Nonlinear Continuum Mechanics of Solids

Nonlinear Continuum Mechanics of Solids PDF

Author: Yavuz Basar

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 201

ISBN-13: 3662042991

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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.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics PDF

Author: Gerhard A. Holzapfel

Publisher:

Published: 2000-04-06

Total Pages: 482

ISBN-13:

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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.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics PDF

Author: Adnan Ibrahimbegovic

Publisher: Springer Science & Business Media

Published: 2009-06-02

Total Pages: 588

ISBN-13: 9048123305

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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.

Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis

Worked Examples in Nonlinear Continuum Mechanics for Finite Element Analysis PDF

Author: Javier Bonet

Publisher: Cambridge University Press

Published: 2012-08-02

Total Pages: 137

ISBN-13: 1139561308

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Many processes in materials science and engineering, such as the load deformation behaviour of certain structures, exhibit nonlinear characteristics. The computer simulation of such processes therefore requires a deep understanding of both the theoretical aspects of nonlinearity and the associated computational techniques. This book provides a complete set of exercises and solutions in the field of theoretical and computational nonlinear continuum mechanics and is the perfect companion to Nonlinear Continuum Mechanics for Finite Element Analysis, where the authors set out the theoretical foundations of the subject. It employs notation consistent with the theory book and serves as a great resource to students, researchers and those in industry interested in gaining confidence by practising through examples. Instructors of the subject will also find the book indispensable in aiding student learning.

Nonlinear Solid Mechanics

Nonlinear Solid Mechanics PDF

Author: Gerhard A. Holzapfel

Publisher:

Published: 2000-04-06

Total Pages: 480

ISBN-13:

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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.

Linear and Non-linear Continuum Solid Mechanics

Linear and Non-linear Continuum Solid Mechanics PDF

Author: Santiago Hernández

Publisher: WIT Press

Published: 2021-06-28

Total Pages: 206

ISBN-13: 1784662712

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Deformable solids, that is to say, those which undergo changes in geometry when subjected to external loads or other types of solicitations, as well as other related topics are the focus of this book. Within the main field, this text deals with advanced linear elasticity and plasticity approaches and the behavioural study of more complex types of materials. This includes composites of more recent manufacture and others whose material characterisation has only recently been possible. It also describes how linear elastic behaviour extends to anisotropic materials in general and how deformations can result in small or large strain components. The information on plastic behaviour expands to include strain hardening of the materials. Amongst other new topics incorporated into this volume are studies of hyperelastic materials, which can represent elastomeric and some types of biological materials. A section of the book deals with viscoelastic materials, i.e. those who deform when subjected to long-term loads. The behaviour of viscoplasticity, as well as elasto-viscoplasticity, describes well other types of materials, including those present in many geotechnical sites. The objective of this volume is to present material that can be used for teaching continuum mechanics to students of mechanical, civil or aeronautical engineering. In order to understand the contents the reader only needs to know linear algebra and differential calculus. Examples have been included throughout the text and at the end of each chapter, exercises are presented which can be used to check on comprehension of the theoretical information presented.

Nonlinear Continuum Mechanics and Large Inelastic Deformations

Nonlinear Continuum Mechanics and Large Inelastic Deformations PDF

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.

Nonlinear Mechanics of Crystals

Nonlinear Mechanics of Crystals PDF

Author: John D. Clayton

Publisher: Springer Science & Business Media

Published: 2010-11-01

Total Pages: 709

ISBN-13: 9400703503

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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.