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The Theory of Composites (Paperback)
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The Theory of Composites (Paperback)
Series: Classics in Applied Mathematics
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Composites have been studied for more than 150 years, and interest
in their properties has been growing. This classic volume provides
the foundations for understanding a broad range of composite
properties, including electrical, magnetic, electromagnetic,
elastic and viscoelastic, piezoelectric, thermal, fluid flow
through porous materials, thermoelectric, pyroelectric,
magnetoelectric, and conduction in the presence of a magnetic field
(Hall effect). Exact solutions of the PDEs in model geometries
provide one avenue of understanding composites; other avenues
include microstructure-independent exact relations satisfied by
effective moduli, for which the general theory is reviewed;
approximation formulae for effective moduli; and series expansions
for the fields and effective moduli that are the basis of numerical
methods for computing these fields and moduli. The range of
properties that composites can exhibit can be explored either
through the model geometries or through microstructure-independent
bounds on the properties. These bounds are obtained through
variational principles, analytic methods, and Hilbert space
approaches. Most interesting is when the properties of the
composite are unlike those of the constituent materials, and there
has been an explosion of interest in such composites, now known as
metamaterials. The Theory of Composites surveys these aspects,
among others, and complements the new body of literature that has
emerged since the book was written. It remains relevant today by
providing historical background, a compendium of numerous results,
and through elucidating many of the tools still used today in the
analysis of composite properties. This book is intended for applied
mathematicians, physicists, and electrical and mechanical
engineers. It will also be of interest to graduate students.
General
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