The Theory of Composites (Cambridge Monographs on Applied and Computational Mathematics, Series Number 6) 1st Edition by Graeme W. Milton (PDF)

Description

The theory of composite materials is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than a hundred years, an explosion of ideas in the past four decades has dramatically increased our understanding of the relationship among the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective moduli that govern the macroscopic behavior. This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification. This book surveys these exciting developments at the frontier of mathematics and presents many new results.

User’s Reviews

Editorial Reviews: Review “…there existed no book or review paper that would allow a newcomer to get a general knowledge of the state of the art. The book of Graeme Milton fills this gap, and it does the job in a splendid manner that will make it the reference book on composite materials for a long time.” Mathematical Reviews Book Description This 2002 book surveys the exciting developments in composite materials which are at the frontier of mathematics and presents many new results. Book Description Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials. Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients. Although extensively studied for more than a hundred years, an explosion of ideas in the last four decades (and particularly in the last two decades) has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective (electrical, thermal, elastic) moduli which govern the macroscopic behavior. This book surveys these exciting developments at the frontier of mathematics and presents many new results. Read more

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