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This book provides a representative selection of the most relevant,
innovative, and useful mathematical methods and models applied to
the analysis and characterization of composites and their behaviour
on micro-, meso-, and macroscale. It establishes the fundamentals
for meaningful and accurate theoretical and computer modelling of
these materials in the future. Although the book is primarily
concerned with fibre-reinforced composites, which have
ever-increasing applications in fields such as aerospace, many of
the results presented can be applied to other kinds of composites.
The topics covered include: scaling and homogenization procedures
in composite structures, thin plate and wave solutions in
anisotropic materials, laminated structures, instabilities,
fracture and damage analysis of composites, and highly efficient
methods for simulation of composites manufacturing. The results
presented are useful in the design, fabrication, testing, and
industrial applications of composite components and structures. The
book is written by well-known experts in different areas of applied
mathematics, physics, and composite engineering and is an essential
source of reference for graduate and doctoral students, as well as
researchers. It is also suitable for non-experts in composites who
wish to have an overview of both the mathematical methods and
models used in this area and the related open problems requiring
further research.
Mathematical Methods and Models in Composites (Second Edition)
provides an in-depth treatment of modern and rigorous mathematical
methods and models applied to composites modeling on the micro-,
meso-, and macro scale. There has been a steady growth in the
diversity of such methods and models that are used in the analysis
and characterization of composites, their behavior, and their
associated phenomena and processes. This second edition expands
upon the success of the first edition, and has been substantially
revised and updated.Written by well-known experts in different
areas of applied mathematics, physics, and composite engineering,
this book is mainly focused on continuous fiber reinforced
composites and their ever increasing range of applications (for
example, in the aerospace industry), though it also covers other
kind of composites. The chapters cover a range of topics including,
but not limited to: scaling and homogenization procedures in
composites, thin plate and wave solutions in anisotropic materials,
laminated structures, fiber-reinforced nonlinearly elastic solids,
buckling and postbuckling, fracture and damage analysis of
composites, and highly efficient methods for simulation of
composites manufacturing such as resin transfer molding. The
results presented are useful for the design, fabrication, testing
and industrial applications of composite components and
structures.This book is an essential reference for graduate and
doctoral students, as well as researchers in mathematics, physics
and composite engineering. Explanations and references in the book
are sufficiently detailed so as to provide the necessary background
to further investigate the fascinating subject of composites
modeling and explore relevant research literature. It is also
suitable for non-experts who wish to have an overview of the
mathematical methods and models used for composites, and of the
open problems in this area that require further research.
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