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Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity
  • Author : Koichi Hashiguchi
  • Publisher :Unknown
  • Release Date :2020-06-19
  • Total pages :420
  • ISBN : 9780128194294
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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

Continuum Mechanics
  • Author : Ellis H. Dill
  • Publisher :Unknown
  • Release Date :2006-11-10
  • Total pages :368
  • ISBN : 0849397790
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Summary : 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.

Nonlinear Continuum Mechanics for Finite Element Analysis

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
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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 Solid Mechanics for Finite Element Analysis: Statics

Nonlinear Solid Mechanics for Finite Element Analysis: Statics
  • Author : Javier Bonet,Antonio J. Gil,Richard D. Wood
  • Publisher :Unknown
  • Release Date :2016-06-23
  • Total pages :350
  • ISBN : 9781107115798
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Summary : A clear and complete postgraduate introduction to the theory and computer programming for the complex simulation of material behavior.

Nonlinear Continuum Mechanics of Solids

Nonlinear Continuum Mechanics of Solids
  • Author : Yavuz Basar,Dieter Weichert
  • Publisher :Unknown
  • Release Date :2013-11-11
  • Total pages :193
  • ISBN : 9783662042991
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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 Solid Mechanics

Nonlinear Solid Mechanics
  • Author : Adnan Ibrahimbegovic
  • Publisher :Unknown
  • Release Date :2009-06-02
  • Total pages :574
  • ISBN : 9789048123308
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Summary : 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
  • Author : Martin H. Sadd
  • Publisher :Unknown
  • Release Date :2018-03-31
  • Total pages :432
  • ISBN : 9780128116494
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Summary : 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

The Mechanics of Constitutive Modeling

The Mechanics of Constitutive Modeling
  • Author : Niels Saabye Ottosen,Matti Ristinmaa
  • Publisher :Unknown
  • Release Date :2005-09-28
  • Total pages :700
  • ISBN : 0080525695
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Summary : 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.

Classical and Computational Solid Mechanics

Classical and Computational Solid Mechanics
  • Author : Yuan-cheng Fung,Pin Tong
  • Publisher :Unknown
  • Release Date :2001
  • Total pages :930
  • ISBN : 9810241240
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Summary : 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.

Continuum Theory of Plasticity

Continuum Theory of Plasticity
  • Author : Akhtar S. Khan,Sujian Huang
  • Publisher :Unknown
  • Release Date :1995-02-06
  • Total pages :440
  • ISBN : 0471310433
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Summary : 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.

Large Strain Finite Element Method

Large Strain Finite Element Method
  • Author : Antonio Munjiza,Earl E. Knight,Esteban Rougier
  • Publisher :Unknown
  • Release Date :2014-11-19
  • Total pages :488
  • ISBN : 9781118535806
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Summary : An introductory approach to the subject of large strains and large displacements in finite elements. Large Strain Finite Element Method: A Practical Course, takes an introductory approach to the subject of large strains and large displacements in finite elements and starts from the basic concepts of finite strain deformability, including finite rotations and finite displacements. The necessary elements of vector analysis and tensorial calculus on the lines of modern understanding of the concept of tensor will also be introduced. This book explains how tensors and vectors can be described using matrices and also introduces different stress and strain tensors. Building on these, step by step finite element techniques for both hyper and hypo-elastic approach will be considered. Material models including isotropic, unisotropic, plastic and viscoplastic materials will be independently discussed to facilitate clarity and ease of learning. Elements of transient dynamics will also be covered and key explicit and iterative solvers including the direct numerical integration, relaxation techniques and conjugate gradient method will also be explored. This book contains a large number of easy to follow illustrations, examples and source code details that facilitate both reading and understanding. Takes an introductory approach to the subject of large strains and large displacements in finite elements. No prior knowledge of the subject is required. Discusses computational methods and algorithms to tackle large strains and teaches the basic knowledge required to be able to critically gauge the results of computational models. Contains a large number of easy to follow illustrations, examples and source code details. Accompanied by a website hosting code examples.

Computational Contact and Impact Mechanics

Computational Contact and Impact Mechanics
  • Author : Tod A. Laursen
  • Publisher :Unknown
  • Release Date :2003-05-12
  • Total pages :454
  • ISBN : 3540429069
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Summary : Many physical systems require the description of mechanical interaction across interfaces if they are to be successfully analyzed. Examples in the engineered world range from the design of prosthetics in biomedical engi neering (e. g. , hip replacements); to characterization of the response and durability of head/disk interfaces in computer magnetic storage devices; to development of pneumatic tires with better handling characteristics and increased longevity in automotive engineering; to description of the adhe sion and/or relative slip between concrete and reinforcing steel in structural engineering. Such mechanical interactions, often called contact/impact in teractions, usually necessitate at minimum the determination of areas over which compressive pressures must act to prevent interpenetration of the mechanical entities involved. Depending on the application, frictional be havior, transient interaction of interfaces with their surroundings (e. g. , in termittent stick/slip), thermo-mechanical coupling, interaction with an in tervening lubricant and/or fluid layer, and damage of the interface (i. e. , wear) may also be featured. When taken together (or even separately!), these features have the effect of making the equations of mechanical evolu tion not only highly nonlinear, but highly nonsmooth as well. While many modern engineering simulation packages possess impressive capabilities in the general area of nonlinear mechanics, it can be contended that methodologies typically utilized for contact interactions are relatively immature in comparison to other components of a nonlinear finite element package, such as large deformation kinematics, inelastic material modeling, nonlinear equation solving, or linear solver technology.

Elastoplasticity Theory

Elastoplasticity Theory
  • Author : Vlado A. Lubarda
  • Publisher :Unknown
  • Release Date :2001-07-16
  • Total pages :648
  • ISBN : 9781420040784
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Summary : Understanding the elastoplastic deformation of metals and geomaterials, including the constitutive description of the materials and analysis of structure undergoing plastic deformation, is an essential part of the background required by mechanical, civil, and geotechnical engineers as well as materials scientists. However, most books address the subject at a introductory level and within the infinitesimal strain context. Elastoplasticity Theory takes a different approach in an advanced treatment presented entirely within the framework of finite deformation. This comprehensive, self-contained text includes an introduction to nonlinear continuum mechanics and nonlinear elasticity. In addition to in-depth analysis of the mathematical and physical theories of plasticity, it furnishes an up-to-date look at contemporary topics, such as plastic stability and localization, monocrystalline plasticity, micro-to-macro transition, and polycrysalline plasticity models. Elastoplasticity Theory reflects recent trends and advances made in the theory of plasticity over the last four decades. It will not only help stimulate further research in the field, but will enable its readers to confidently select the appropriate constitutive models for the materials or structural members relevant to their own applications.

Nonlinear Mechanics of Crystals

Nonlinear Mechanics of Crystals
  • Author : John D. Clayton
  • Publisher :Unknown
  • Release Date :2010-11-01
  • Total pages :700
  • ISBN : 9789400703506
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Summary : 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 and Large Inelastic Deformations

Nonlinear Continuum Mechanics and Large Inelastic Deformations
  • Author : Yuriy I. Dimitrienko
  • Publisher :Unknown
  • Release Date :2010-12-25
  • Total pages :721
  • ISBN : 9400700342
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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.

Computational Continuum Mechanics

Computational Continuum Mechanics
  • Author : Ahmed A. Shabana
  • Publisher :Unknown
  • Release Date :2011-12-12
  • Total pages :229
  • ISBN : 9781139505420
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Summary : This second edition presents the theory of continuum mechanics using computational methods. The text covers a broad range of topics including general problems of large rotation and large deformations and the development and limitations of finite element formulations in solving such problems. Dr Shabana introduces theories on motion kinematics, strain, forces and stresses and goes on to discuss linear and nonlinear constitutive equations, including viscoelastic and plastic constitutive models. General nonlinear continuum mechanics theory is used to develop small and large finite element formulations which correctly describe rigid body motion for use in engineering applications. This second edition features a new chapter that focuses on computational geometry and finite element analysis. This book is ideal for graduate and undergraduate students, professionals and researchers who are interested in continuum mechanics.

Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics

Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics
  • Author : Erwin Stein
  • Publisher :Unknown
  • Release Date :2007-04-02
  • Total pages :363
  • ISBN : 9783211380604
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Summary : This course with 6 lecturers intends to present a systematic survey of recent re search results of well-known scientists on error-controlled adaptive finite element methods in solid and structural mechanics with emphasis to problem-dependent concepts for adaptivity, error analysis as well as h- and p-adaptive refinement techniques including meshing and remeshing. Challenging applications are of equal importance, including elastic and elastoplastic deformations of solids, con tact problems and thin-walled structures. Some major topics should be pointed out, namely: (i) The growing importance of goal-oriented and local error estimates for quan tities of interest—in comparison with global error estimates—based on dual finite element solutions; (a) The importance of the p-version of the finite element method in conjunction with parameter-dependent hierarchical approximations of the mathematical model, for example in boundary layers of elastic plates; (Hi) The choice of problem-oriented error measures in suitable norms, consider ing residual, averaging and hierarchical error estimates in conjunction with the efficiency of the associated adaptive computations; (iv) The importance of implicit local postprocessing with enhanced test spaces in order to get constant-free, i. e. absolute-not only relative-discretizati- error estimates; (v) The coupling of error-controlled adaptive discretizations and the mathemat ical modeling in related subdomains, such as boundary layers. The main goals of adaptivity are reliability and efficiency, combined with in sight and access to controls which are independent of the applied discretization methods. By these efforts, new paradigms in Computational Mechanics should be realized, namely verifications and even validations of engineering models.

The Mechanics and Thermodynamics of Continua

The Mechanics and Thermodynamics of Continua
  • Author : Morton E. Gurtin,Eliot Fried,Lallit Anand
  • Publisher :Unknown
  • Release Date :2010-04-19
  • Total pages :229
  • ISBN : 9781139482158
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Summary : 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.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics
  • Author : Gerhard A. Holzapfel
  • Publisher :Unknown
  • Release Date :2000-04-06
  • Total pages :455
  • ISBN : UCSD:31822028236313
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Summary : 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.

Courses and Degrees

Courses and Degrees
  • Author : Stanford University
  • Publisher :Unknown
  • Release Date :1993
  • Total pages :229
  • ISBN : STANFORD:36105016092046
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Summary :

Nonlinear Finite Element Methods

Nonlinear Finite Element Methods
  • Author : Peter Wriggers
  • Publisher :Unknown
  • Release Date :2008-09-24
  • Total pages :560
  • ISBN : 9783540710004
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Summary : 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.