physical properties ofcontinuum mechanics. They progress to explain a finiteelastoplastic constitutive model, discuss numerical issues onstress computation, implement the numerical algorithms for stresscomputation into large-deformation finite element analysis andillustrate several numerical examples of boundary-value problems.Programs for the stress computation of finite elastoplastic modelsexplained in this book are included in an appendix, and the codecan be downloaded from an accompanying website.

Nonlinear Finite Element Methods

Nonlinear Finite Element Methods
A Book

by Peter Wriggers

  • Publisher : Springer Science & Business Media
  • Release : 2008-09-24
  • Pages : 560
  • ISBN : 3540710000
  • Language : En, Es, Fr & De
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Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.

Government Reports Announcements

Government Reports Announcements
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1973
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Peterson's Annual Guides to Graduate Study

Peterson's Annual Guides to Graduate Study
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 1982-12
  • Pages : 800
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Computational Methods for Plasticity

Computational Methods for Plasticity
Theory and Applications

by Eduardo A. de Souza Neto,Djordje Peric,David R. J. Owen

  • Publisher : John Wiley & Sons
  • Release : 2011-09-21
  • Pages : 814
  • ISBN : 1119964547
  • Language : En, Es, Fr & De
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The subject of computational plasticity encapsulates the numerical methods used for the finite element simulation of the behaviour of a wide range of engineering materials considered to be plastic – i.e. those that undergo a permanent change of shape in response to an applied force. Computational Methods for Plasticity: Theory and Applications describes the theory of the associated numerical methods for the simulation of a wide range of plastic engineering materials; from the simplest infinitesimal plasticity theory to more complex damage mechanics and finite strain crystal plasticity models. It is split into three parts - basic concepts, small strains and large strains. Beginning with elementary theory and progressing to advanced, complex theory and computer implementation, it is suitable for use at both introductory and advanced levels. The book: Offers a self-contained text that allows the reader to learn computational plasticity theory and its implementation from one volume. Includes many numerical examples that illustrate the application of the methodologies described. Provides introductory material on related disciplines and procedures such as tensor analysis, continuum mechanics and finite elements for non-linear solid mechanics. Is accompanied by purpose-developed finite element software that illustrates many of the techniques discussed in the text, downloadable from the book’s companion website. This comprehensive text will appeal to postgraduate and graduate students of civil, mechanical, aerospace and materials engineering as well as applied mathematics and courses with computational mechanics components. It will also be of interest to research engineers, scientists and software developers working in the field of computational solid mechanics.