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Nonlinear Continuum Mechanics and Large Inelastic Deformations

Author: Yuriy I. Dimitrienko

Publisher: Springer Science & Business Media

Published: 2010-12-25

Total Pages: 742

ISBN-13: 9400700342

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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.

Book Synopsis Nonlinear Continuum Mechanics and Large Inelastic Deformations by : Yuriy I. Dimitrienko

Download or read book Nonlinear Continuum Mechanics and Large Inelastic Deformations written by Yuriy I. Dimitrienko and published by Springer Science & Business Media. This book was released on 2010-12-25 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elasticity and Plasticity of Large Deformations

Author: Albrecht Bertram

Publisher: Springer

Published: 2011-12-07

Total Pages: 343

ISBN-13: 9783642246142

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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.

Book Synopsis Elasticity and Plasticity of Large Deformations by : Albrecht Bertram

Download or read book Elasticity and Plasticity of Large Deformations written by Albrecht Bertram and published by Springer. This book was released on 2011-12-07 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Non-Linear Elastic Deformations

Author: R. W. Ogden

Publisher: Courier Corporation

Published: 2013-04-26

Total Pages: 544

ISBN-13: 0486318710

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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.

Book Synopsis Non-Linear Elastic Deformations by : R. W. Ogden

Download or read book Non-Linear Elastic Deformations written by R. W. Ogden and published by Courier Corporation. This book was released on 2013-04-26 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of Solids

Author: Yavuz Basar

Publisher: Springer Science & Business Media

Published: 2000-02-25

Total Pages: 216

ISBN-13: 9783540666011

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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.

Book Synopsis Nonlinear Continuum Mechanics of Solids by : Yavuz Basar

Download or read book Nonlinear Continuum Mechanics of Solids written by Yavuz Basar and published by Springer Science & Business Media. This book was released on 2000-02-25 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is the presentation of the fundamental mathematical and physical concepts of continuum mechanics of solids in a unified description so as to bring young researchers rapidly close to their research area. Accordingly, emphasis is given to concepts of permanent interest, and details of minor importance are omitted. The formulation is achieved systematically in absolute tensor notation, which is almost exclusively used in modern literature. This mathematical tool is presented such that study of the book is possible without permanent reference to other works.

Nonlinear Continuum Mechanics for Finite Element Analysis

Author: Javier Bonet

Publisher: Cambridge University Press

Published: 1997-09-28

Total Pages: 272

ISBN-13: 9780521572729

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A unified treatment of nonlinear continuum analysis and finite element techniques.

Book Synopsis Nonlinear Continuum Mechanics for Finite Element Analysis by : Javier Bonet

Download or read book Nonlinear Continuum Mechanics for Finite Element Analysis written by Javier Bonet and published by Cambridge University Press. This book was released on 1997-09-28 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified treatment of nonlinear continuum analysis and finite element techniques.

Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis

Author: Javier Bonet

Publisher: Cambridge University Press

Published: 2012-08-02

Total Pages: 137

ISBN-13: 1107603617

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

Book Synopsis Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis by : Javier Bonet

Download or read book Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis written by Javier Bonet and published by Cambridge University Press. This book was released on 2012-08-02 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author: John D. Clayton

Publisher: Springer

Published: 2019-05-17

Total Pages: 483

ISBN-13: 3030153304

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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.

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

Download or read book Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids written by John D. Clayton and published by Springer. This book was released on 2019-05-17 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Continuum Mechanics

Author: Carlos Agelet de Saracibar

Publisher: Springer Nature

Published: 2023-08-22

Total Pages: 356

ISBN-13: 3031152077

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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.

Book Synopsis Nonlinear Continuum Mechanics by : Carlos Agelet de Saracibar

Download or read book Nonlinear Continuum Mechanics written by Carlos Agelet de Saracibar and published by Springer Nature. This book was released on 2023-08-22 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Finite Elasticity and Viscoelasticity

Author: Aleksey D. Drozdov

Publisher: World Scientific

Published: 1996-01-01

Total Pages: 464

ISBN-13: 9789810224332

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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.

Book Synopsis Finite Elasticity and Viscoelasticity by : Aleksey D. Drozdov

Download or read book Finite Elasticity and Viscoelasticity written by Aleksey D. Drozdov and published by World Scientific. This book was released on 1996-01-01 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elasticity and Plasticity of Large Deformations

Author: Albrecht Bertram

Publisher: Springer Nature

Published: 2021-04-07

Total Pages: 410

ISBN-13: 3030723283

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This book presents an introduction to material theory and, in particular, to elasticity, plasticity and viscoelasticity, to bring the reader close to the frontiers of today’s knowledge in these particular fields. It starts right from the beginning without assuming much knowledge of the subject. Hence, the book is generally comprehensible to all engineers, physicists, mathematicians, and others. At the beginning of each new section, a brief Comment on the Literature contains recommendations for further reading. This book includes an updated reference list and over 100 changes throughout the book. It contains the latest knowledge on the subject. Two new chapters have been added in this new edition. Now finite viscoelasticity is included, and an Essay on gradient materials, which have recently drawn much attention.

Book Synopsis Elasticity and Plasticity of Large Deformations by : Albrecht Bertram

Download or read book Elasticity and Plasticity of Large Deformations written by Albrecht Bertram and published by Springer Nature. This book was released on 2021-04-07 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to material theory and, in particular, to elasticity, plasticity and viscoelasticity, to bring the reader close to the frontiers of today’s knowledge in these particular fields. It starts right from the beginning without assuming much knowledge of the subject. Hence, the book is generally comprehensible to all engineers, physicists, mathematicians, and others. At the beginning of each new section, a brief Comment on the Literature contains recommendations for further reading. This book includes an updated reference list and over 100 changes throughout the book. It contains the latest knowledge on the subject. Two new chapters have been added in this new edition. Now finite viscoelasticity is included, and an Essay on gradient materials, which have recently drawn much attention.