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This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof. It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.
This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.​
New engineering materials, techniques and applications are constantly being researched and developed, and keeping up to speed with the latest advances is crucial for engineers if they are to successfully address the challenges they face in their work. This book presents the selected proceedings of MMSE2023, the 9th International Conference on Advances in Machinery, Materials Science and Engineering Applications, jointly organized by the SAE-Supmeca, France and China University of Geosciences (Wuhan) and held on 22 and 23 July 2023 in Wuhan, China. For the past 12 years, this annual conference has collated recent advances and experiences, identified emerging trends and provided a platform for participants from academia and industry to exchange information and views, helping to address the world’s machinery and engineering challenges. The book contains 4 sections: mechanical engineering, material science and manufacturing technology; electrical engineering, automation and control; modeling, simulation and optimization techniques in engineering; and advanced engineering technologies and applications. A total of 241 submissions were received for MMSE2023, of which 151 papers were selected for the conference and for publication by means of a rigorous international peer-review process. These papers present exciting ideas and methods that will open novel research directions for different communities. Offering a current overview of the latest research and applications in machinery and materials-science engineering, the book will be of interest to all those working in the field.
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.
An introduction to the mathematical theory of the homogenization of multiple integrals, this book describes the overall properties of such functionals with various applications ranging from cellular elastic materials to Riemannian metrics.
Composite materials are widely used in industry: well-known examples of this are the superconducting multi-filamentary composites which are used in the composition of optical fibres. Such materials are complicated to model, as different points in the material will have different properties. The mathematical theory of homogenization is designed to deal with this problem, and hence is used to model the behaviour of these important materials. This book provides a self-contained and authoritative introduction to the subject for graduates and researchers in the field.
This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.
Keeping up to date with advances in material science and applied engineering is essential for those working in the field if they are to understand and tackle the challenges they face in an efficient manner and adopt the best and most appropriate solutions available. This book presents the proceedings of MMSE 2022, the 8th International Conference on Advances in Machinery, Materials Science and Engineering Application, held as a hybrid event (both in-person and online) in Wuhan, China, on 23 and 24 July 2022. For the past 12 years, the MMSE international conferences have collated recent advances and experiences, identified emerging trends in technology and encouraged lively debate between students, specialists, engineers and associations from around the world, all of which have had a positive impact in helping to address the world’s engineering challenges. The book contains 121 papers, selected by means of a rigorous international peer-review process by editors and reviewers from the 215 submissions received. Topics covered include the latest advancements in applied mechanics, intelligent manufacturing technology, mechanical and electromechanical engineering, heat transfer, combustion, advanced materials sciences, industrial applications, applied mathematics, simulation and interdisciplinary engineering. Presenting a wealth of exciting ideas for solving real problems in the real world and opening novel research directions, the book will be of interest to materials specialists and engineers from both academia and industry everywhere.
This book encompasses the science, measurement, fabrica tion, and use of superconducting materials in large scale and small scale technologies. The present book is in some sense a continuation and completion of a series of two earlier books based on NA TO Advanced Study Institutes held over the last decade. The first book in the series entitled Superconducting Machines ~nd Devices: Large Systems Appli cations edited by S. Foner and B. B. Schwartz (1974) represented a compilation of all the applications of superconducting technology. The second book entitled Superconductor Applications: Squids and Machines, edited by B. B. Schwartz and S. Foner (1977) reviewed small scale applications and up-dated the large scale applications of superconductiv ity at that time. These two books are both introductions and advanced reference volumes for almost all aspects of the applications of super conductivity. The growth of applied superconductivity has mushroomed in the decade of the 1970's. Technologies which were discussed in the beginning of the 1970's are now beyond the prototype stage. Materials development and performance in operating systems is the basis of the continued applications and economic viability of super conducting technology. In this book, a complete review of all materials technology is presented by leading authorities who were instrumental in the development of superconducting materials technology. The present book is based on the NATO Advanced Study vi PREFACE Institute entitled Superconducting Materials: Science and Technology which was held from August 20 to August 30, 1980 in Sintra, Portugal.