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Author: P. Ponte Castaneda
Publisher: Springer Science & Business Media
ISBN: 1402026234
Category : Technology & Engineering
Languages : en
Pages : 371
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Book Description
Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended. The key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin films, smart materials, and structural and topology optimization. One lecture deals with a topic important for nanomaterials: the passage from discrete to continuum problems by using nonlinear homogenization methods. Some papers reveal the role of parameterized or Young measures in description of microstructures and in optimal design. Other papers deal with recently developed methods – both analytical and computational – for estimating the effective behavior and field fluctuations in composites and polycrystals with nonlinear constitutive behavior. All in all, the volume offers a cross-section of current activity in nonlinear homogenization including a broad range of physical and engineering applications. The careful reader will be able to identify challenging open problems in this still evolving field. For instance, there is the need to improve bounding techniques for nonconvex problems, as well as for solving geometrically nonlinear optimum shape-design problems, using relaxation and homogenization methods.
Author: P. Ponte Castaneda
Publisher: Springer Science & Business Media
ISBN: 1402026234
Category : Technology & Engineering
Languages : en
Pages : 371
Get Book Here
Book Description
Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended. The key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin films, smart materials, and structural and topology optimization. One lecture deals with a topic important for nanomaterials: the passage from discrete to continuum problems by using nonlinear homogenization methods. Some papers reveal the role of parameterized or Young measures in description of microstructures and in optimal design. Other papers deal with recently developed methods – both analytical and computational – for estimating the effective behavior and field fluctuations in composites and polycrystals with nonlinear constitutive behavior. All in all, the volume offers a cross-section of current activity in nonlinear homogenization including a broad range of physical and engineering applications. The careful reader will be able to identify challenging open problems in this still evolving field. For instance, there is the need to improve bounding techniques for nonconvex problems, as well as for solving geometrically nonlinear optimum shape-design problems, using relaxation and homogenization methods.
Author: Victor Goldade
Publisher: CRC Press
ISBN: 1498716202
Category : Science
Languages : en
Pages : 266
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Book Description
Smart materials have been categorized employing taxonomical methods used in classification of cybernetics systems. This approach has allowed the systematization of the variety of smart materials (both developed and conceptualized) as well to substantiate the three-stage process of the materials' making. This book proposes a phenomenological model d
Author: Jesús Ildefonso Díaz
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110648997
Category : Mathematics
Languages : en
Pages : 200
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Book Description
The behavior of materials at the nanoscale is a key aspect of modern nanoscience and nanotechnology. This book presents rigorous mathematical techniques showing that some very useful phenomenological properties which can be observed at the nanoscale in many nonlinear reaction-diffusion processes can be simulated and justified mathematically by means of homogenization processes when a certain critical scale is used in the corresponding framework.
Author: A. A. Kolpakov
Publisher: CRC Press
ISBN: 9781439801765
Category : Mathematics
Languages : en
Pages : 335
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Book Description
Is it possible to apply a network model to composites with conical inclusions? How does the energy pass through contrast composites? Devoted to the analysis of transport problems for systems of densely packed, high-contrast composite materials, Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications answers questions such as these and presents new and modified asymptotic methods for real-world applications in composite materials development. A mathematical discussion of phenomena related to natural sciences and engineering, this book covers historical developments and new progress in mathematical calculations, computer techniques, finite element computer programs, and presentation of results of numerical computations. The "transport problem"—which is described with scalar linear elliptic equations—implies problems of thermoconductivity, diffusion, and electrostatics. To address this "problem," the authors cover asymptotic analysis of partial differential equations, material science, and the analysis of effective properties of electroceramics. Providing numerical calculations of modern composite materials that take into account nonlinear effects, the book also: Presents results of numerical analysis, demonstrating specific properties of distributions of local fields in high-contrast composite structures and systems of closely placed bodies Assesses whether total flux, energy, and capacity exhaust characteristics of the original continuum model Illustrates the expansion of the method for systems of bodies to highly filled contrast composites This text addresses the problem of loss of high-contrast composites, as well as transport and elastic properties of thin layers that cover or join solid bodies. The material presented will be particularly useful for applied mathematicians interested in new methods, and engineers dealing with prospective materials and design methods.
Author: Lobos Fernández, Mauricio
Publisher: KIT Scientific Publishing
ISBN: 3731507706
Category : Materials
Languages : en
Pages : 224
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Book Description
This work approaches the fields of homogenization and of materials design for the linear and nonlinear mechanical properties with prescribed properties-profile. The set of achievable properties is bounded by the zeroth-order bounds (which are material specific), the first-order bounds (containing volume fractions of the phases) and the second-order Hashin-Shtrikman bounds with eigenfields in terms of tensorial texture coefficients for arbitrarily anisotropic textured materials.
Author: Igor V. Andrianov
Publisher: Springer
ISBN: 3319657860
Category : Science
Languages : en
Pages : 333
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Book Description
In this book the authors show that it is possible to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly used for controlling processes arising in connection with composite material systems. The book focuses on this asymptotic-modeling-based approach because it allows us to define the most important out of numerous parameters describing the system, or, in other words, the asymptotic methods allow us to estimate the sensitivity of the system parameters. Further, the book addresses the construction of nonlocal and higher-order homogenized models. Local fields on the micro-level and the influence of so-called non-ideal contact between the matrix and inclusions are modeled and investigated. The book then studies composites with non-regular structure and cluster type composite conductivity, and analyzes edge effects in fiber composite materials. Transition of load from a fiber to a matrix for elastic and viscoelastic composites, various types of fiber composite fractures, and buckling of fibers in fiber-reinforced composites is also investigated. Last but not least, the book includes studies on perforated membranes, plates, and shells, as well as the asymptotic modeling of imperfect nonlinear interfaces.
Author: Manoochehr Zoghi
Publisher: CRC Press
ISBN: 1420003747
Category : Technology & Engineering
Languages : en
Pages : 692
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Book Description
Fiber-reinforced polymer (FRP) composites have become an integral part of the construction industry because of their versatility, enhanced durability and resistance to fatigue and corrosion, high strength-to-weight ratio, accelerated construction, and lower maintenance and life-cycle costs. Advanced FRP composite materials are also emerging for a w
Author: Andrea Braides
Publisher: Springer Science & Business Media
ISBN: 354036546X
Category : Mathematics
Languages : en
Pages : 326
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Book Description
The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
Author: Shuichi Miyazaki
Publisher: Cambridge University Press
ISBN: 0521885760
Category : Science
Languages : en
Pages : 487
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Book Description
The first dedicated book describing the properties, preparation, characterization and device applications of TiNi-based shape memory alloys.
Author: Christian Lexcellent
Publisher: John Wiley & Sons
ISBN: 1118577957
Category : Technology & Engineering
Languages : en
Pages : 295
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Book Description
The aim of this book is to understand and describe the martensitic phase transformation and the process of martensite platelet reorientation. These two key elements enable the author to introduce the main features associated with the behavior of shape-memory alloys (SMAs), i.e. the one-way shape-memory effect, pseudo-elasticity, training and recovery. Attention is paid in particular to the thermodynamical frame for solid materials modeling at the macroscopic scale and its applications, as well as to the particular use of such alloys – the simplified calculations for the bending of bars and their torsion. Other chapters are devoted to key topics such as the use of the “crystallographical theory of martensite” for SMA modeling, phenomenological and statistical investigations of SMAs, magneto-thermo-mechanical behavior of magnetic SMAs and the fracture mechanics of SMAs. Case studies are provided on the dimensioning of SMA elements offering the reader an additional useful framework on the subject. Contents 1. Some General Points about SMAs. 2. The World of Shape-memory Alloys. 3. Martensitic Transformation. 4. Thermodynamic Framework for the Modeling of Solid Materials. 5. Use of the “CTM” to Model SMAs. 6. Phenomenological and Statistical Approaches for SMAs. 7. Macroscopic Models with Internal Variables. 8. Design of SMA Elements: Case Studies. 9. Behavior of Magnetic SMAs. 10. Fracture Mechanics of SMAs. 11. General Conclusion. Appendix 1. Intrinsic Properties of Rotation Matrices. Appendix 2. “Twinning Equation” Demonstration. Appendix 3. Calculation of the Parameters a, n and Q from the “Twinning” Equation. Appendix 4. “Twinned” Austenite/Martensite Equation. About the Authors Christian Lexcellent is Emeritus Professor at the École National Supérieure de Mécanique et des Microtechniques de Besançon and a researcher in the Department of Applied Mechanics at FEMTO-ST in France. He is a specialist in the mechanics of materials and phase transition and has taught in the subjects of mechanics of continuum media and shape memory alloys. He is also a member of the International Committee of ESOMAT.
