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Author: Seiichi Nomura
Publisher: John Wiley & Sons
ISBN: 1118385691
Category : Science
Languages : en
Pages : 290
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Book Description
Demonstrates the simplicity and effectiveness of Mathematica as the solution to practical problems in composite materials. Designed for those who need to learn how micromechanical approaches can help understand the behaviour of bodies with voids, inclusions, defects, this book is perfect for readers without a programming background. Thoroughly introducing the concept of micromechanics, it helps readers assess the deformation of solids at a localized level and analyse a body with microstructures. The author approaches this analysis using the computer algebra system Mathematica, which facilitates complex index manipulations and mathematical expressions accurately. The book begins by covering the general topics of continuum mechanics such as coordinate transformations, kinematics, stress, constitutive relationship and material symmetry. Mathematica programming is also introduced with accompanying examples. In the second half of the book, an analysis of heterogeneous materials with emphasis on composites is covered. Takes a practical approach by using Mathematica, one of the most popular programmes for symbolic computation Introduces the concept of micromechanics with worked-out examples using Mathematica code for ease of understanding Logically begins with the essentials of the topic, such as kinematics and stress, before moving to more advanced areas Applications covered include the basics of continuum mechanics, Eshelby's method, analytical and semi-analytical approaches for materials with inclusions (composites) in both infinite and finite matrix media and thermal stresses for a medium with inclusions, all with Mathematica examples Features a problem and solution section on the book’s companion website, useful for students new to the programme
Author: Seiichi Nomura
Publisher: John Wiley & Sons
ISBN: 1118385691
Category : Science
Languages : en
Pages : 290
Get Book Here
Book Description
Demonstrates the simplicity and effectiveness of Mathematica as the solution to practical problems in composite materials. Designed for those who need to learn how micromechanical approaches can help understand the behaviour of bodies with voids, inclusions, defects, this book is perfect for readers without a programming background. Thoroughly introducing the concept of micromechanics, it helps readers assess the deformation of solids at a localized level and analyse a body with microstructures. The author approaches this analysis using the computer algebra system Mathematica, which facilitates complex index manipulations and mathematical expressions accurately. The book begins by covering the general topics of continuum mechanics such as coordinate transformations, kinematics, stress, constitutive relationship and material symmetry. Mathematica programming is also introduced with accompanying examples. In the second half of the book, an analysis of heterogeneous materials with emphasis on composites is covered. Takes a practical approach by using Mathematica, one of the most popular programmes for symbolic computation Introduces the concept of micromechanics with worked-out examples using Mathematica code for ease of understanding Logically begins with the essentials of the topic, such as kinematics and stress, before moving to more advanced areas Applications covered include the basics of continuum mechanics, Eshelby's method, analytical and semi-analytical approaches for materials with inclusions (composites) in both infinite and finite matrix media and thermal stresses for a medium with inclusions, all with Mathematica examples Features a problem and solution section on the book’s companion website, useful for students new to the programme
Author: Seiichi Nomura
Publisher: Springer Nature
ISBN: 3031130677
Category : Technology & Engineering
Languages : en
Pages : 177
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Book Description
Complex variable theory is attractive for engineers as it offers elegant approaches for certain types of differential equations in engineering including heat transfer, solid mechanics, and fluid mechanics. However, a gap exists between books written by mathematicians and books written by engineers in their specific fields. Naturally, mathematicians tend to emphasize rigorousness and consistency while less emphasizing applications. On the other hand, books written by engineers often jump directly to the specific topics assuming that the readers already have sufficient background of complex variables and the pathway from theory to the application is not clearly elucidated. This book closes the gap in the literature. providing a smooth transition from basic theory to the application is accomplished. Although it is not possible to cover all the topics in engineering exhaustively, the readers can at least find the logic of how and why complex variables are effective for some of the engineering problems. Another motivation for writing this book is to demonstrate that the readers can take advantage of a computer algebra system, Mathematica, to facilitate tedious algebra and visualize complex functions so that they can focus on principles instead of spending endless hours on algebra by hand. Unlike numerical tools such as MATLAB and FORTRAN, Mathematica can expand, differentiate, and integrate complex-valued functions symbolically. Mathematica can be used as a stand-alone symbolic calculator or a programming tool using the Wolfram Language. If Mathematica is not available locally, Wolfram Cloud Basic can be used online as a free service to execute Mathematica statements.
Author: Seiichi Nomura
Publisher: John Wiley & Sons
ISBN: 1119945038
Category : Science
Languages : en
Pages : 290
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Book Description
Demonstrates the simplicity and effectiveness of Mathematica as the solution to practical problems in composite materials. Designed for those who need to learn how micromechanical approaches can help understand the behaviour of bodies with voids, inclusions, defects, this book is perfect for readers without a programming background. Thoroughly introducing the concept of micromechanics, it helps readers assess the deformation of solids at a localized level and analyse a body with microstructures. The author approaches this analysis using the computer algebra system Mathematica, which facilitates complex index manipulations and mathematical expressions accurately. The book begins by covering the general topics of continuum mechanics such as coordinate transformations, kinematics, stress, constitutive relationship and material symmetry. Mathematica programming is also introduced with accompanying examples. In the second half of the book, an analysis of heterogeneous materials with emphasis on composites is covered. Takes a practical approach by using Mathematica, one of the most popular programmes for symbolic computation Introduces the concept of micromechanics with worked-out examples using Mathematica code for ease of understanding Logically begins with the essentials of the topic, such as kinematics and stress, before moving to more advanced areas Applications covered include the basics of continuum mechanics, Eshelby's method, analytical and semi-analytical approaches for materials with inclusions (composites) in both infinite and finite matrix media and thermal stresses for a medium with inclusions, all with Mathematica examples Features a problem and solution section on the book’s companion website, useful for students new to the programme
Author: S. Stupkiewicz
Publisher: Springer Science & Business Media
ISBN: 354049717X
Category : Technology & Engineering
Languages : en
Pages : 200
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Book Description
Micromechanics provides a link between the structure and the properties at different scales of observation. This book deals with micromechanical analysis of interfaces and interface layers and presents several modelling tools. These range from the rigorous method of asymptotic expansions to practical finite element simulations, suitable for this class of problems. The corresponding two parts of the book are self-contained, so they can be read separately.
Author: Rainer Glüge
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110793652
Category : Technology & Engineering
Languages : en
Pages : 218
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Book Description
Almost all materials are inhomogeneous at the microscale. Typical examples are fiber- and grain structures made of anisotropic phases. These cannot be accounted for in detail in engineering calculations. Instead, effective, homogeneous material properties are used. These are obtained from the inhomogeneous structures by homogenization methods. This book provides a structured overview of the analytical homogenization methods, including the most common estimates, bounds, and Fourier methods. The focus is on linear and anisotropic constitutive relationships, like Hookean elasticity and Fourier’s law for thermal conduction. All sections are accompanied by example calculations, including program code that is also available online.
Author: Seiichi Nomura
Publisher: Morgan & Claypool Publishers
ISBN: 1681733366
Category : Technology & Engineering
Languages : en
Pages : 350
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Book Description
This book is aimed at those in engineering/scientific fields who have never learned programming before but are eager to master the C language quickly so as to immediately apply it to problem solving in numerical analysis. The book skips unnecessary formality but explains all the important aspects of C essential for numerical analysis. Topics covered in numerical analysis include single and simultaneous equations, differential equations, numerical integration, and simulations by random numbers. In the Appendices, quick tutorials for gnuplot, Octave/MATLAB, and FORTRAN for C users are provided.
Author: Vasyl Michael Harik
Publisher: Springer Science & Business Media
ISBN: 9400710135
Category : Technology & Engineering
Languages : en
Pages : 251
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Book Description
This volume consists of the state-of-the-art reports on new developments in micromechanics and the modeling of nanoscale effects, and is a companion book to the recent Kluwer volume on nanomechanics and mul- scale modeling (it is entitled Trends in Nanoscale Mechanics). The two volumes grew out of a series of discussions held at NASA Langley Research Center (LaRC), lectures and other events shared by many researchers from the national research laboratories and academia. The key events include the 2001 Summer Series of Round-Table Discussions on Nanotechnology at ICASE Institute (NASA LaRC) organized by Drs. V. M. Harik and M. D. Salas and the 2002 NASA LaRC Workshop on Multi-scale Modeling. The goal of these interactions was to foster collaborations between academic researchers and the ICASE Institute (NASA LaRC), a universi- based institute, which has pioneered world-class computational, theoretical and experimental research in the disciplines that are important to NASA. Editors gratefully acknowledge help of Ms. E. Todd (ICASE, NASA LaRC), the ICASE Director M. D. Salas and all reviewers, in particular, Dr. B. Diskin (ICASE/NIA, NASA LaRC), Prof. R. Haftka (University of Florida), Dr. V. M. Harik (ICASE/Swales Aerospace, NASA LaRC), Prof.
Author: Mark Kachanov
Publisher: Springer
ISBN: 3319762044
Category : Science
Languages : en
Pages : 723
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Book Description
This book on micromechanics explores both traditional aspects and the advances made in the last 10–15 years. The viewpoint it assumes is that the rapidly developing field of micromechanics, apart from being of fundamental scientific importance, is motivated by materials science applications. The introductory chapter provides the necessary background together with some less traditional material, examining e.g. approximate elastic symmetries, Rice’s technique of internal variables and multipole expansions. The remainder of the book is divided into the following parts: (A) classic results, which consist of Rift Valley Energy (RVE), Hill’s results, Eshelby’s results for ellipsoidal inhomogeneities, and approximate schemes for the effective properties; (B) results aimed at overcoming these limitations, such as volumes smaller than RVE, quantitative characterization of “irregular” microstructures, non-ellipsoidal inhomogeneities, and cross-property connections; (C) local fields and effects of interactions on them; and lastly (D) – the largest section – which explores applications to eight classes of materials that illustrate how to apply the micromechanics methodology to specific materials.
Author: Shaker A. Meguid
Publisher: Springer
ISBN: 3319527940
Category : Science
Languages : en
Pages : 524
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Book Description
This book elucidates the most recent and highly original developments in the fields of micro- and nanomechanics and the corresponding homogenization techniques that can be reliably adopted and applied in determining the local properties, as well as the linear and nonlinear effective properties of the final architecture of these complex composite structures. Specifically, this volume, divided into three main sections—Fundamentals, Modeling, and Applications—provides recent developments in the mathematical framework of micro- and nanomechanics, including Green’s function and Eshelby’s inclusion problem, molecular mechanics, molecular dynamics, atomistic based continuum, multiscale modeling, and highly localized phenomena such as microcracks and plasticity. It is a compilation of the most recent efforts by a group of the world’s most talented and respected researchers. Ideal for graduate students in aerospace, mechanical, civil, material science, life sciences, and biomedical engineering, researchers, practicing engineers, and consultants, the book provides a unified approach in compiling micro- and nano-scale phenomena. · Elucidates recent and highly original developments in the fields of micromechanics and nanomechanics and the corresponding homogenization techniques; · Includes several new topics that are not covered in the current literature, such as micromechanics of metamaterials, electrical conductivity of CNT and graphene nanocomposites, ferroelectrics, piezoelectric, and electromagnetic materials; · Addresses highly localized phenomena such as coupled field problems, microcracks, inelasticity, dispersion of CNTs, synthesis, characterization and a number of interesting applications; · Maximizes readers’ ability to apply theories of micromechanics and nanomechanics to heterogeneous solids; · Illustrates application of micro- and nanomechanical theory to design novel composite and nanocomposite materials.
Author: H.H. Shen
Publisher: Elsevier
ISBN: 1483291286
Category : Technology & Engineering
Languages : en
Pages : 476
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Book Description
The 45 papers presented in this volume all share the common goal of constructing continuum models based on the micro behaviours of granular materials. Computer simulations continue to provide observations to aid modelling, while new experimental works begin to show promise for increased understanding in this area. Theoretical studies have extended into transitions between the rapid and quasi-static regimes and the fluid and solid mixture flows. Exciting new topics discussed in this volume include: concepts of a measure for randomness in quasi-static granular materials, which is analogous to the granular temperature in a rapid flow; scaling effects in granular media and their implications in both physical and computer simulations; instability; and boundary effects on heterogeneous behavior in simple flow configurations, which are posing new challenges for mathematical modelling. The volume will prove indispensable reading for researchers interested in the current developments in the fundamental aspects of mechanics of granular materials.
