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Continuum Mechanics

Continuum Mechanics Author Ellis H. Dill
ISBN-10 0849397790
Release 2006-11-10
Pages 368
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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.

Continuum Mechanics Modeling of Material Behavior

Continuum Mechanics Modeling of Material Behavior Author Martin H. Sadd
ISBN-10 9780128116494
Release 2018-03-31
Pages 432
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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

Lattice Dynamical Foundations of Continuum Theories

Lattice Dynamical Foundations of Continuum Theories Author Attila Askar
ISBN-10 9789814518956
Release 1986-07-01
Pages 208
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This book presents a discussion of lattice dynamics for perfect and imperfect lattices and their relation to continuum theories of elasticity, piezoelectricity, viscoelasticity and plasticity. Some of the material is rather classical and close in spirit to solid state physics. A major aim here is to present a coherent theory for the four basic behavior types in the style of continuum mechanics. In each case, emphasis is on an explicit display of the physical mechanisms involved rather than general formalisms. The material is presented in terms of an atomistic picture for the discrete system. The basic ideas are believed to be relevant also at an intermediate scale in the continuum description of media with structure such as granular materials and composites. Contents: Perfect Crystal Lattices:Elasticity and PiezoelectricityInteratomic ForcesOne-Dimensional Simple Lattices and Classical ElasticityOne-Dimensional Nonsimple Lattices and Special Continuum TheoriesMulti-Dimensional Perfect Lattices and Continuum Theory of ElasticityPolarizable Lattices and PiezoelectricityCrystal Lattices with Defect:Defects in CrystalsEnergy Loss Mechanisms ViscoelasticityDislocations and Plasticity Readership: Physicists and material scientists. Keywords:Continuum Mechanics;Interatomic Forces;Simple Lattices;Classical Elasticity;One-Dimensional Nonsimple Lattices;Special Continuum Theories;Polarizable Lattices;Piezoelectricity;Crystal Lattices

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials Author Peter Haupt
ISBN-10 9783662047750
Release 2013-03-14
Pages 643
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The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials Author Peter Haupt
ISBN-10 354066114X
Release 2000-01
Pages 583
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This treatise attempts to portray the ideas and general principles of the theory of materials within the framework of phenomenological continuum mechanics. It is a mathematical introduction to classical continuum mechanics and deals with concepts such as elasticity, plasticity, viscoelasticity and viscoplasticity in nonlinear materials. The aim of a general theory of material behaviour is to provide a classified range of possibilities from which a user can select the constitutive model that applies best. The book will be invaluable to graduate students of materials science in engineering and in physics.

An Introduction to Continuum Mechanics

An Introduction to Continuum Mechanics Author J. N. Reddy
ISBN-10 9781107025431
Release 2013-07-29
Pages 470
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This best-selling textbook presents the concepts of continuum mechanics, and the second edition includes additional explanations, examples and exercises.

Continuum Mechanics

Continuum Mechanics Author Fridtjov Irgens
ISBN-10 3540742980
Release 2008-01-10
Pages 661
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This book presents an introduction into the entire science of Continuum Mechanics in three parts. The presentation is modern and comprehensive. Its introduction into tensors is very gentle. The book contains many examples and exercises, and is intended for scientists, practitioners and students of mechanics.

Solid Mechanics

Solid Mechanics Author Albrecht Bertram
ISBN-10 9783319195667
Release 2015-06-13
Pages 318
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This textbook offers an introduction to modeling the mechanical behavior of solids within continuum mechanics and thermodynamics. To illustrate the fundamental principles, the book starts with an overview of the most important models in one dimension. Tensor calculus, which is called for in three-dimensional modeling, is concisely presented in the second part of the book. Once the reader is equipped with these essential mathematical tools, the third part of the book develops the foundations of continuum mechanics right from the beginning. Lastly, the book’s fourth part focuses on modeling the mechanics of materials and in particular elasticity, viscoelasticity and plasticity. Intended as an introductory textbook for students and for professionals interested in self-study, it also features numerous worked-out examples to aid in understanding.

Continuum Mechanics for Engineers Third Edition

Continuum Mechanics for Engineers  Third Edition Author G. Thomas Mase
ISBN-10 1439832579
Release 1999-06-18
Pages 400
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The second edition of this popular text continues to provide a solid, fundamental introduction to the mathematics, laws, and applications of continuum mechanics. With the addition of three new chapters and eight new sections to existing chapters, the authors now provide even better coverage of continuum mechanics basics and focus even more attention on its applications. Beginning with the basic mathematical tools needed-including matrix methods and the algebra and calculus of Cartesian tensors-the authors develop the principles of stress, strain, and motion and derive the fundamental physical laws relating to continuity, energy, and momentum. With this basis established, they move to their expanded treatment of applications, including linear and nonlinear elasticity, fluids, and linear viscoelasticity Mastering the contents of Continuum Mechanics: Second Edition provides the reader with the foundation necessary to be a skilled user of today's advanced design tools, such as sophisticated simulation programs that use nonlinear kinematics and a variety of constitutive relationships. With its ample illustrations and exercises, it offers the ideal self-study vehicle for practicing engineers and an excellent introductory text for advanced engineering students.

Introduction to Linear Elasticity

Introduction to Linear Elasticity Author Phillip L Gould
ISBN-10 9781461448334
Release 2013-03-14
Pages 346
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Introduction to Linear Elasticity, 3rd Edition provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing its subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, and finite method analysis.

The Mechanical and Thermodynamical Theory of Plasticity

The Mechanical and Thermodynamical Theory of Plasticity Author Mehrdad Negahban
ISBN-10 9781466563216
Release 2012-04-26
Pages 784
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Born out of 15 years of courses and lectures on continuum mechanics, nonlinear mechanics, continuum thermodynamics, viscoelasticity, plasticity, crystal plasticity, and thermodynamic plasticity, The Mechanical and Thermodynamical Theory of Plasticity represents one of the most extensive and in-depth treatises on the mechanical and thermodynamical aspects of plastic and visicoplastic flow. Suitable for student readers and experts alike, it offers a clear and comprehensive presentation of multi-dimensional continuum thermodynamics to both aid in initial understanding and introduce and explore advanced topics. Covering a wide range of foundational subjects and presenting unique insights into the unification of disparate theories and practices, this book offers an extensive number of problems, figures, and examples to help the reader grasp the subject from many levels. Starting from one-dimensional axial motion in bars, the book builds a clear understanding of mechanics and continuum thermodynamics during plastic flow. This approach makes it accessible and applicable for a varied audience, including students and experts from engineering mechanics, mechanical engineering, civil engineering, and materials science.

Applied Mechanics of Solids

Applied Mechanics of Solids Author Allan F. Bower
ISBN-10 1439802483
Release 2009-10-05
Pages 820
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Modern computer simulations make stress analysis easy. As they continue to replace classical mathematical methods of analysis, these software programs require users to have a solid understanding of the fundamental principles on which they are based. Develop Intuitive Ability to Identify and Avoid Physically Meaningless Predictions Applied Mechanics of Solids is a powerful tool for understanding how to take advantage of these revolutionary computer advances in the field of solid mechanics. Beginning with a description of the physical and mathematical laws that govern deformation in solids, the text presents modern constitutive equations, as well as analytical and computational methods of stress analysis and fracture mechanics. It also addresses the nonlinear theory of deformable rods, membranes, plates, and shells, and solutions to important boundary and initial value problems in solid mechanics. The author uses the step-by-step manner of a blackboard lecture to explain problem solving methods, often providing the solution to a problem before its derivation is presented. This format will be useful for practicing engineers and scientists who need a quick review of some aspect of solid mechanics, as well as for instructors and students. Select and Combine Topics Using Self-Contained Modules and Subsections Borrowing from the classical literature on linear elasticity, plasticity, and structural mechanics, this book: Introduces concepts, analytical techniques, and numerical methods used to analyze deformation, stress, and failure in materials or components Discusses the use of finite element software for stress analysis Assesses simple analytical solutions to explain how to set up properly posed boundary and initial-value problems Provides an understanding of algorithms implemented in software code Complemented by the author’s website, which features problem sets and sample code for self study, this book offers a crucial overview of problem solving for solid mechanics. It will help readers make optimal use of commercial finite element programs to achieve the most accurate prediction results possible.

Variational Methods in the Mechanics of Solids

Variational Methods in the Mechanics of Solids Author S. Nemat-Nasser
ISBN-10 9781483145839
Release 2017-01-31
Pages 428
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Variational Methods in the Mechanics of Solids contains the proceedings of the International Union of Theoretical and Applied Mechanics Symposium on Variational Methods in the Mechanics of Solids, held at Northwestern University in Evanston, Illinois, on September 11-13, 1978. The papers focus on advances in the application of variational methods to a variety of mathematically and technically significant problems in solid mechanics. The discussions are organized around three themes: thermomechanical behavior of composites, elastic and inelastic boundary value problems, and elastic and inelastic dynamic problems. This book is comprised of 58 chapters and opens by addressing some questions of asymptotic expansions connected with composite and with perforated materials. The following chapters explore mathematical and computational methods in plasticity; variational irreversible thermodynamics of open physical-chemical continua; macroscopic behavior of elastic material with periodically spaced rigid inclusions; and application of the Lanczos method to structural vibration. Finite deformation of elastic beams and complementary theorems of solid mechanics are also considered, along with numerical contact elastostatics; periodic solutions in plasticity and viscoplasticity; and the convergence of the mixed finite element method in linear elasticity. This monograph will appeal to practitioners of mathematicians as well as theoretical and applied mechanics.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics Author Adnan Ibrahimbegovic
ISBN-10 9789048123308
Release 2009-06-02
Pages 574
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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.

Foundations of the Theory of Elasticity Plasticity and Viscoelasticity

Foundations of the Theory of Elasticity  Plasticity  and Viscoelasticity Author Eduard Starovoitov
ISBN-10 9781926895116
Release 2012-07-18
Pages 320
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Foundations of the Theory of Elasticity, Plasticity, and Viscoelasticity details fundamental and practical skills and approaches for carrying out research in the field of modern problems in the mechanics of deformed solids, which involves the theories of elasticity, plasticity, and viscoelasticity. The book includes all modern methods of research as well as the results of the authors’ recent work and is presented with sufficient mathematical strictness and proof. The first six chapters are devoted to the foundations of the theory of elasticity. Theory of stress-strain state, physical relations and problem statements, variation principles, contact and 2D problems, and the theory of plates are presented, and the theories are accompanied by examples of solving typical problems. The last six chapters will be useful to postgraduates and scientists engaged in nonlinear mechanics of deformed inhomogeneous bodies. The foundations of the modern theory of plasticity (general, small elastoplastic deformations and the theory of flow), linear, and nonlinear viscoelasticity are set forth. Corresponding research of three-layered circular plates of various materials is included to illustrate methods of problem solving. Analytical solutions and numerical results for elastic, elastoplastic, lineaer viscoelastic and viscoelastoplastic plates are also given. Thermoviscoelastoplastic characteristics of certain materials needed for numerical account are presented in the eleventh chapter. The informative book is intended for scientists, postgraduates and higher-level students of engineering spheres and will provide important practical skills and approaches.

Introduction to the Mechanics of a Continuous Medium

Introduction to the Mechanics of a Continuous Medium Author Lawrence E. Malvern
ISBN-10 OCLC:2309235
Release 1969
Pages 713
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Introduction to the Mechanics of a Continuous Medium has been writing in one form or another for most of life. You can find so many inspiration from Introduction to the Mechanics of a Continuous Medium also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Introduction to the Mechanics of a Continuous Medium book for free.

Continuum Mechanics for Engineers Third Edition

Continuum Mechanics for Engineers  Third Edition Author G. Thomas Mase
ISBN-10 9781420085396
Release 2009-07-28
Pages 398
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Continuum Mechanics for Engineers, Third Edition provides engineering students with a complete, concise, and accessible introduction to advanced engineering mechanics. The impetus for this latest edition was the need to suitably combine the introduction of continuum mechanics, linear and nonlinear elasticity, and viscoelasticity for a graduate-level course sequence. An outgrowth of course notes and problems used to teach these subjects, the third edition of this bestselling text explores the basic concepts behind these topics and demonstrates their application in engineering practice. Presents Material Consistent with Modern Literature A new rearranged and expanded chapter on elasticity more completely covers Saint-Venant’s solutions. Subsections on extension, torsion, pure bending and flexure present an excellent foundation for posing and solving basic elasticity problems. The authors’ presentation enables continuum mechanics to be applied to biological materials, in light of their current importance. They have also altered the book’s notation—a common struggle for many students—to better align it with modern continuum mechanics literature. This book addresses students’ need to understand the sophisticated simulation programs that use nonlinear kinematics and various constitutive relationships. It includes an introduction to problem solution using MATLAB®, emphasizing this language’s value in enabling users to stay focused on fundamentals. This book provides information that is useful in emerging engineering areas, such as micro-mechanics and biomechanics. With an abundance of worked examples and chapter problems, it carefully explains necessary mathematics as required and presents numerous illustrations, giving students and practicing professionals an excellent self-study guide to enhance their skills. Through a mastery of this volume’s contents and additional rigorous finite element training, they will develop the mechanics foundation necessary to skillfully use modern, advanced design tools.