Nonlinear Continuum Mechanics And Large Inelastic Deformations

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Nonlinear Continuum Mechanics and Large Inelastic Deformations

Yuriy I. Dimitrienko
Nonlinear Continuum Mechanics and Large Inelastic Deformations Book PDF

Author : Yuriy I. Dimitrienko
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 45,7 Mb
Release : 2010-12-25
Category : Science
ISBN : 9789400700345

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Nonlinear Continuum Mechanics and Large Inelastic Deformations by Yuriy I. Dimitrienko Pdf

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 for Finite Element Analysis

Javier Bonet,Richard D. Wood
Nonlinear Continuum Mechanics for Finite Element Analysis Book PDF

Author : Javier Bonet,Richard D. Wood
Publisher : Cambridge University Press
Page : 349 pages
File Size : 49,8 Mb
Release : 2008-03-13
Category : Science
ISBN : 9781139467544

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Nonlinear Continuum Mechanics for Finite Element Analysis by Javier Bonet,Richard D. Wood Pdf

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.

Elasticity and Plasticity of Large Deformations

Albrecht Bertram
Elasticity and Plasticity of Large Deformations Book PDF

Author : Albrecht Bertram
Publisher : Springer
Page : 343 pages
File Size : 52,6 Mb
Release : 2011-12-07
Category : Technology & Engineering
ISBN : 3642246141

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Elasticity and Plasticity of Large Deformations by Albrecht Bertram Pdf

Nonlinear Continuum Mechanics is a rapidly growing field of research. Since the last edition of this book, many important results in this field have been published. This new edition refers to the most important results. The part on hyperelastic models and anisotropic yield criteria has been enlarged and an outlook on Material Plasticity has been added.

Nonlinear Continuum Mechanics of Solids

Yavuz Basar,Dieter Weichert
Nonlinear Continuum Mechanics of Solids Book PDF

Author : Yavuz Basar,Dieter Weichert
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 44,9 Mb
Release : 2000-02-25
Category : Technology & Engineering
ISBN : 354066601X

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Nonlinear Continuum Mechanics of Solids by Yavuz Basar,Dieter Weichert Pdf

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.

Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis

Javier Bonet,Antonio J. Gil,Richard D. Wood
Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis Book PDF

Author : Javier Bonet,Antonio J. Gil,Richard D. Wood
Publisher : Cambridge University Press
Page : 137 pages
File Size : 53,8 Mb
Release : 2012-08-02
Category : Mathematics
ISBN : 9781107603615

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Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis by Javier Bonet,Antonio J. Gil,Richard D. Wood Pdf

Extensive solved exercises and solutions to complement the authors' theoretical text Nonlinear Continuum Mechanics for Finite Element Analysis.

Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids

John D. Clayton
Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids Book PDF

Author : John D. Clayton
Publisher : Springer
Page : 483 pages
File Size : 40,6 Mb
Release : 2019-05-17
Category : Science
ISBN : 9783030153304

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Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids by John D. Clayton Pdf

This book describes thermoelastic and inelastic deformation processes in crystalline solids undergoing loading by shock compression. Constitutive models with a basis in geometrically nonlinear continuum mechanics supply these descriptions. Large deformations such as finite strains and rotations, are addressed. The book covers dominant mechanisms of nonlinear thermoelasticity, dislocation plasticity, deformation twinning, fracture, flow, and other structure changes. Rigorous derivations of theoretical results are provided, with approximately 1300 numbered equations and an extensive bibliography of over 500 historical and modern references spanning from the 1920s to the present day. Case studies contain property data, as well as analytical, and numerical solutions to shock compression problems for different materials. Such materials are metals, ceramics, and minerals, single crystalline and polycrystalline. The intended audience of this book is practicing scientists (physicists, engineers, materials scientists, and applied mathematicians) involved in advanced research on shock compression of solid materials.

Non-Linear Elastic Deformations

R. W. Ogden
Non Linear Elastic Deformations Book PDF

Author : R. W. Ogden
Publisher : Courier Corporation
Page : 544 pages
File Size : 48,6 Mb
Release : 2013-04-26
Category : Technology & Engineering
ISBN : 9780486318714

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Non-Linear Elastic Deformations by R. W. Ogden Pdf

Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

Nonlinear Continuum Mechanics

Carlos Agelet de Saracibar
Nonlinear Continuum Mechanics Book PDF

Author : Carlos Agelet de Saracibar
Publisher : Springer Nature
Page : 356 pages
File Size : 41,8 Mb
Release : 2023-08-22
Category : Technology & Engineering
ISBN : 9783031152078

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Nonlinear Continuum Mechanics by Carlos Agelet de Saracibar Pdf

This textbook on Continuum Mechanics presents 9 chapters. Chapters 1 and 2 are devoted to Tensor Algebra and Tensor Analysis. Part I of the book includes the next 3 chapters. All the content here is valid for both solid and fluid materials. At the end of Part I, the reader should be able to set up in local spatial/material form, the fundamental governing equations and inequalities for a Continuum Mechanics problem. Part II of the book, Chapters 6 to 10, is devoted to presenting some nonlinear constitutive models for Nonlinear Solid Mechanics, including Finite Deformation Hyperelasticity, Finite Deformation Plasticity, Finite Deformation Coupled Thermoplasticity, and Finite Deformation Contact Mechanics. The constitutive equations are derived within a thermodynamically consistent framework. Finite deformation elastoplasticity models are based on a multiplicative decomposition of the deformation gradient and the notion of an intermediate configuration. Different formulations based on the intermediate configuration, the current or spatial configuration, and the material configuration are considered. The last chapter is devoted to Variational Methods in Solid Mechanics, a fundamental topic in Computational Mechanics. The book may be used as a textbook for an advanced Master’s course on Nonlinear Continuum Mechanics for graduate students in Civil, Mechanical or Aerospace Engineering, Applied Mathematics, or Applied Physics, with an interest in Continuum Mechanics and Computational Mechanics.

Notes on Continuum Mechanics

Eduardo WV Chaves
Notes on Continuum Mechanics Book PDF

Author : Eduardo WV Chaves
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 50,9 Mb
Release : 2013-06-13
Category : Science
ISBN : 9789400759862

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Notes on Continuum Mechanics by Eduardo WV Chaves Pdf

This publication is aimed at students, teachers, and researchers of Continuum Mechanics and focused extensively on stating and developing Initial Boundary Value equations used to solve physical problems. With respect to notation, the tensorial, indicial and Voigt notations have been used indiscriminately. The book is divided into twelve chapters with the following topics: Tensors, Continuum Kinematics, Stress, The Objectivity of Tensors, The Fundamental Equations of Continuum Mechanics, An Introduction to Constitutive Equations, Linear Elasticity, Hyperelasticity, Plasticity (small and large deformations), Thermoelasticity (small and large deformations), Damage Mechanics (small and large deformations), and An Introduction to Fluids. Moreover, the text is supplemented with over 280 figures, over 100 solved problems, and 130 references.

Elasticity and Plasticity of Large Deformations

Albrecht Bertram
Elasticity and Plasticity of Large Deformations Book PDF

Author : Albrecht Bertram
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 44,5 Mb
Release : 2011-10-07
Category : Science
ISBN : 9783642246159

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Elasticity and Plasticity of Large Deformations by Albrecht Bertram Pdf

Nonlinear Continuum Mechanics is a rapidly growing field of research. Since the last edition of this book, many important results in this field have been published. This new edition refers to the most important results. The part on hyperelastic models and anisotropic yield criteria has been enlarged and an outlook on Material Plasticity has been added.

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

Koichi Hashiguchi
Nonlinear Continuum Mechanics for Finite Elasticity Plasticity Book PDF

Author : Koichi Hashiguchi
Publisher : Elsevier
Page : 420 pages
File Size : 54,6 Mb
Release : 2020-06-19
Category : Technology & Engineering
ISBN : 9780128194294

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Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity by Koichi Hashiguchi Pdf

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

Error Estimates for Advanced Galerkin Methods

Marcus Olavi Rüter
Error Estimates for Advanced Galerkin Methods Book PDF

Author : Marcus Olavi Rüter
Publisher : Springer Nature
Page : 496 pages
File Size : 51,5 Mb
Release : 2019-11-07
Category : Science
ISBN : 9783030061739

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Error Estimates for Advanced Galerkin Methods by Marcus Olavi Rüter Pdf

This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.

Finite Elasticity and Viscoelasticity

Aleksey D. Drozdov
Finite Elasticity and Viscoelasticity Book PDF

Author : Aleksey D. Drozdov
Publisher : World Scientific
Page : 464 pages
File Size : 44,8 Mb
Release : 1996-01-01
Category : Science
ISBN : 9810224338

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Finite Elasticity and Viscoelasticity by Aleksey D. Drozdov Pdf

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.

Nonlinear Solid Mechanics for Finite Element Analysis: Statics

Javier Bonet,Antonio J. Gil,Richard D. Wood
Nonlinear Solid Mechanics for Finite Element Analysis Statics Book PDF

Author : Javier Bonet,Antonio J. Gil,Richard D. Wood
Publisher : Cambridge University Press
Page : 343 pages
File Size : 55,7 Mb
Release : 2016-06-23
Category : Mathematics
ISBN : 9781107115798

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Nonlinear Solid Mechanics for Finite Element Analysis: Statics by Javier Bonet,Antonio J. Gil,Richard D. Wood Pdf

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

Nonlinear Solid Mechanics

Adnan Ibrahimbegovic
Nonlinear Solid Mechanics Book PDF

Author : Adnan Ibrahimbegovic
Publisher : Springer Science & Business Media
Page : 574 pages
File Size : 46,8 Mb
Release : 2009-04-02
Category : Computers
ISBN : 9789048123315

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Nonlinear Solid Mechanics by Adnan Ibrahimbegovic Pdf

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.