# Generalized Continuum Mechanics and Engineering Applications

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## Generalized Continuum Mechanics and Engineering Applications

Author | : Angela Madeo |

Publsiher | : Elsevier |

Total Pages | : 146 |

Release | : 2015-10-31 |

ISBN 10 | : 0081004672 |

ISBN 13 | : 9780081004678 |

Language | : EN, FR, DE, ES & NL |

**Generalized Continuum Mechanics and Engineering Applications Book Review:**

The new concept of metamaterial is increasingly attracting the interest of physicists and mechanical engineers. Such materials are obtained by suitably assembling multiple individual elements but usually arranged in (quasi-)periodic substructures in order to show exotic global mechanical properties. Indeed, the particular shape, geometry, size, orientation and arrangement of their constituting elements can affect, the propagation of waves of light or sound in a manner not observed in natural materials, creating material properties which may give rise to unexpected engineering applications. Particularly promising in the design and description of metamaterials are those micro-structures which present high contrasts in their mechanical properties: these micro-structures, once homogenized, may produce generalized continuum media, for example, second gradient or micromorphic. Many scientific challenges related to the application of generalized continuum theories to the characterization and conception of high-performance metamaterials can be identified. In this book we identify and discuss four main potential fields of applications of generalized continuum theories, namely, mechanical behavior of fibrous composite reinforcements, wave propagation in metamaterials, mechanical behavior of concrete and mechanically driven remodeling of bone in presence of bio-resorbable materials. For each field, we underline how the use of a generalized continuum theory can be of help for describing how the presence of microstructure can affect the global mechanical behavior of the considered metamaterials. Covers four main fields of the application of continuum theories Learn how to apply generalised continuum theory to describe the effects of microstructure on the mechanical behavior of materials Decipher the material properties which aid your engineering applications

## Generalized Continua from the Theory to Engineering Applications

Author | : Holm Altenbach,Victor A. Eremeyev |

Publsiher | : Springer Science & Business Media |

Total Pages | : 387 |

Release | : 2012-10-17 |

ISBN 10 | : 3709113717 |

ISBN 13 | : 9783709113714 |

Language | : EN, FR, DE, ES & NL |

**Generalized Continua from the Theory to Engineering Applications Book Review:**

On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua. The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.

## Geometrical Foundations of Continuum Mechanics

Author | : Paul Steinmann |

Publsiher | : Springer |

Total Pages | : 517 |

Release | : 2015-03-25 |

ISBN 10 | : 3662464608 |

ISBN 13 | : 9783662464601 |

Language | : EN, FR, DE, ES & NL |

**Geometrical Foundations of Continuum Mechanics Book Review:**

This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear continuum mechanics. Together with the discussion on the integrability conditions for the distortions and double-distortions, the concepts of dislocation, disclination and point-defect density tensors are introduced. For concreteness, after touching on nonlinear fir st- and second-order elasticity, a detailed discussion of the kinematics of (multiplicative) first- and second-order elasto-plasticity is given. The discussion naturally culminates in a comprehensive set of different types of dislocation, disclination and point-defect density tensors. It is argued, that these can potentially be used to model densities of geometrically necessary defects and the accompanying hardening in crystalline materials. Eventually Part IV summarizes the above findings on integrability whereby distinction is made between the straightforward conditions for the distortion and the double-distortion being integrable and the more involved conditions for the strain (metric) and the double-strain (connection) being integrable. The book addresses readers with an interest in continuum modelling of solids from engineering and the sciences alike, whereby a sound knowledge of tensor calculus and continuum mechanics is required as a prerequisite.

## Applications Of Tensor Analysis In Continuum Mechanics

Author | : Michael J Cloud,Victor A Eremeyev,Leonid P Lebedev |

Publsiher | : World Scientific |

Total Pages | : 428 |

Release | : 2018-07-10 |

ISBN 10 | : 9813238984 |

ISBN 13 | : 9789813238985 |

Language | : EN, FR, DE, ES & NL |

**Applications Of Tensor Analysis In Continuum Mechanics Book Review:**

'A strong point of this book is its coverage of tensor theory, which is herein deemed both more readable and more substantial than many other historic continuum mechanics books. The book is self-contained. It serves admirably as a reference resource on fundamental principles and equations of tensor mathematics applied to continuum mechanics. Exercises and problem sets are useful for teaching … The book is highly recommended as both a graduate textbook and a reference work for students and more senior researchers involved in theoretical and mathematical modelling of continuum mechanics of materials. Key concepts are well described in the text and are supplemented by informative exercises and problem sets with solutions, and comprehensive Appendices provide important equations for ease of reference.'Contemporary PhysicsA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas.The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.

## Generalized Continua from the Theory to Engineering Applications

Author | : Holm Altenbach,Victor A. Eremeyev |

Publsiher | : Springer Science & Business Media |

Total Pages | : 388 |

Release | : 2012-10-18 |

ISBN 10 | : 3709113709 |

ISBN 13 | : 9783709113707 |

Language | : EN, FR, DE, ES & NL |

**Generalized Continua from the Theory to Engineering Applications Book Review:**

On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua. The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.

## Mechanics of Generalized Continua

Author | : Gérard A. Maugin,Andrei V. Metrikine |

Publsiher | : Springer Science & Business Media |

Total Pages | : 337 |

Release | : 2010-03-24 |

ISBN 10 | : 1441956956 |

ISBN 13 | : 9781441956958 |

Language | : EN, FR, DE, ES & NL |

**Mechanics of Generalized Continua Book Review:**

In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

## Mechanics of Generalized Continua

Author | : Holm Altenbach,Gérard A. Maugin,Vladimir Erofeev |

Publsiher | : Springer Science & Business Media |

Total Pages | : 352 |

Release | : 2011-04-02 |

ISBN 10 | : 9783642192197 |

ISBN 13 | : 364219219X |

Language | : EN, FR, DE, ES & NL |

**Mechanics of Generalized Continua Book Review:**

This collection on „Mechanics of Generalized Continua - from Micromechanical Basics to Engineering Applications“ brings together leading scientists in this field from France, Russian Federation, and Germany. The attention in this publication is be focussed on the most recent research items, i.e., - new models, - application of well-known models to new problems, - micro-macro aspects, - computational effort, - possibilities to identify the constitutive equations, and - old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

## Continuum Mechanics for Engineers

Author | : G. Thomas Mase,Ronald E. Smelser,Jenn Stroud Rossmann |

Publsiher | : CRC Press |

Total Pages | : 434 |

Release | : 2020-05-01 |

ISBN 10 | : 1482238691 |

ISBN 13 | : 9781482238693 |

Language | : EN, FR, DE, ES & NL |

**Continuum Mechanics for Engineers Book Review:**

A bestselling textbook in its first three editions, Continuum Mechanics for Engineers, Fourth Edition provides engineering students with a complete, concise, and accessible introduction to advanced engineering mechanics. It provides information that is useful in emerging engineering areas, such as micro-mechanics and biomechanics. Through a mastery of this volume’s contents and additional rigorous finite element training, readers will develop the mechanics foundation necessary to skillfully use modern, advanced design tools. Features: Provides a basic, understandable approach to the concepts, mathematics, and engineering applications of continuum mechanics Updated throughout, and adds a new chapter on plasticity Features an expanded coverage of fluids Includes numerous all new end-of-chapter problems With an abundance of worked examples and chapter problems, it carefully explains necessary mathematics and presents numerous illustrations, giving students and practicing professionals an excellent self-study guide to enhance their skills.

## Non Classical Continuum Mechanics

Author | : Gérard A. Maugin |

Publsiher | : Springer |

Total Pages | : 259 |

Release | : 2016-09-24 |

ISBN 10 | : 9811024340 |

ISBN 13 | : 9789811024344 |

Language | : EN, FR, DE, ES & NL |

**Non Classical Continuum Mechanics Book Review:**

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.

## Fundamentals of Continuum Mechanics of Soils

Author | : Yehuda Klausner |

Publsiher | : Springer Science & Business Media |

Total Pages | : 607 |

Release | : 2012-12-06 |

ISBN 10 | : 1447116771 |

ISBN 13 | : 9781447116776 |

Language | : EN, FR, DE, ES & NL |

**Fundamentals of Continuum Mechanics of Soils Book Review:**

Fundamentals of Continuum Mechanics of Soils provides a long-needed general scheme for the study of the important yet problematic material of soil. It closes the gap between two disciplines, soil mechanics and con- tinuum mechanics, showing that the familiar concepts of soil mechanics evolve directly from continuum mechanics. It confirms concepts such as pore pressures, cohesion and dependence of the shear stress on consolidation, and rejects the view that continuum mechanics cannot be applied to a material such as soil. The general concepts of continuum mechanics, field equations and constitutive equations are discussed. It is shown how the theory of mixtures evolves from these equations and how, along with energetics and irrevers- ible thermodynamics, it can be applied to soils. The discussion also sheds light on some aspects of mechanics of materials, especially compressible materials. Examples are the introduction of the Hencky measure of strain, the requirement of dual constitutive equations, and the dependence of the spent internal energy on the stored internal energy. Researchers in engineering mechanics and material sciences may find that the results of experiments on soils can be generalized and extended to other materials. The book is a reference text for students familiar with the fundamentals of mechanics, for scholars of soil engineering, and for soil scientists. It is also suitable as an advanced undergraduate course in soil mechanics.

## Mathematical Analysis of Continuum Mechanics and Industrial Applications

Author | : Hiromichi Itou,Masato Kimura,Vladimír Chalupecký,Kohji Ohtsuka,Daisuke Tagami,Akira Takada |

Publsiher | : Springer |

Total Pages | : 231 |

Release | : 2016-11-18 |

ISBN 10 | : 9811026335 |

ISBN 13 | : 9789811026331 |

Language | : EN, FR, DE, ES & NL |

**Mathematical Analysis of Continuum Mechanics and Industrial Applications Book Review:**

This book focuses on mathematical theory and numerical simulation related to various aspects of continuum mechanics, such as fracture mechanics, elasticity, plasticity, pattern dynamics, inverse problems, optimal shape design, material design, and disaster estimation related to earthquakes. Because these problems have become more important in engineering and industry, further development of mathematical study of them is required for future applications. Leading researchers with profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry provide the contents of this book. They help readers to understand that mathematical theory can be applied not only to different types of industry, but also to a broad range of industrial problems including materials, processes, and products.

## Introduction to Continuum Mechanics

Author | : W Michael Lai,Erhard Krempl,David Rubin |

Publsiher | : Elsevier |

Total Pages | : 570 |

Release | : 2014-06-28 |

ISBN 10 | : 0080509134 |

ISBN 13 | : 9780080509136 |

Language | : EN, FR, DE, ES & NL |

**Introduction to Continuum Mechanics Book Review:**

Introduction to Continuum Mechanics is a recently updated and revised text which is perfect for either introductory courses in an undergraduate engineering curriculum or for a beginning graduate course. Continuum Mechanics studies the response of materials to different loading conditions. The concept of tensors is introduced through the idea of linear transformation in a self-contained chapter, and the interrelation of direct notation, indicial notation, and matrix operations is clearly presented. A wide range of idealized materials are considered through simple static and dynamic problems, and the book contains an abundance of illustrative examples of problems, many with solutions. Serves as either a introductory undergraduate course or a beginning graduate course textbook. Includes many problems with illustrations and answers.

## Continuum Mechanics Through the Twentieth Century

Author | : Gerard A Maugin |

Publsiher | : Springer Science & Business Media |

Total Pages | : 314 |

Release | : 2013-04-08 |

ISBN 10 | : 9400763530 |

ISBN 13 | : 9789400763531 |

Language | : EN, FR, DE, ES & NL |

**Continuum Mechanics Through the Twentieth Century Book Review:**

This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.

## Advanced Methods of Continuum Mechanics for Materials and Structures

Author | : Konstantin Naumenko,Marcus Aßmus |

Publsiher | : Springer |

Total Pages | : 558 |

Release | : 2018-05-27 |

ISBN 10 | : 9789811092947 |

ISBN 13 | : 981109294X |

Language | : EN, FR, DE, ES & NL |

**Advanced Methods of Continuum Mechanics for Materials and Structures Book Review:**

This volume presents a collection of contributions on advanced approaches of continuum mechanics, which were written to celebrate the 60th birthday of Prof. Holm Altenbach. The contributions are on topics related to the theoretical foundations for the analysis of rods, shells and three-dimensional solids, formulation of constitutive models for advanced materials, as well as development of new approaches to the modeling of damage and fractures.

## Applied Mechanics of Solids

Author | : Allan F. Bower |

Publsiher | : CRC Press |

Total Pages | : 820 |

Release | : 2009-10-05 |

ISBN 10 | : 1439802483 |

ISBN 13 | : 9781439802489 |

Language | : EN, FR, DE, ES & NL |

**Applied Mechanics of Solids Book Review:**

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 PredictionsApplied Mechanics o

## Introduction to Engineering Mechanics

Author | : Jenn Stroud Rossmann,Clive L. Dym,Lori Bassman |

Publsiher | : CRC Press |

Total Pages | : 462 |

Release | : 2015-03-24 |

ISBN 10 | : 1482219530 |

ISBN 13 | : 9781482219531 |

Language | : EN, FR, DE, ES & NL |

**Introduction to Engineering Mechanics Book Review:**

Integrated Mechanics Knowledge Essential for Any EngineerIntroduction to Engineering Mechanics: A Continuum Approach, Second Edition uses continuum mechanics to showcase the connections between engineering structure and design and between solids and fluids and helps readers learn how to predict the effects of forces, stresses, and strains. T

## Recent Developments in the Theory and Application of Generalized and Oriented Media

Author | : P. G. Glockner,Marcelo Epstein,D. J. Malcolm,American Academy of Mechanics,Canadian Society for Mechanical Engineering. Division of Mechanics and Applied Mathematics |

Publsiher | : Calgary : [s.n.] |

Total Pages | : 250 |

Release | : 1979 |

ISBN 10 | : |

ISBN 13 | : CORNELL:31924004315457 |

Language | : EN, FR, DE, ES & NL |

**Recent Developments in the Theory and Application of Generalized and Oriented Media Book Review:**

## Continuum Mechanics Volume II

Author | : José Merodio,Giuseppe Saccomandi |

Publsiher | : EOLSS Publications |

Total Pages | : 446 |

Release | : 2011-11-30 |

ISBN 10 | : 1848263732 |

ISBN 13 | : 9781848263734 |

Language | : EN, FR, DE, ES & NL |

**Continuum Mechanics Volume II Book Review:**

The main objective of continuum mechanics is to predict the response of a body that is under the action of external and/or internal influences, i.e. to capture and describe different mechanisms associated with the motion of a body that is under the action of loading. A body in continuum mechanics is considered to be matter continuously distributed in space. Hence, no attention is given to the microscopic (atomic) structure of real materials although non-classical generalized theories of continuum mechanics are able to deal with the mesoscopic structure of matter (i.e. defects, cracks, dispersive lengths, ...). Matter occupies space in time and the response of a body in continuum mechanics is restricted to the Newtonian space-time of classical mechanics in this volume. Einstein’s theory of relativity is not considered. In the classical sense, loading is considered as any action that changes the motion of the body. This includes, for instance, a change in temperature or a force applied. By introducing the concept of configurational forces a load may also be considered as a force that drives a change in the material space, for example the opening of a crack. Continuum mechanics refers to field descriptions of phenomena that are usually modeled by partial differential equations and, from a mathematical point of view, require non-standard knowledge of non-simple technicalities. One purpose in this volume has been to present the different subjects in a self-contained way for a general audience. The organization of the volume is as follows. Mathematically, to predict the response of a body it is necessary to formulate boundary value problems governed by balance laws. The theme of the volume, that is an overview of the subject, has been written with this idea in mind for beginners in the topic. Chapter 1 is an introduction to continuum mechanics based on a one-dimensional framework in which, simultaneously, a more detailed organization of the chapters of this volume is given. A one-dimensional approach to continuum mechanics in some aspects maybe misleading since the analysis is oversimplified. Nevertheless, it allows us to introduce the subject through the early basic steps of the continuum analysis for a general audience. Chapters 3, 4 and 5 are devoted to the mathematical setting of continuum analysis: kinematics, balance laws and thermodynamics, respectively. Chapters 6 and 7 are devoted to constitutive equations. Chapters 8 and 9 deal with different issues in the context of linear elastostatics and linear elastodynamics and waves, respectively, for solids. Linear Elasticity is a classical and central theory of continuum mechanics. Chapter 10 deals with fluids while chapter 11 analyzes the coupled theory of thermoelasticity. Chapter 12 deals with nonlinear elasticity and its role in the continuum framework. Chapters 13 and 14 are dedicated to different applications of solid and fluid mechanics, respectively. The rest of the chapters involve some advanced topics. Chapter 15 is dedicated to turbulence, one of the main challenges in fluid mechanics. Chapter 16 deals with electro-magneto active materials (a coupled theory). Chapter 17 deals with specific ideas of soft matter and chapter 18 deals with configurational forces. In chapter 19, constitutive equations are introduced in a general (implicit) form. Well-posedness (existence, time of existence, uniqueness, continuity) of the equations of the mechanics of continua is an important topic which involves sophisticated mathematical machinery. Chapter 20 presents different analyses related to these topics. Continuum Mechanics is an interdisciplinary subject that attracts the attention of engineers, mathematicians, physicists, etc., working in many different disciplines from a purely scientific environment to industrial applications including biology, materials science, engineering, and many other subjects.

## Generalized Models and Non classical Approaches in Complex Materials 2

Author | : Holm Altenbach,Joël Pouget,Martine Rousseau,Bernard Collet,Thomas Michelitsch |

Publsiher | : Springer |

Total Pages | : 328 |

Release | : 2018-06-26 |

ISBN 10 | : 3319775049 |

ISBN 13 | : 9783319775043 |

Language | : EN, FR, DE, ES & NL |

**Generalized Models and Non classical Approaches in Complex Materials 2 Book Review:**

This book is the 2nd special volume dedicated to the memory of Gérard Maugin. Over 30 leading scientists present their contribution to reflect the vast field of scientific activity of Gérard Maugin. The topics of contributions employing often non-standard methods (generalized model) in this volume show the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro-macro aspects, computational efforts, possibilities to identify the constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

## Tensor Algebra and Tensor Analysis for Engineers

Author | : Mikhail Itskov |

Publsiher | : Springer Science & Business Media |

Total Pages | : 272 |

Release | : 2012-08-13 |

ISBN 10 | : 3642308791 |

ISBN 13 | : 9783642308796 |

Language | : EN, FR, DE, ES & NL |

**Tensor Algebra and Tensor Analysis for Engineers Book Review:**

There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area. This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.