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Nonlinear homogenization and its applications to composites, polycrystals and smart materials [Electronic resource] : научное издание / eds: P. P. Castaсeda, J.J.Telega, B. Gambin. - Dordrecht : Kluwer Acad. Publ., 2004 : Springer Science + Business Media, Inc., 2005. - 355 p. - (NATO Science Ser. Ser. II: Mathematics, Physics, and Chemistry ; vol. 170 ). - ISSN 1-4020-26. - ISBN eBook ISBN: 1-4020-2623-4
Электронная книга находится на постоянном доступе по адресу: http://ebooks.springerlink.com
Рубрики: Физика
Техника
Кл.слова (ненормированные):
композиты -- поликристаллы -- твердые материалы
Аннотация: After more than 30 years, the term ”homogenization” is now commonly used in several felds of science and engineering. From the mathematical point of view, homogenization deals with sequences of functionals or operators, ??not necessarily linear, depending on a small parameter. The meaning of this parameter depends upon the problem considered. For instance, it may characterize the microstructure, as in the size of a typical fiber in a metal-matrix composite, or of a grain in an ice polycrystal. To perform a homogenization process meansfinding the limit problem when the small parameter tends to zero (in a proper sense). However, the general theory of functionals and operators with dependence on a small parameter tending to zero has a much wider range of applicability. Consider, for example the development of two-dimensional models for thin plates and shells from their three-dimensional counterparts. A combination of several small parameters, as in reiterated homogenization, and for thin structures with microstructures is also important. 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 full 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 key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin .lms, 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 methodsboth analytical and computational-for estimating the e.ective behavior and field fuctuations 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.
Перейти: Springer eBooks
Доп.точки доступа: Castaсeda, P.P. \ed.\; Telega, J.J. \ed.\; Gambin, B. \ed.\
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